Merge pull request #4 from FOSSEE/master

Update fork. DONE

96 files changed, 3143 insertions, 409 deletions

diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/README.md
index a2f71d7..10786d6 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/README.md
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/README.md
@@ -4,5 +4,8 @@
 **file2_circle_curvature.py** <br>
 ![file2_circle_curvature.py](https://raw.githubusercontent.com/saarthdeshpande/FSF-mathematics-python-code-archive/master/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file2_circle_curvature.gif)
 
+**file3_curvature_interpretation.py** <br>
+![file3_curvature_interpretation.py](https://github.com/saarthdeshpande/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif)
+
 **file4_different_curvature_single_curve.py** <br>
 ![file4_different_curvature_single_curve.py](https://raw.githubusercontent.com/saarthdeshpande/FSF-mathematics-python-code-archive/master/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.gif)
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.gif
index 858a8de..3f7ecd1 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.gif
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.gif
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.py
index 7ab8908..45058d7 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.py
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file1_simple_visualization.py
@@ -32,6 +32,8 @@ class randomcurve(GraphScene):
         dot6 = Dot(tgt6.get_start(), color = RED)
         dot7 = Dot(tgt7.get_start(), color = RED)
 
+        arc = ArcBetweenPoints(dot1.get_center(), dot2.get_center(), color = GREEN_SCREEN, angle = 10*DEGREES).rotate(180*DEGREES)
+
         dots = VGroup(*[dot1, dot2, dot3, dot4, dot5, dot6, dot7])
 
         ds = CurvedArrow((-4, 2, 0), (tgt1.get_start() + tgt2.get_start()) / 2, color = YELLOW)
@@ -43,15 +45,13 @@ class randomcurve(GraphScene):
         self.wait(2)
         self.play(FadeOut(intro))
         self.setup_axes(hideaxes=False)
-        self.play(ShowCreation(graphobj), FadeIn(dots), FadeIn(ds), FadeIn(ds_text))
+        self.play(ShowCreation(graphobj), FadeIn(dots), FadeIn(ds), FadeIn(ds_text), FadeIn(arc))
         self.wait(1)
-        self.play(FadeOut(self.axes), FadeOut(graphobj),FadeIn(mid), FadeOut(dots), FadeOut(ds), FadeOut(ds_text))
-        self.wait(2)
+        self.play(FadeOut(self.axes), FadeOut(arc), FadeOut(graphobj),FadeIn(mid), FadeOut(dots), FadeOut(ds), FadeOut(ds_text))
+        self.wait(3)
         self.play(FadeOut(mid))
         self.play(FadeIn(self.axes), FadeIn(graphobj), FadeIn(dots))
 
-
-
         tangents = [tgt1, tgt2, tgt3, tgt4, tgt5, tgt6, tgt7]
         for tangent in tangents:
             self.play(ShowCreation(tangent), run_time = 0.2)
@@ -60,7 +60,7 @@ class randomcurve(GraphScene):
         self.play(FadeOut(self.axes), FadeOut(graphobj), FadeOut(tangents), FadeOut(dots))
         self.wait(1)
         self.play(FadeIn(outro))
-        self.wait(2)
+        self.wait(3)
         self.play(FadeOut(outro))
         self.wait(1)
 
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif
new file mode 100644
index 0000000..22a450a
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.gif
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py
new file mode 100644
index 0000000..d8dd0a4
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_interpretation.py
@@ -0,0 +1,42 @@
+from manimlib.imports import *
+
+class interpretation(Scene):
+    def construct(self):
+        tgt = Vector((1, 2, 0), color = YELLOW)
+        tgtText = TextMobject(r'$r\prime (t)$').next_to(tgt, UP, buff = 0).scale(0.7)
+        tgt2 = DashedLine((0,0,0),(1, 2, 0), color = GRAY).shift(DOWN + 2*RIGHT)
+
+        nm = Vector((2, -1, 0), color = BLUE)
+        nmText = TextMobject(r'$r\prime\prime (t)$').next_to(nm, DOWN+RIGHT, buff = 0).scale(0.7)
+        nm2 = DashedLine((0,0,0),(2, -1, 0), color = GRAY).shift(2*UP + RIGHT)
+        square = Square(fill_color = WHITE, fill_opacity = 0.2).rotate(63*DEGREES).shift(0.5*UP +1.5*RIGHT).scale(1.1)
+        square.set_stroke(width = 0.1)
+        arrow = CurvedArrow(square.get_center() + np.array([2,1,0]), square.get_center() + np.array([0.5,0,0]))
+        arrowText = TextMobject(r'$r\prime (t)\times r\prime\prime (t)$').next_to(arrow.get_start(), DOWN+1*RIGHT, buff = 0).scale(0.7)
+
+        text1 = TextMobject(r'$\left|\frac{dT}{ds}\right| = \frac{\left|\frac{dT}{dt}\right|}{\left|\frac{ds}{dt}\right|}$').shift(UP+3*LEFT)
+        text2 = TextMobject(r'$\left|\frac{dT}{ds}\right| = \frac{\frac{r\prime\prime (t)}{\left| r\prime (t)\right|}\times\frac{r\prime (t)}{\left| r\prime (t)\right|}}{\left|r\prime (t)\right|}$').next_to(text1, DOWN, buff = 0.1)
+        unit = VGroup(*[tgt, tgt2, nm, nm2])
+
+        # self.play(FadeIn(VGroup(*[tgt, tgt2, nm, nm2, nmText, tgtText, square, arrow, arrowText])))
+        tgt2text = TextMobject(r'$\frac{r\prime (t)}{\left| r\prime (t)\right|}$').shift(1.1*UP).scale(0.7).rotate(63*DEGREES  )
+        nm2text = TextMobject(r'$\frac{r\prime\prime (t)}{\left| r\prime (t)\right|}$').scale(0.7).shift(0.7*RIGHT+0.8*DOWN).rotate(-25*DEGREES)
+        unit2 = unit.copy().scale(0.5).shift(0.75*LEFT+0.25*DOWN)
+
+        self.play(FadeIn(VGroup(*[tgt, tgtText])))
+        self.wait(1)
+        self.play(FadeIn(VGroup(*[nm, nmText])))
+        self.wait(1)
+        self.play(FadeIn(VGroup(*[tgt2, nm2])))
+        self.wait(1)
+        self.play(FadeIn(VGroup(*[square, arrow, arrowText])))
+        self.wait(1)
+        self.play(FadeIn(unit2))
+        self.wait(1)
+        self.play(FadeIn(VGroup(*[tgt2text, nm2text])))
+        self.wait(1)
+        self.play(FadeIn(text1))
+        self.wait(1)
+        self.play(FadeIn(text2))
+        self.wait(2)
+        self.play(FadeOut(VGroup(*[tgt2text, nm2text, text1, text2, tgt, tgtText,nm, nmText,tgt2, nm2,square, arrow, arrowText,unit2])))
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_intuition.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_intuition.gif
deleted file mode 100644
index 0d6fdcf..0000000
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file3_curvature_intuition.gif
+++ /dev/null
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py
index d71adda..56b7fbb 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/arc-length-and-curvature/file4_different_curvature_single_curve.py
@@ -8,7 +8,9 @@ class GR(GraphScene):
         "x_max": 6,
         "y_min": -6,
         "y_max": 10,
-        "graph_origin": ORIGIN
+        "graph_origin": ORIGIN,
+        'x_tick_frequency': 20,
+        'y_tick_frequency': 20
     }
 
     def construct(self):
@@ -21,7 +23,7 @@ class GR(GraphScene):
 
         tracker = ValueTracker(-3)
 
-        text = TextMobject(r'The curvature at point $P_{1}$ is \\ lesser than that at point $P_{2}$: \\ as $\kappa = \frac{1}{R}$').shift(3.2*RIGHT+3*UP).scale(0.6)
+        text = TextMobject(r'$\because R_{1} > R_{2}$, the curvature at \\ point $P_{1}$ is less than that \\ at point $P_{2}$ as $\kappa = \frac{1}{R}$').shift(3.2*RIGHT+3*UP).scale(0.6)
 
         dot1 = Dot((0,3,0), color = YELLOW)
         dot1label = TextMobject(r'$P_{1}$').next_to(dot1, UP+RIGHT, buff = 0.1)
@@ -47,10 +49,30 @@ class GR(GraphScene):
             line.move_to(p0)
             return line
 
+        circle1 = Circle(radius = 0.8, color = GREY, opacity = 0.2).shift(2.2*UP)
+        tgt1 = Line((-2,3,0), (2,3,0), color = GREY, opacity = 0.2).scale(0.4)
+
+        r1 = Line(circle1.get_center(), circle1.get_center() + np.array([0,0.8,0]), color=GREEN_SCREEN)
+        r1label = TextMobject(r'$R_{1}$',color=WHITE).next_to(r1, RIGHT, buff = 0.1).scale(0.6)
+
+        curvature1 = VGroup(*[circle1, tgt1, r1, r1label])
+
+        circle2 = Circle(radius = 0.6, color = GREY, opacity = 0.2).shift(0.4*DOWN + 4*RIGHT)
+        tgt2 = Line((4,-2,0), (6, -2, 0), color = GREY, opacity = 0.2).scale(0.5).shift(LEFT + UP)
+
+        r2 = Line(circle2.get_center(), circle2.get_center() + np.array([0,-0.6,0]), color=GREEN_SCREEN)
+        r2label = TextMobject(r'$R_{2}$', color=WHITE).next_to(r2, 0.9*RIGHT, buff = 0).scale(0.6)
+
+        curvature2 = VGroup(*[circle2, tgt2, r2, r2label])
+
         line = always_redraw(get_tangent_line)
 
         self.add(graph,line, dots, text)
         self.wait(1.2)
-        self.play(tracker.set_value, 6, rate_func=smooth, run_time=13)
-        self.play(FadeOut(VGroup(*[graph, self.axes, line, dots, text])))
+        self.play(tracker.set_value, 0, rate_func=smooth, run_time=5)
+        self.play(FadeIn(curvature1))
+        self.play(tracker.set_value, 4, rate_func=smooth, run_time=5)
+        self.play(FadeIn(curvature2))
+        self.play(tracker.set_value, 6, rate_func=smooth, run_time=3)
+        self.play(FadeOut(VGroup(*[curvature1, curvature2, graph, self.axes, line, dots, text])))
         self.wait()
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file1_parametric_circle.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file1_parametric_circle.py
index 40b5150..37d079e 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file1_parametric_circle.py
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file1_parametric_circle.py
@@ -11,12 +11,15 @@ class parametricCircle(ThreeDScene, GraphScene):
         self.y_axis_label =  ""
         self.x_axis_width = 10
         self.y_axis_height = 10
+        self.y_tick_frequency = 1.9
+        self.x_tick_frequency = 1.4
 
         axes = []
 
-        self.setup_axes()
-        self.axes.scale(0.5).shift(3*LEFT)
-        axes.append(self.axes)
+        # self.setup_axes()
+        ax = Axes(y_tick_frequency = 1, x_axis_width = 10, y_axis_height = 10, y_min = -5, x_max = 5, y_max = 5, x_tick_frequency = 1, x_axis_label =  "", y_axis_label =  "", x_min = -5, )
+        ax.scale(0.5).shift(3*LEFT)
+        axes.append(ax)
         self.setup_axes()
         self.axes.scale(0.3).shift(3*RIGHT + 2*UP)
         axes.append(self.axes)
@@ -38,7 +41,7 @@ class parametricCircle(ThreeDScene, GraphScene):
         asint = ParametricFunction(
         lambda t: np.array([
         t,
-        np.sin(t),
+        2*np.sin(t),
         0
         ]), t_min = -np.pi, t_max = np.pi, color = GREEN_E
         ).shift(3*RIGHT + 2*UP).scale(0.4)
@@ -50,7 +53,7 @@ class parametricCircle(ThreeDScene, GraphScene):
         acost = ParametricFunction(
         lambda t: np.array([
         t,
-        np.cos(t),
+        2*np.cos(t),
         0
         ]), t_min = -np.pi, t_max = np.pi, color = BLUE
         ).shift(3*RIGHT + 2*DOWN).scale(0.4)
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid.gif
deleted file mode 100644
index 39656de..0000000
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/general-parametric-curves/file2_cycloid.gif
+++ /dev/null
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md
index 34885b2..7874f43 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/README.md
@@ -1,2 +1,15 @@
-**file2_tnb_frame_manim.py** <br>
-![file2_tnb_frame_manim.py](https://github.com/saarthdeshpande/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif)
+**file1_tnb_creation.py**<br>
+![file1_tnb_creation.py](https://github.com/saarthdeshpande/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.gif)
+
+
+**file2_tnb_basic.py** <br>
+![file2_tnb_basic.py](https://github.com/saarthdeshpande/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.gif)
+
+**file3_tnb_frame_manim.py** <br>
+![file3_tnb_frame_manim.py](https://github.com/saarthdeshpande/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.gif)
+
+**file4_fs1.py** <br>
+![file4_fs1.py](https://github.com/saarthdeshpande/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.gif)
+
+**file5_fs2.py** <br>
+![file5_fs2.py](https://github.com/saarthdeshpande/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.gif)
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_prescribed_plane.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_prescribed_plane.gif
deleted file mode 100644
index c8668e3..0000000
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_prescribed_plane.gif
+++ /dev/null
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.gif
new file mode 100644
index 0000000..eae8686
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.gif
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.py
new file mode 100644
index 0000000..80372ee
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file1_tnb_creation.py
@@ -0,0 +1,66 @@
+from manimlib.imports import *
+
+class tnb(ThreeDScene):
+    def construct(self):
+        self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES)
+
+        helix1 = ParametricFunction(
+                lambda t: np.array([
+                np.cos(TAU*t),
+                np.sin(TAU*t),
+                0.4*t
+                ]), t_min = -2*np.pi/3, t_max = -1.638*np.pi/3, color = WHITE
+                )
+
+        helix2 = ParametricFunction(
+                lambda t: np.array([
+                np.cos(TAU*t),
+                np.sin(TAU*t),
+                0.4*t
+                ]), t_min = -1.638*np.pi/3, t_max = -1.33*np.pi/3, color = WHITE
+                )
+
+        pointText = TextMobject(r'Consider an arbitrary point \\ on the given curve.').scale(0.8).shift(1.5*UP)
+        tgtText = TextMobject(r'Unit', ' tangent ', r'vector at \\ this point is given as:').scale(0.8).shift(1.5*UP)
+        tgtText.set_color_by_tex_to_color_map({
+            "tangent": YELLOW
+        })
+        normalText = TextMobject(r'Unit', ' normal ', r'vector at \\ this point is given as:').scale(0.8).shift(1.5*UP)
+        normalText.set_color_by_tex_to_color_map({
+            "normal": BLUE
+        })
+        planeText = TextMobject(r'$\overrightarrow{T}$ and $\overrightarrow{N}$ \\ prescribe a plane.').scale(0.8).shift(1.5*UP)
+        bnmText = TextMobject(r'The vector normal to this plane \\ is called the', ' binormal ', 'vector.').scale(0.8).shift(1.5*UP)
+        bnmText.set_color_by_tex_to_color_map({
+            "binormal": GREEN_E
+        })
+
+        dot1 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([0,0.2,0]), radius = 0.16, color=RED)
+        tgt1 = Arrow((0,0,0), (-2,-0.55,0), color = YELLOW).shift(dot1.get_center() + np.array([0.18,0.04,0]))
+        nm1 = Arrow((0,0,0), (0.4,-2,0), color = BLUE).shift(dot1.get_center() + np.array([0,0.26,0]))
+        bnm1 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(2.1*RIGHT+2*DOWN)
+        plane1 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot1.get_center() + np.array([-0.4, -0.6, 0])).rotate(13*DEGREES).scale(1.2)
+        point1 = VGroup(*[dot1, tgt1, nm1, plane1]).scale(0.8).shift(np.array([1,4.86,0])).rotate(-15*DEGREES)
+
+
+
+        helix = VGroup(*[helix1, helix2])
+        self.play(FadeIn(helix))
+        self.play(ApplyMethod(helix.scale, 4))
+        self.add_fixed_in_frame_mobjects(pointText)
+        self.play(FadeIn(dot1), FadeIn(pointText))
+        self.wait(2)
+        self.add_fixed_in_frame_mobjects(tgtText)
+        self.play(Write(tgt1), ReplacementTransform(pointText, tgtText))
+        self.wait(2)
+        self.add_fixed_in_frame_mobjects(normalText)
+        self.play(Write(nm1), ReplacementTransform(tgtText, normalText))
+        self.wait(2)
+        self.add_fixed_in_frame_mobjects(planeText)
+        self.play(FadeIn(plane1), ReplacementTransform(normalText, planeText))
+        self.wait(2)
+        self.add_fixed_in_frame_mobjects(bnmText)
+        self.add_fixed_in_frame_mobjects(bnm1)
+        self.play(ReplacementTransform(planeText, bnmText), Write(bnm1))
+        self.wait(2)
+        self.play(FadeOut(VGroup(*[helix, bnm1, bnmText, dot1, tgt1, nm1, plane1])))
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.gif
new file mode 100644
index 0000000..67aaea2
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.gif
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.py
new file mode 100644
index 0000000..c870210
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_basic.py
@@ -0,0 +1,36 @@
+from manimlib.imports import *
+
+class tnb(ThreeDScene):
+    def construct(self):
+        t = TextMobject(r'T', color = YELLOW)
+        n = TextMobject(r'N', color = BLUE).next_to(t, RIGHT, buff=0)
+        b = TextMobject(r'B', color = GREEN_E).next_to(n, RIGHT, buff=0)
+        frame = TextMobject(r'Frame').next_to(b, RIGHT, buff=0.2)
+        f1 = TextMobject(r'$\overrightarrow{B}$ ', color = GREEN_E)
+        f2 = TextMobject(r' = $\overrightarrow{T}$', color = YELLOW).next_to(f1, RIGHT, buff=0.2)
+        f3 = TextMobject(r'$\times\overrightarrow{N}$', color = BLUE).next_to(f2, RIGHT, buff=0.1)
+        formula = VGroup(*[f1, f2, f3]).move_to(ORIGIN).shift(3*UP)
+
+        # text = VGroup(*[t,n,b,frame]).move_to(ORIGIN).shift(3*UP)
+        curve = ParametricFunction(
+        lambda t: np.array([
+        np.sin(TAU*t),
+        np.cos(TAU*t),
+        0
+        ])
+        ).scale(2.5)
+        dot = Dot(color = RED).scale(1.5).shift(1.05*LEFT)
+        tgt = Arrow(dot.get_center(), (-2, 2, 0), color = YELLOW).shift(0.3*DOWN + 0.09*RIGHT)
+        normal = Arrow(tgt.get_start(), (1, 1, 0), color = BLUE).shift(0.2*LEFT + 0.05*DOWN)
+        binormal = Arrow(dot.get_center() - np.array([0,0,0.3]), (tgt.get_start()[0], tgt.get_start()[1],2), color = GREEN)
+        square = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).move_to(tgt.get_start()).rotate(27*DEGREES).shift(UP+0.4*RIGHT).scale(1.2)
+        group = VGroup(*[dot, tgt, normal, square, binormal]).shift(np.array([-1.24,-1,0]))
+
+        self.add_fixed_in_frame_mobjects(formula)
+        self.add(curve, group)
+        self.wait(1)
+        self.move_camera(phi = 75*DEGREES, theta=45*DEGREES, run_time = 2)
+        self.add_fixed_in_frame_mobjects(formula)
+        self.begin_ambient_camera_rotation(rate = 0.5)
+        self.wait(5)
+        self.play(FadeOut(VGroup(*[formula, curve, dot, tgt, normal, square, binormal])))
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame.gif
deleted file mode 100644
index 097652f..0000000
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame.gif
+++ /dev/null
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif
deleted file mode 100644
index 784b6a6..0000000
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.gif
+++ /dev/null
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.gif
new file mode 100644
index 0000000..78e3aa3
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.gif
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.py
index ee5e717..176cac5 100644
--- a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file2_tnb_frame_manim.py
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file3_tnb_frame_manim.py
@@ -79,15 +79,16 @@ class tnb(ThreeDScene):
         self.play(FadeIn(helix), FadeIn(text))
         self.play(ApplyMethod(helix.scale, 4))
         self.add_fixed_in_frame_mobjects(bnm0)
-        self.play(FadeIn(point0), MoveAlongPath(helix_dot, helix1, run_time=5))
+        self.play(FadeIn(point0))
+        self.play(ApplyMethod(point0.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix1, run_time=5))
 
         self.add_fixed_in_frame_mobjects(bnm1)
-        self.play(ApplyMethod(point0.set_color, GRAY), FadeIn(point1))
-        self.play(MoveAlongPath(helix_dot, helix2, run_time = 5))
+        self.play(FadeIn(point1))
+        self.play(ApplyMethod(point1.set_color, GRAY, opacity = 0.1), ApplyMethod(bnm1.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix2, run_time = 5))
 
         self.add_fixed_in_frame_mobjects(bnm2)
-        self.play(ApplyMethod(point1.set_color, GRAY), ApplyMethod(bnm1.set_color, GRAY), FadeIn(point2))
-        self.play(MoveAlongPath(helix_dot, helix3, run_time=5))
+        self.play(FadeIn(point2))
+        self.play(ApplyMethod(point2.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix3, run_time=5))
 
         dot3 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([3.3,-0.25,0]), radius = 0.16, color=RED)
         tgt3 = Arrow((0,0,0), (0,2,0), color = YELLOW).shift(helix_dot.get_center() - np.array([-0.05,0.2,0]))
@@ -111,15 +112,15 @@ class tnb(ThreeDScene):
         point5 = VGroup(*[tgt5, nm5, bnm5, plane5])
 
         self.add_fixed_in_frame_mobjects(bnm3)
-        self.play(ApplyMethod(point2.set_color, GRAY), FadeIn(point3))
-        self.play(MoveAlongPath(helix_dot, helix4, run_time=5))
+        self.play(FadeIn(point3))
+        self.play(ApplyMethod(point3.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix4, run_time=5))
 
         self.add_fixed_in_frame_mobjects(bnm4)
-        self.play(ApplyMethod(point3.set_color, GRAY), FadeIn(point4))
-        self.play(MoveAlongPath(helix_dot, helix5, run_time=5))
+        self.play(FadeIn(point4))
+        self.play(ApplyMethod(point4.set_color, GRAY, opacity = 0.1), MoveAlongPath(helix_dot, helix5, run_time=5))
 
         self.add_fixed_in_frame_mobjects(bnm5)
-        self.play(ApplyMethod(point4.set_color, GRAY), FadeIn(point5))
+        self.play(FadeIn(point5))
         self.wait(2)
 
-        self.play(FadeOut(VGroup(*[helix, bnm1, point0, point1, point2, point3, point4, point5, helix_dot])))
+        self.play(FadeOut(VGroup(*[text, helix, bnm1, point0, point1, point2, point3, point4, point5, helix_dot])))
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.gif
new file mode 100644
index 0000000..6b4b438
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.gif
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py
new file mode 100644
index 0000000..c719a1d
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file4_fs1.py
@@ -0,0 +1,23 @@
+from manimlib.imports import *
+
+class fs1(ThreeDScene):
+    def construct(self):
+
+
+        self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES)
+        dot1 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([0,0.2,0]), radius = 0.16, color=RED)
+        tgt1 = Arrow((0,0,0), (-2,-0.55,0), color = YELLOW).shift(dot1.get_center() + np.array([0.18,0.04,0]))
+        nm1 = Arrow((0,0,0), (0.4,-2,0), color = BLUE).shift(dot1.get_center() + np.array([0,0.26,0])).shift(np.array([0.8,4.76,0])).rotate(-15*DEGREES).scale(0.8)
+        bnm1 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(2.1*RIGHT+2*DOWN)
+        plane1 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot1.get_center() + np.array([-0.4, -0.6, 0])).rotate(13*DEGREES).scale(1.2)
+        point1 = VGroup(*[dot1, tgt1, plane1]).scale(0.8).shift(np.array([1,4.86,0])).rotate(-15*DEGREES)
+        t = TextMobject(r'$T$', color = YELLOW).move_to(ORIGIN).shift(3.2*RIGHT + DOWN)
+        n = TextMobject(r'$N$', color = BLUE).shift(DOWN + RIGHT)
+        b = TextMobject(r'$B$', color = GREEN_E).next_to(bnm1, UP, buff = 0.1)
+        text = VGroup(*[t, n, b])
+        self.add_fixed_in_frame_mobjects(bnm1, text)
+        self.play(FadeIn(point1), FadeIn(bnm1), FadeIn(text))
+        self.wait()
+        self.play(TransformFromCopy(tgt1, nm1, run_time = 2))
+        self.wait(2)
+        self.play(FadeOut(VGroup(*[bnm1, text, point1, nm1])))
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.gif b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.gif
new file mode 100644
index 0000000..ce367b6
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.gif
diff --git a/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.py b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.py
new file mode 100644
index 0000000..0261fed
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/geometry-of-planes-and-curves/tnb-frame-and-serret-frenet-formulae/file5_fs2.py
@@ -0,0 +1,28 @@
+from manimlib.imports import *
+
+class fs1(ThreeDScene):
+    def construct(self):
+
+
+        self.set_camera_orientation(phi = 75*DEGREES, theta=45*DEGREES)
+        dot1 = Dot(np.array([np.cos(-np.pi/3), np.sin(-np.pi/3), -0.4*np.pi/3]) + np.array([0,0.2,0]), radius = 0.16, color=RED)
+        tgt1 = Arrow((0,0,0), (-2,-0.55,0), color = YELLOW).shift(dot1.get_center() + np.array([0.18,0.04,0]))
+        nm1 = Arrow((0,0,0), (0.4,-2,0), color = BLUE).shift(dot1.get_center() + np.array([0,0.26,0])).shift(np.array([0.8,4.76,0])).rotate(-15*DEGREES).scale(0.8)
+        bnm1 = Arrow((0,0,0), (0,2,0), color=GREEN_E).shift(2.1*RIGHT+2*DOWN)
+
+        bnms = Line((0,0,0), (0,0,1.6), color = GREEN_E).shift(np.array([3.1,5.2,0])).scale(0.6)
+        bnmsa = ArrowTip(color = GREEN_E).next_to(bnms, np.array([0,0,1]), buff = 0).rotate(45*DEGREES)
+        bns = VGroup(*[bnms, bnmsa])
+
+        plane1 = Square(color = DARK_BROWN, fill_color = WHITE, fill_opacity=0.3).shift(dot1.get_center() + np.array([-0.4, -0.6, 0])).rotate(13*DEGREES).scale(1.2)
+        point1 = VGroup(*[dot1, tgt1, plane1]).scale(0.8).shift(np.array([1,4.86,0])).rotate(-15*DEGREES)
+        t = TextMobject(r'$T$', color = YELLOW).move_to(ORIGIN).shift(3.2*RIGHT + DOWN)
+        n = TextMobject(r'$N$', color = BLUE).shift(DOWN + RIGHT)
+        b = TextMobject(r'$B$', color = GREEN_E).next_to(bnm1, UP, buff = 0.1)
+        text = VGroup(*[t, n, b])
+        self.add_fixed_in_frame_mobjects(bnm1, text)
+        self.play(FadeIn(point1), FadeIn(text), FadeIn(bnm1))
+        self.wait()
+        self.play(TransformFromCopy(bnms, nm1, run_time = 3))
+        self.wait(2)
+        self.play(FadeOut(VGroup(*[bnms, text, point1, nm1, bnm1])))
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md
index 7ff6b61..97a0fb7 100644
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/README.md
@@ -4,6 +4,6 @@ Github Account : <a href="https://github.com/nishanpoojary">nishanpoojary</a>
 ## Sub-Topics Covered:

 + Scalar Functions

 + Multivariable Functions

-+ Limits and Continuity of Multivariable Functions

++ Multivariable Limits and Continuity

 + Partial Derivatives

 + Directonal Derivatives

diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file1_directional_deriv.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file1_directional_deriv.py
new file mode 100644
index 0000000..677d821
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file1_directional_deriv.py
@@ -0,0 +1,85 @@
+from manimlib.imports import *

+

+class GeomRepresen(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() 

+

+        paraboloid = ParametricSurface(

+            lambda u, v: np.array([

+                3*np.sin(u)*np.cos(v),

+                3*np.sin(u)*np.sin(v),

+                -0.25*3*3*np.sin(u)*np.sin(u)+2

+            ]),u_min=0,u_max=PI/4,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.7,

+            resolution=(15, 32)).scale(1)

+

+        parabola_curve = ParametricFunction(

+                lambda u : np.array([

+                u,

+                -u,

+                -0.5*(u*u)+2

+            ]),color=PINK,t_min=-1.5,t_max=1.5,

+            )

+

+        circle = Circle(radius = 2.22 , color = BLACK, fill_color = BLUE_C, fill_opacity= 0.3, stroke_width=0.1)

+

+        plane = Polygon(np.array([2.5,-2.5,0]),np.array([-2.5,2.5,0]),np.array([-2.5,2.5,2.5]),np.array([2.5,-2.5,2.5]),np.array([2.5,-2.5,0]), color = BLACK, fill_color = PINK, fill_opacity= 0.2, stroke_width=0.1)

+

+        line = DashedLine(np.array([1,-1,0]), np.array([1,-1,1.5]), color = YELLOW_C) 

+

+        tangent_line = Line(np.array([1.5,-1.5,1]), np.array([0.5,-0.5,2]), color = RED_C)

+

+        vector = Arrow(np.array([1,-1,0]), np.array([0.5,-0.5,0]), buff=0.01, color = GREEN_C)

+

+        dot1 =Sphere(radius=0.08).move_to(np.array([1,-1,0])).set_fill(YELLOW_C)

+        dot2 =Sphere(radius=0.08).move_to(np.array([1,-1,1.5])).set_fill(YELLOW_C)

+

+        dot1_lab = TextMobject(r"$P_0$").scale(0.6).move_to(np.array([1,-1,1.8])).set_color(RED_C)

+        dot2_lab = TextMobject(r"$(x_0,y_0)$").scale(0.6).move_to(np.array([1.6,-1,0])).set_color(PURPLE)

+        vector_lab = TextMobject(r"$\hat{u}$").scale(0.8).move_to(np.array([1.2,-0.5,0])).set_color(GREEN_C)

+        domain_lab = TextMobject(r"$D$").scale(0.6).move_to(np.array([1,1,0])).set_color(GREEN_C)

+        func_lab = TextMobject(r"$z = f(x,y)$").scale(0.6).move_to(1*UP + 2.8*RIGHT).set_color(BLUE_C)

+        directional_deriv_lab = TextMobject(r"Slope = $D_{\hat{u}}f(x_0,y_0)$").scale(0.6).move_to(2.2*UP + 1.5*RIGHT).set_color(YELLOW_C)

+

+        self.add(axes)

+

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(np.array([0,0,3.7]))

+

+        self.add_fixed_orientation_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1]) 

+

+        self.set_camera_orientation(phi=65 * DEGREES, theta = 20*DEGREES)

+

+        self.play(ShowCreation(paraboloid))

+        self.add_fixed_in_frame_mobjects(func_lab)

+        self.wait()

+

+        #self.play(ShowCreation(circle))

+        self.bring_to_front(circle)

+        self.wait()

+        self.add_fixed_orientation_mobjects(domain_lab)

+        self.wait()

+

+        self.play(ShowCreation(plane), ShowCreation(parabola_curve))

+        self.play(ShowCreation(dot1), GrowArrow(line), ShowCreation(dot2))

+        self.add_fixed_orientation_mobjects(dot1_lab)

+        self.wait()

+        self.add_fixed_orientation_mobjects(dot2_lab)

+        self.wait()

+

+        self.play(ShowCreation(tangent_line))

+        self.add_fixed_in_frame_mobjects(directional_deriv_lab)

+        self.wait()

+

+        self.play(GrowArrow(vector))

+        self.add_fixed_orientation_mobjects(vector_lab)

+        self.wait()

+

+        

+        self.begin_ambient_camera_rotation(rate=0.1)

+        self.wait(3)

+

+    

diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file2_gradient.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file2_gradient.py
new file mode 100644
index 0000000..e9fef50
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file2_gradient.py
@@ -0,0 +1,103 @@
+from manimlib.imports import *

+

+class Gradient(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() # creates a 3D Axis

+        

+

+        quadrant = ParametricSurface(

+            lambda u, v: np.array([

+                2*np.sin(u)*np.cos(v),

+                2*np.sin(u)*np.sin(v),

+                2*np.cos(u)

+            ]),u_min=0,u_max=PI/3,v_min=0,v_max=PI/2,checkerboard_colors=[GREEN_C, GREEN_E],

+            resolution=(15, 32)).scale(1)

+

+        quadrant_curve = ParametricSurface(

+            lambda u, v: np.array([

+                2*np.sin(u)*np.cos(v),

+                2*np.sin(u)*np.sin(v),

+                2*np.cos(u)

+            ]),u_min=34*DEGREES,u_max=38*DEGREES,v_min=0,v_max=PI/2,checkerboard_colors=[YELLOW_C, YELLOW_E],

+            resolution=(15, 32)).scale(1)

+

+

+

+        dot1 =Sphere(radius=0.05).move_to(np.array([1,1,0])).set_fill(YELLOW_C)

+        dot2 =Sphere(radius=0.05).move_to(np.array([1,1,1.732])).set_fill(YELLOW_C)

+

+        dot1_line = DashedLine(np.array([1,1,1.732]), np.array([0,2,2]), color = WHITE)

+        dot1_lab = TextMobject(r"$P_0(x_0,y_0,z_0)$").move_to(np.array([0,2.1,2.2])).set_color(YELLOW_C).scale(0.6)

+        #dot2_line = Line(np.array([0.8,0.8,0]), np.array([1,0.6,0]), color = PINK)

+

+        positive_vector = Arrow(np.array([1,1,0]), np.array([0.5,0.5,0]), buff=0.001, color = BLUE_C)

+        positive_gradient = Arrow(np.array([1,1,1.732]), np.array([0.5,0.5,1.9362]), buff=0.001, color = BLUE_C)

+        positive_gradient_lab = TextMobject(r"$\nabla f$").move_to(np.array([0.5,0.3,0])).set_color(BLUE_C).scale(0.5)

+

+        negative_vector = Arrow(np.array([1,1,0]), np.array([1.5,1.5,0]), buff=0.001, color = RED_C)

+        negative_gradient = Arrow(np.array([1,1,1.732]), np.array([1.5,1.5,1.322]), buff=0.001, color = RED_C)

+        negative_gradient_lab = TextMobject(r"$-\nabla f$").move_to(np.array([1.6,1.6,0])).set_color(RED_C).scale(0.5)

+

+        positive_vector_line = DashedLine(np.array([0.8,0.8,0]), np.array([1,-2,0]), color = WHITE)

+        positive_vector_lab = TextMobject(r"Most Rapid increase in $f$").move_to(np.array([1.6,-3.6,0])).set_color(BLUE_C).scale(0.6)

+        negative_vector_line = DashedLine(np.array([1.2,1.2,0]), np.array([3,-1.5,0]), color = WHITE)

+        negative_vector_lab = TextMobject(r"Most Rapid decrease in $f$").move_to(np.array([3.6,-3,0])).set_color(RED_C).scale(0.6)

+

+

+

+        line1 = DashedLine(np.array([0.5,0.5,0]), np.array([0.5,0.5,1.9362]), color = BLUE_C)

+        line2 = DashedLine(np.array([1,1,0]), np.array([1,1,1.732]), color = YELLOW_C)

+        line3 = DashedLine(np.array([1.5,1.5,0]), np.array([1.5,1.5,1.322]), color = RED_C)

+

+        curve_vector1 = Arrow(np.array([1,1,0]), np.array([1.5,0.5,0]), buff=0.001, color = YELLOW_C)

+        curve_vector2 = Arrow(np.array([1,1,0]), np.array([0.5,1.5,0]), buff=0.001, color = YELLOW_C)

+

+        curve_vector1_line = DashedLine(np.array([1.2,0.8,0]), np.array([1,2.5,0]), color = WHITE)

+        curve_vector2_line = DashedLine(np.array([0.8,1.2,0]), np.array([1,2.5,0]), color = WHITE)

+        curve_vector_lab = TextMobject(r"Zero Change in $f$").move_to(np.array([0.7,3.6,0])).set_color(PINK).scale(0.6)

+

+        #square = Square(side_length = 0.5).rotate(45*DEGREES).move_to(np.array([1.025,0.975,0]))

+        line_x = Line(np.array([0.8,0.8,0]), np.array([1,0.6,0]), color = PINK)

+        line_y = Line(np.array([1.2,0.8,0]), np.array([1,0.6,0]), color = PINK)

+

+        ninety_degree = VGroup(line_x, line_y)

+        

+        self.set_camera_orientation(phi=60* DEGREES, theta = 20*DEGREES)

+

+        self.add(axes)

+

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(np.array([0,0,3.7]))

+

+        self.add_fixed_orientation_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1]) 

+

+        self.play(ShowCreation(quadrant))

+        self.wait()

+        self.play(ShowCreation(dot1),  ShowCreation(dot2))

+        self.wait()

+        self.play(GrowArrow(positive_vector), GrowArrow(positive_gradient))

+        self.wait()

+        self.play(GrowArrow(negative_vector), GrowArrow(negative_gradient))

+        self.wait()

+        self.play(GrowArrow(line1), GrowArrow(line2), GrowArrow(line3))

+        self.wait()

+        self.play(ShowCreation(quadrant_curve))

+        self.wait()

+        self.play(GrowArrow(curve_vector1), GrowArrow(curve_vector2), ShowCreation(ninety_degree))

+        self.wait()

+        self.play(GrowArrow(dot1_line))

+        self.add_fixed_orientation_mobjects(dot1_lab)

+        self.wait()

+        self.play(GrowArrow(curve_vector1_line), GrowArrow(curve_vector2_line))

+        self.add_fixed_orientation_mobjects(curve_vector_lab)

+        self.wait()

+        self.add_fixed_orientation_mobjects(positive_gradient_lab, negative_gradient_lab)

+        self.wait()

+        self.play(GrowArrow(positive_vector_line), GrowArrow(negative_vector_line))

+        self.add_fixed_orientation_mobjects(positive_vector_lab, negative_vector_lab)

+        self.begin_ambient_camera_rotation(rate=0.1)

+        self.wait(3)
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file3_gradient_level_curves.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file3_gradient_level_curves.py
new file mode 100644
index 0000000..a3b88e5
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/file3_gradient_level_curves.py
@@ -0,0 +1,107 @@
+from manimlib.imports import *

+

+class GradientLevelCurves(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() 

+

+        paraboloid = ParametricSurface(

+            lambda u, v: np.array([

+                u*np.cos(v),

+                u*np.sin(v),

+                -u*u+2

+            ]),u_min=-1.414,u_max=1.414,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1,

+            resolution=(15, 32)).scale(1)

+        

+        plane_0 = Polygon(np.array([2,-2,0]),np.array([2,2,0]),np.array([-2,2,0]),np.array([-2,-2,0]),np.array([2,-2,0]), color = BLUE_E, fill_color = BLUE_E, fill_opacity = 0.3)

+        plane_0_lab = TextMobject("C = 0").move_to(0.4*UP+3.2*RIGHT).set_color(BLUE_E).scale(0.6)

+        circle_0 = Circle(radius = 1.414 , color = BLUE_E)

+        circle_0_lab = TextMobject("0").move_to(1.1*DOWN+1.1*RIGHT).set_color(BLUE_E).scale(0.6)

+

+        plane_0_5 = Polygon(np.array([2,-2,0.5]),np.array([2,2,0.5]),np.array([-2,2,0.5]),np.array([-2,-2,0.5]),np.array([2,-2,0.5]), color = GREEN_C, fill_color = GREEN_C, fill_opacity = 0.3)

+        plane_0_5_lab = TextMobject("C = 0.5").move_to(0.8*UP+3.4*RIGHT).set_color(GREEN_C).scale(0.6)

+        circle_0_5 = Circle(radius = 1.224 , color = GREEN_C)

+        circle_0_5_lab = TextMobject("0.5").move_to(0.9*DOWN+0.9*RIGHT).set_color(GREEN_C).scale(0.6)

+        circle_0_5_copy = circle_0_5.copy().move_to(np.array([0,0,0.5]))

+

+        plane_1 = Polygon(np.array([2,-2,1]),np.array([2,2,1]),np.array([-2,2,1]),np.array([-2,-2,1]),np.array([2,-2,1]), color = YELLOW_C, fill_color = YELLOW_C, fill_opacity = 0.3)

+        plane_1_lab = TextMobject("C = 1").move_to(1.2*UP+3.3*RIGHT).set_color(YELLOW_C).scale(0.6)

+        circle_1 = Circle(radius = 1 , color = YELLOW_C)

+        circle_1_lab = TextMobject("1").move_to(0.7*DOWN+0.7*RIGHT).set_color(YELLOW_C).scale(0.6)

+        circle_1_copy = circle_1.copy().move_to(np.array([0,0,1]))

+

+        plane_1_5 = Polygon(np.array([2,-2,1.5]),np.array([2,2,1.5]),np.array([-2,2,1.5]),np.array([-2,-2,1.5]),np.array([2,-2,1.5]), color = ORANGE, fill_color = ORANGE, fill_opacity = 0.3)

+        plane_1_5_lab = TextMobject("C = 1.5").move_to(1.7*UP+3.4*RIGHT).set_color(ORANGE).scale(0.6)

+        circle_1_5 = Circle(radius = 0.707 , color = ORANGE)

+        circle_1_5_lab = TextMobject("1.5").move_to(0.5*DOWN+0.5*RIGHT).set_color(ORANGE).scale(0.6)

+        circle_1_5_copy = circle_1_5.copy().move_to(np.array([0,0,1.5]))

+

+        plane_2 = Polygon(np.array([2,-2,2]),np.array([2,2,2]),np.array([-2,2,2]),np.array([-2,-2,2]),np.array([2,-2,2]), color = RED_C, fill_color = RED_C, fill_opacity = 0.3)

+        plane_2_lab = TextMobject("C = 2").move_to(2.1*UP+3.3*RIGHT).set_color(RED_C).scale(0.6)

+        dot_2 = Dot().set_fill(RED_C)

+        circle_2_lab = TextMobject("2").move_to(0.2*DOWN+0.2*RIGHT).set_color(RED_C).scale(0.6)

+        dot_2_copy = dot_2.copy().move_to(np.array([0,0,2]))

+

+        vector1 = Arrow(np.array([0.99,-0.99,0]), np.array([0.865,-0.865,0.5]), buff=0.01, color = RED_C).set_stroke(width=3)

+        gradient1 = Arrow(np.array([0.99,-0.99,0]), np.array([0.865,-0.865,0]), buff=0.01, color = RED_C).set_stroke(width=3)

+

+        vector2 = Arrow(np.array([0.865,-0.865,0.5]), np.array([0.707,-0.707,1]), buff=0.01, color = RED_C).set_stroke(width=3)

+        gradient2 = Arrow(np.array([0.865,-0.865,0]), np.array([0.707,-0.707,0]), buff=0.01, color = RED_C).set_stroke(width=3)

+

+        vector3 = Arrow(np.array([0.707,-0.707,1]), np.array([0.499,-0.499,1.5]), buff=0.01, color = RED_C).set_stroke(width=3)

+        gradient3 = Arrow(np.array([0.707,-0.707,0]), np.array([0.499,-0.499,0]), buff=0.01, color = RED_C).set_stroke(width=3)

+

+        vector4 = Arrow(np.array([0.499,-0.499,1.5]), np.array([0,0,2]), buff=0.01, color = RED_C).set_stroke(width=3)

+        gradient4 = Arrow(np.array([0.499,-0.499,0]), np.array([0,0,0]), buff=0.01, color = RED_C).set_stroke(width=3)

+

+

+        self.set_camera_orientation(phi=80 * DEGREES, theta = 0*DEGREES)

+        #self.set_camera_orientation(phi=45 * DEGREES, theta = -20*DEGREES)

+

+        self.add(axes)

+

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(np.array([0,0,3.7]))

+

+        self.add_fixed_orientation_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1]) 

+        

+        self.play(Write(paraboloid))

+        self.wait()

+        self.play(ShowCreation(plane_0), ShowCreation(circle_0))

+        self.add_fixed_in_frame_mobjects(plane_0_lab)

+        self.wait()

+        self.play(ShowCreation(plane_0_5), ShowCreation(circle_0_5_copy), ShowCreation(circle_0_5))

+        self.add_fixed_in_frame_mobjects(plane_0_5_lab)

+        self.wait()

+        self.play(ShowCreation(plane_1), ShowCreation(circle_1_copy), ShowCreation(circle_1))

+        self.add_fixed_in_frame_mobjects(plane_1_lab)

+        self.wait()

+        self.play(ShowCreation(plane_1_5), ShowCreation(circle_1_5_copy), ShowCreation(circle_1_5))

+        self.add_fixed_in_frame_mobjects(plane_1_5_lab)

+        self.wait()

+        self.play(ShowCreation(plane_2), ShowCreation(dot_2_copy), ShowCreation(dot_2))

+        self.add_fixed_in_frame_mobjects(plane_2_lab)

+        self.wait()

+        self.move_camera(phi=60 * DEGREES, theta = 30*DEGREES,run_time=3)

+        self.play(FadeOut(plane_0), FadeOut(plane_0_lab), FadeOut(plane_0_5), FadeOut(plane_0_5_lab), FadeOut(plane_1), FadeOut(plane_1_lab), FadeOut(plane_1_5), FadeOut(plane_1_5_lab), FadeOut(plane_2), FadeOut(plane_2_lab))

+        self.play(FadeOut(circle_0_5_copy), FadeOut(circle_1_copy), FadeOut(circle_1_5_copy), FadeOut(dot_2_copy))

+

+        self.move_camera(phi=45 * DEGREES, theta = -20*DEGREES,run_time=3)

+        self.play(Write(vector1), Write(gradient1))

+        self.wait()

+        self.play(Write(vector2), Write(gradient2))

+        self.wait()

+        self.play(Write(vector3), Write(gradient3))

+        self.wait()

+        self.play(Write(vector4), Write(gradient4))

+        self.wait()

+        self.move_camera(phi=0 * DEGREES, theta = 0*DEGREES,run_time=3)

+        self.play(FadeOut(paraboloid))

+        self.play(FadeOut(vector1), FadeOut(vector2), FadeOut(vector3), FadeOut(vector4))

+        self.wait()

+        self.add_fixed_in_frame_mobjects(circle_0_lab, circle_0_5_lab, circle_1_lab, circle_1_5_lab,circle_2_lab)

+        self.wait(4)

+        
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/gifs/file1_directional_deriv.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/gifs/file1_directional_deriv.gif
new file mode 100644
index 0000000..39305d5
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/gifs/file1_directional_deriv.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/gifs/file2_gradient.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/gifs/file2_gradient.gif
new file mode 100644
index 0000000..d96f330
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/gifs/file2_gradient.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/gifs/file3_gradient_level_curves.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/gifs/file3_gradient_level_curves.gif
new file mode 100644
index 0000000..f1bf06a
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/directional-derivatives/gifs/file3_gradient_level_curves.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_epsilon_delta_defn.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_epsilon_delta_defn.py
deleted file mode 100644
index 63b6165..0000000
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file1_epsilon_delta_defn.py
+++ /dev/null
@@ -1,120 +0,0 @@
-from manimlib.imports import *

-

-class EpsilonDelta(ThreeDScene):

-    def construct(self):

-        axes = ThreeDAxes() # creates a 3D Axis

-        

-

-        sphere = ParametricSurface(

-            lambda u, v: np.array([

-                2*np.sin(u)*np.cos(v),

-                2*np.sin(u)*np.sin(v),

-                2*np.cos(u)

-            ]),u_min=0,u_max=PI/4,v_min=0,v_max=PI/2,checkerboard_colors=[RED_D, RED_E],

-            resolution=(15, 32)).scale(2)

-        #sphere.shift(0.5*RIGHT+0.5*UP)

-

-        #self.set_camera_orientation(phi=0*DEGREES,theta=270*DEGREES)

-        self.set_camera_orientation(phi=75 * DEGREES)

-        

-

-

-        circle = Circle(radius= 0.4,color = GREEN)

-        circle.shift(0.5*RIGHT+0.5*UP)

-

-        line1 = DashedLine(np.array([0.5, 0.1,0]), np.array([0.5, 0.1,2.1]), color = BLUE_E)

-        line2 = DashedLine(np.array([0.5, 0.9,0]), np.array([0.5, 0.9,1.7]), color = BLUE_E)

-        line3 = DashedLine(np.array([0, 0,2.1]), np.array([0.5, 0.1,2.1]), color = YELLOW_C)

-        line4 = DashedLine(np.array([0, 0,1.7]), np.array([0.5, 0.9,1.7]), color = YELLOW_C)

-

-        dot1 = Sphere()

-        dot1.scale(0.01)

-        dot1.move_to(np.array([0,0,1.9]))

-        dot1.set_fill(BLUE_E)

-

-        temp_func1 = TextMobject(r"$L$")

-        temp_func1.scale(0.6)

-        temp_func1.set_color(BLUE_E)

-

-        dot2 = Sphere()

-        dot2.scale(0.01)

-        dot2.move_to(np.array([0,0,1.7]))

-        dot2.set_fill(PURPLE)

-

-        temp_func2 = TextMobject(r"$L - \epsilon$")

-        temp_func2.scale(0.6)

-        temp_func2.set_color(PURPLE)

-

-        dot3 = Sphere()

-        dot3.scale(0.01)

-        dot3.move_to(np.array([0,0,2.1]))

-        dot3.set_fill(PURPLE)

-

-        temp_func3 = TextMobject(r"$L + \epsilon$")

-        temp_func3.scale(0.6)

-        temp_func3.set_color(PURPLE)

-

-        self.add(axes)

-

-        self.play(ShowCreation(dot1))

-        self.add_fixed_in_frame_mobjects(temp_func1)

-        temp_func1.move_to(1.9*UP)

-        self.play(Write(temp_func1))

-

-        self.play(ShowCreation(dot2))

-        self.add_fixed_in_frame_mobjects(temp_func2)

-        temp_func2.move_to(1.7*UP)

-        self.play(Write(temp_func2))

-

-        self.play(ShowCreation(dot3))

-        self.add_fixed_in_frame_mobjects(temp_func3)

-        temp_func3.move_to(2.1*UP)

-        self.play(Write(temp_func3))

-

-

-        circle_center = Sphere()

-        circle_center.scale(0.05)

-        circle_center.move_to(np.array([0.5,0.5,0]))

-        circle_center.set_fill(GREEN)

-

-        temp_circle_center = TextMobject(r"$(a,b,0)$")

-        temp_circle_center.scale(0.5)

-        temp_circle_center.set_color(GREEN)

-

-        curve_circle_center = Sphere()

-        curve_circle_center.scale(0.05)

-        curve_circle_center.move_to(np.array([0.5,0.5,1.9]))

-        curve_circle_center.set_fill(BLUE_E)

-

-        temp_curve_circle_center = TextMobject(r"$(a,b,L)$")

-        temp_curve_circle_center.scale(0.5)

-        temp_curve_circle_center.set_color(BLUE)

-

-        delta_lab = TextMobject(r"$\delta - disk$")

-        delta_lab.scale(0.5)

-        delta_lab.set_color(PINK)   

-

-        self.play(ShowCreation(circle_center))

-        self.add_fixed_in_frame_mobjects(temp_circle_center)

-        temp_circle_center.move_to(1.5*RIGHT)

-        self.play(Write(temp_circle_center))

-

-        self.play(ShowCreation(curve_circle_center))

-        self.add_fixed_in_frame_mobjects(temp_curve_circle_center)

-        temp_curve_circle_center.move_to(1.9*UP+1*RIGHT)

-        self.play(Write(temp_curve_circle_center))

-

-

-        self.add_fixed_in_frame_mobjects(delta_lab)

-        delta_lab.move_to(0.4*DOWN+1.7*RIGHT)

-        self.play(Write(delta_lab))

-

-

-

-

-

-        self.begin_ambient_camera_rotation(rate=0.2)

-        self.play(Write(sphere))

-        self.play(ShowCreation(circle), ShowCreation(line1), ShowCreation(line2))

-        self.play(ShowCreation(line3), ShowCreation(line4))

-        self.wait(8)

diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file3_limit_func.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file3_limit_func.py
deleted file mode 100644
index 02e00e8..0000000
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file3_limit_func.py
+++ /dev/null
@@ -1,30 +0,0 @@
-from manimlib.imports import *

-

-class LimitFunc(ThreeDScene):

-    def construct(self):

-        axes = ThreeDAxes() 

-

-        text3d = TextMobject(r"$f(x,y) = \frac{x^2 - y^2}{x^2 + y^2}$")

-        self.add_fixed_in_frame_mobjects(text3d)

-       

-        text3d.to_corner(UL)

-      

-        text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

-

-        self.play(Write(text3d))

-        self.wait(1)

-

-        limit_func = ParametricSurface(

-            lambda u, v: np.array([

-                u*np.cos(v),

-                u*np.sin(v),

-                (np.cos(v)*np.cos(v) - np.sin(v)*np.sin(v))/3

-            ]),u_min=-3,u_max=3,v_min=0,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E],

-            resolution=(15, 32)).scale(2)

-

-        self.set_camera_orientation(phi=80 * DEGREES)

-        self.begin_ambient_camera_rotation(rate=0.3)

-

-        self.add(axes)

-        self.play(Write(limit_func))

-        self.wait(10)
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file4_continuity_func.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file4_continuity_func.py
deleted file mode 100644
index 551c8a8..0000000
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file4_continuity_func.py
+++ /dev/null
@@ -1,32 +0,0 @@
-from manimlib.imports import *

-

-class ContinuityFunc(ThreeDScene):

-    def construct(self):

-        axes = ThreeDAxes() 

-

-        text3d = TextMobject(r"$f(x,y) = \frac{3x^2y}{x^2 + y^2}$")

-        self.add_fixed_in_frame_mobjects(text3d)

-       

-        text3d.to_corner(UL)

-      

-        text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

-

-        self.play(Write(text3d))

-        self.wait(1)

-

-        continuity_func = ParametricSurface(

-            lambda u, v: np.array([

-                u*np.cos(v),

-                u*np.sin(v),

-                3*u*np.cos(v)*np.cos(v)*np.sin(v)

-            ]),u_min=-1.5,u_max=1.5,v_min=0,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E],

-            resolution=(15, 32)).scale(2)

-

-    

-

-        self.set_camera_orientation(phi=80 * DEGREES)

-        self.begin_ambient_camera_rotation(rate=0.3)

-

-        self.add(axes)

-        self.play(Write(continuity_func))

-        self.wait(8)
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file1_epsilon_delta_defn.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file1_epsilon_delta_defn.gif
deleted file mode 100644
index 68f637e..0000000
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file1_epsilon_delta_defn.gif
+++ /dev/null
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file3_limit_func.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file3_limit_func.gif
deleted file mode 100644
index 07b23be..0000000
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file3_limit_func.gif
+++ /dev/null
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file4_continuity_func.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file4_continuity_func.gif
deleted file mode 100644
index 560e0f1..0000000
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file4_continuity_func.gif
+++ /dev/null
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivar_func_examples.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivar_func_examples.py
new file mode 100644
index 0000000..55b2b7e
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivar_func_examples.py
@@ -0,0 +1,167 @@
+from manimlib.imports import *

+

+class Examples1(GraphScene):

+    def construct(self):

+       

+        rectangle = Rectangle(height = 3, width = 4, color = GREEN)

+        rectangle_area_func = TexMobject("Area", "=", "f(", "Length", ",", "Breadth", ")").scale(0.6)

+        rectangle_area_func[0].set_color(RED_C)

+        rectangle_area_func[2].set_color(ORANGE)

+        rectangle_area_func[3].set_color(YELLOW_C)

+        rectangle_area_func[5].set_color(BLUE_C)

+        rectangle_area_func[6].set_color(ORANGE)

+

+

+        rectangle_area = TexMobject("Area", "=", "Length", "\\times", "Breadth").scale(0.6)

+        rectangle_area[0].set_color(RED_C)

+        rectangle_area[2].set_color(YELLOW_C)

+        rectangle_area[4].set_color(BLUE_C)

+

+

+        square = Square(side_length = 5, color = PURPLE)

+        square_area_func = TexMobject("Area", "=", "f(", "Length", ")")

+        square_area_func[0].set_color(GREEN_C)

+        square_area_func[2].set_color(ORANGE)

+        square_area_func[3].set_color(BLUE_C)

+        square_area_func[4].set_color(ORANGE)

+

+        square_area = TexMobject("Area", "=", "Length^2")

+        square_area[0].set_color(GREEN_C)

+        square_area[2].set_color(BLUE_C)

+

+

+        circle = Circle(radius = 2, color = PINK)

+        circle_area_func = TexMobject("Area", "=", "f(", "r", ")")

+        circle_area_func[0].set_color(YELLOW_C)

+        circle_area_func[2].set_color(ORANGE)

+        circle_area_func[3].set_color(GREEN_C)

+        circle_area_func[4].set_color(ORANGE)

+

+        circle_area = TexMobject("Area", "=", "\\pi", "r^2")

+        circle_area[0].set_color(YELLOW_C)

+        circle_area[2].set_color(BLUE_C)

+        circle_area[3].set_color(GREEN_C)

+

+        radius = Line(ORIGIN,2*RIGHT, color = RED_C)

+        

+

+

+        braces_rect1 = Brace(rectangle, LEFT)

+        eq_text1 = braces_rect1.get_text("Length").set_color(YELLOW_C)

+        braces_rect2 = Brace(rectangle, UP)

+        eq_text2 = braces_rect2.get_text("Breadth").set_color(BLUE_C)

+

+        braces_square = Brace(square, LEFT)

+        braces_square_text = braces_square.get_text("Length").set_color(BLUE_C)

+

+        radius_text = TexMobject("r", color = GREEN_C).next_to(radius,UP)

+        

+

+

+        self.play(ShowCreation(rectangle))

+        self.wait(1)

+        self.play(GrowFromCenter(braces_rect1),Write(eq_text1),GrowFromCenter(braces_rect2),Write(eq_text2))

+        self.wait(1)

+        self.play(Write(rectangle_area_func))

+        self.wait(1)

+        self.play(Transform(rectangle_area_func, rectangle_area))

+        self.wait(1)

+        self.play(FadeOut(braces_rect1),FadeOut(eq_text1),FadeOut(braces_rect2),FadeOut(eq_text2),FadeOut(rectangle_area_func))

+

+

+        self.play(Transform(rectangle, square))

+        self.wait(1)

+        self.play(GrowFromCenter(braces_square),Write(braces_square_text))

+        self.wait(1)

+        self.play(Write(square_area_func))

+        self.wait(1)

+        self.play(Transform(square_area_func, square_area))

+        self.wait(1)

+        self.play(FadeOut(braces_square),FadeOut(braces_square_text),FadeOut(square_area_func))

+

+

+        self.play(Transform(rectangle, circle))

+        self.wait(1)

+        self.play(ShowCreation(radius),Write(radius_text))

+        self.wait(1)

+        self.play(FadeOut(radius_text),FadeOut(radius))

+        self.wait(1)

+        self.play(Write(circle_area_func))

+        self.wait(1)

+        self.play(Transform(circle_area_func, circle_area))

+        self.wait(1)

+        self.play(FadeOut(circle_area_func))

+

+

+

+class Examples2(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() 

+        

+        rectangle_x_y_0 = Polygon(np.array([-1,-2,0]),np.array([-1,2,0]),np.array([1,2,0]),np.array([1,-2,0]),np.array([-1,-2,0]), color = RED_E, fill_color = RED_C, fill_opacity = 0.1)

+        rectangle_x_y_3 = Polygon(np.array([-1,-2,3]),np.array([-1,2,3]),np.array([1,2,3]),np.array([1,-2,3]),np.array([-1,-2,3]), color = RED_E, fill_color = RED_C, fill_opacity = 0.1)

+

+        rectangle_y_z_1 = Polygon(np.array([1,-2,3]),np.array([1,2,3]),np.array([1,2,0]),np.array([1,-2,0]),np.array([1,-2,3]), color = RED_E, fill_color = RED_C, fill_opacity = 0.1)

+        rectangle_y_z_minus_1 = Polygon(np.array([-1,-2,3]),np.array([-1,2,3]),np.array([-1,2,0]),np.array([-1,-2,0]),np.array([-1,-2,3]), color = RED_E, fill_color = RED_C, fill_opacity = 0.1)

+

+        rectangle_x_z_2 = Polygon(np.array([1,2,3]),np.array([-1,2,3]),np.array([-1,2,0]),np.array([1,2,0]),np.array([1,2,3]), color = RED_E, fill_color = RED_C, fill_opacity = 0.1)

+        rectangle_x_z_minus_2 = Polygon(np.array([1,-2,3]),np.array([-1,-2,3]),np.array([-1,-2,0]),np.array([1,-2,0]),np.array([1,-2,3]), color = RED_E, fill_color = RED_C, fill_opacity = 0.1)

+

+        box = VGroup(rectangle_x_y_0, rectangle_x_y_3, rectangle_y_z_1, rectangle_y_z_minus_1, rectangle_x_z_2, rectangle_x_z_minus_2)

+

+        braces_rectangle_x_y_0 = Line(np.array([1,2,0]), np.array([1,-2,0]), color = BLUE_C)

+        braces_rectangle_x_y_0_text = TextMobject("Length").set_color(BLUE_C).move_to(np.array([2,-1,0]))

+

+        braces_rectangle_y_z_1 = Line(np.array([1,2,0]), np.array([1,2,3]), color = YELLOW_C)

+        braces_rectangle_y_z_1_text = TextMobject("Height").set_color(YELLOW_C).move_to(np.array([2,3.8,2]))

+

+        braces_rectangle_x_z_2 = Line(np.array([1,2,3]), np.array([-1,2,3]), color = PURPLE)

+        braces_rectangle_x_z_2_text = TextMobject("Breadth").set_color(PURPLE).move_to(np.array([0,3.8,3.3]))

+

+        box_area_func = TexMobject("Area =", "f(", "Length", ",", "Breadth", ",", "Height", ")").move_to(4*LEFT+3.5*UP).scale(0.6)

+        box_area_func[0].set_color(GREEN_C)

+        box_area_func[1].set_color(ORANGE)

+        box_area_func[2].set_color(BLUE_C)

+        box_area_func[4].set_color(PURPLE)

+        box_area_func[6].set_color(YELLOW_C)

+        box_area_func[7].set_color(ORANGE)

+

+        box_area_func_2 = TexMobject("Area =", "Length", "\\times", "Breadth", "\\times", "Height").move_to(4*LEFT+3.5*UP).scale(0.6)

+        box_area_func_2[0].set_color(GREEN_C)

+        box_area_func_2[1].set_color(BLUE_C)

+        box_area_func_2[3].set_color(PURPLE)

+        box_area_func_2[5].set_color(YELLOW_C)

+

+

+        self.set_camera_orientation(phi=70 * DEGREES, theta = 45*DEGREES)

+

+        self.add(axes)

+        

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(3.7*UP)

+

+        self.add_fixed_in_frame_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1])

+

+        self.play(ShowCreation(box), ShowCreation(braces_rectangle_x_y_0))

+        self.add_fixed_orientation_mobjects(braces_rectangle_x_y_0_text)

+        self.play(ShowCreation(braces_rectangle_y_z_1))

+        self.add_fixed_orientation_mobjects(braces_rectangle_y_z_1_text)

+        self.play(ShowCreation(braces_rectangle_x_z_2))

+        self.add_fixed_orientation_mobjects(braces_rectangle_x_z_2_text)

+        self.wait(2)

+

+        self.move_camera(phi=60* DEGREES,theta=80*DEGREES)

+        self.add_fixed_in_frame_mobjects(box_area_func)

+        self.play(Write(box_area_func))

+        self.wait()

+

+        

+        self.play(ReplacementTransform(box_area_func,box_area_func_2))

+        self.add_fixed_in_frame_mobjects(box_area_func_2)

+        

+        

+        self.wait(3)        
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivariable_func_respresentation.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivariable_func_respresentation.py
deleted file mode 100644
index 4bfcf21..0000000
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file1_multivariable_func_respresentation.py
+++ /dev/null
@@ -1,80 +0,0 @@
-from manimlib.imports import *

-

-class MultivariableFunc(Scene):

-    def construct(self):

-

-        topic = TextMobject("Multivariable Functions")

-        topic.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

-        topic.scale(2)

-

-        self.play(Write(topic))

-        self.wait(1)

-        self.play(FadeOut(topic))

-

-

-        circle = Circle()

-        circle.scale(3)

-

-        eqn1 = TextMobject(r"f(x,y) = $x^2y$")

-        eqn1.set_color(YELLOW)

-        

-

-

-        number1 = TextMobject("(2,1)")

-        number1.move_to(3*UP+ 3*LEFT)

-        number1.scale(1.2)

-        number1.set_color(GREEN)

-

-        output1 = TextMobject("4")

-        output1.scale(1.5)

-        output1.set_color(BLUE)

-

-        eqn1_1 = TextMobject(r"f(2,1) = $2^2(1)$")

-        eqn1_1.set_color(YELLOW)

-

-

-        self.play(ShowCreation(circle),Write(eqn1))

-        self.wait(1)

-        self.play(ApplyMethod(number1.move_to, 0.6*LEFT))

-        self.play(FadeOut(number1))

-        self.play(Transform(eqn1, eqn1_1))

-        self.wait(1)

-        self.play(ApplyMethod(output1.move_to, 3*DOWN+4*RIGHT))

-        self.wait(1)

-        self.play(FadeOut(output1))

-

-

-        eqn2 = TextMobject(r"f(x,y,z) = $x^2y+2yz$")

-        eqn2.set_color(YELLOW)

-

-        number2 = TextMobject("(2,1,3)")

-        number2.move_to(3*UP+ 3*LEFT)

-        number2.scale(1.2)

-        number2.set_color(GREEN)

-

-        output2 = TextMobject("8")

-        output2.scale(1.5)

-        output2.set_color(BLUE)

-

-        eqn2_1 = TextMobject(r"f(2,1,3) = $2^2(1) + 2(1)(3)$")

-        eqn2_1.set_color(YELLOW)

-

-        eqn2_2 = TextMobject(r"f(2,1,3) = $2 + 6$")

-        eqn2_2.set_color(YELLOW)

-

-

-        

-        self.play(FadeOut(eqn1))

-        self.play(Write(eqn2))

-

-        self.wait(1)

-        self.play(ApplyMethod(number2.move_to, 1.2*LEFT))

-        self.play(FadeOut(number2))

-        self.play(Transform(eqn2, eqn2_1))

-        self.wait(1)

-        self.play(Transform(eqn2, eqn2_2))

-        self.wait(1)

-        self.play(ApplyMethod(output2.move_to, 3*DOWN+4*RIGHT))

-        self.wait(1)

-        self.play(FadeOut(output2),FadeOut(eqn2),FadeOut(circle))

-        self.wait(2)
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_examples.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_examples.py
deleted file mode 100644
index 7322e47..0000000
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_examples.py
+++ /dev/null
@@ -1,69 +0,0 @@
-from manimlib.imports import *

-

-class Examples(GraphScene):

-    def construct(self):

-       

-        rectangle = Rectangle(height = 3, width = 4, color = GREEN)

-        square = Square(side_length = 5, color = PURPLE)

-        circle = Circle(radius = 2, color = PINK)

-        radius = Line(ORIGIN,2*RIGHT)

-        

-        radius.set_color(RED)

-

-        rectangle_area_func = TextMobject(r"$Area = f(Length, Breadth)$")

-        rectangle_area_func.scale(0.6)

-        square_area_func = TextMobject(r"$Area = f(Length)$")

-        circle_area_func = TextMobject(r"$Area = f(r)$")

-

-

-        rectangle_area = TextMobject(r"$Area = Length \times Breadth$")

-        rectangle_area.scale(0.6)

-        square_area = TextMobject(r"$Area = Length^2$")

-        circle_area = TextMobject(r"$Area = \pi r^2$")

-

-        braces_rect1 = Brace(rectangle, LEFT)

-        eq_text1 = braces_rect1.get_text("Length")

-        braces_rect2 = Brace(rectangle, UP)

-        eq_text2 = braces_rect2.get_text("Breadth")

-

-        braces_square = Brace(square, LEFT)

-        braces_square_text = braces_square.get_text("Length")

-

-        radius_text = TextMobject("r")

-        radius_text.next_to(radius,UP)

-

-        

-

-        self.play(ShowCreation(rectangle))

-        self.wait(1)

-        self.play(GrowFromCenter(braces_rect1),Write(eq_text1),GrowFromCenter(braces_rect2),Write(eq_text2))

-        self.wait(1)

-        self.play(Write(rectangle_area_func))

-        self.wait(1)

-        self.play(Transform(rectangle_area_func, rectangle_area))

-        self.wait(1)

-        self.play(FadeOut(braces_rect1),FadeOut(eq_text1),FadeOut(braces_rect2),FadeOut(eq_text2),FadeOut(rectangle_area_func))

-

-

-        self.play(Transform(rectangle, square))

-        self.wait(1)

-        self.play(GrowFromCenter(braces_square),Write(braces_square_text))

-        self.wait(1)

-        self.play(Write(square_area_func))

-        self.wait(1)

-        self.play(Transform(square_area_func, square_area))

-        self.wait(1)

-        self.play(FadeOut(braces_square),FadeOut(braces_square_text),FadeOut(square_area_func))

-

-

-        self.play(Transform(rectangle, circle))

-        self.wait(1)

-        self.play(ShowCreation(radius),Write(radius_text))

-        self.wait(1)

-        self.play(FadeOut(radius_text),FadeOut(radius))

-        self.wait(1)

-        self.play(Write(circle_area_func))

-        self.wait(1)

-        self.play(Transform(circle_area_func, circle_area))

-        self.wait(1)

-        self.play(FadeOut(circle_area_func))
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_respresentation.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_respresentation.py
new file mode 100644
index 0000000..d10ff0a
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file2_multivariable_func_respresentation.py
@@ -0,0 +1,98 @@
+from manimlib.imports import *

+

+class MultivariableFunc(Scene):

+    def construct(self):

+

+        topic = TextMobject("Multivariable Functions")

+        topic.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

+        topic.scale(1.5)

+

+        self.play(Write(topic))

+        self.wait()

+        self.play(FadeOut(topic))

+

+

+        #circle = Circle()

+        #circle.scale(3)

+

+        scalar_function = TextMobject("Scalar Valued Function")

+        scalar_function.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

+        scalar_function.scale(1.5)

+        scalar_function.move_to(2.5*UP)

+

+        rectangle = Rectangle(height = 2, width = 4)

+        rectangle.set_color(PURPLE)

+

+        eqn1 = TextMobject(r"f(x,y) = $x^2y$")

+        eqn1.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE)

+        

+

+

+        number1 = TextMobject("(2,1)")

+        number1.move_to(2.5*UP+ 4*LEFT)

+        number1.scale(1.2)

+        number1.set_color(ORANGE)

+

+        output1 = TextMobject("4")

+        output1.scale(1.5)

+        output1.set_color(BLUE_C)

+        output1.move_to(3*RIGHT)

+

+        eqn1_1 = TextMobject(r"f(2,1) = $2^2(1)$")

+        eqn1_1.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE)

+

+

+        self.play(Write(eqn1),ShowCreation(rectangle))

+        self.wait()

+        self.play(ApplyMethod(number1.move_to, 3*LEFT))

+        self.play(FadeOut(number1))

+        self.play(Transform(eqn1, eqn1_1))

+        self.wait()

+        self.play(ApplyMethod(output1.move_to, 2.5*DOWN+4*RIGHT))

+        self.wait()

+        self.play(Write(scalar_function))

+        self.play(FadeOut(output1), FadeOut(scalar_function), FadeOut(eqn1))

+

+

+        vector_function = TextMobject("Vector Valued Function")

+        vector_function.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

+        vector_function.scale(1.5)

+        vector_function.move_to(2.5*UP)

+

+

+        eqn2 = TextMobject(r"f(x,y,z) = $ \begin{bmatrix} x^2y \\ 2yz  \end{bmatrix}$")

+        eqn2.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

+

+        number2 = TextMobject("(2,1,3)")

+        number2.move_to(2.5*UP+ 4*LEFT)

+        number2.scale(1.2)

+        number2.set_color(ORANGE)

+

+        output2 = TextMobject(r"$ \begin{bmatrix} 4 \\ 6  \end{bmatrix}$")

+        #output2.scale(1.5)

+        output2.set_color(BLUE_C)

+        output2.move_to(3*RIGHT)

+

+        #eqn2_1 = TextMobject(r"f(2,1,3) = $2^2(1) + 2(1)(3)$")

+        #eqn2_1.set_color(YELLOW)

+

+        #eqn2_2 = TextMobject(r"f(2,1,3) = $2 + 6$")

+        #eqn2_2.set_color(YELLOW)

+

+

+        self.play(Write(eqn2))

+

+        self.wait()

+        self.play(ApplyMethod(number2.move_to, 3*LEFT))

+        self.play(FadeOut(number2))

+

+        #self.play(Transform(eqn2, eqn2_1))

+        #self.wait(1)

+        #self.play(Transform(eqn2, eqn2_2))

+        #self.wait(1)

+

+        self.play(ApplyMethod(output2.move_to, 2.5*DOWN+4*RIGHT))

+        self.wait()

+        self.play(Write(vector_function))

+        self.play(FadeOut(output2),FadeOut(eqn2), FadeOut(vector_function), FadeOut(rectangle))

+        self.wait()
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_plot_sphere.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_plot_sphere.py
deleted file mode 100644
index baf08b1..0000000
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_plot_sphere.py
+++ /dev/null
@@ -1,42 +0,0 @@
-from manimlib.imports import *

-

-class Sphere(ThreeDScene):

-    def construct(self):

-        axes = ThreeDAxes() # creates a 3D Axis

-

-        sphere = ParametricSurface(

-            lambda u, v: np.array([

-                np.sin(u)*np.cos(v),

-                np.sin(u)*np.sin(v),

-                np.cos(u)

-            ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI,checkerboard_colors=[RED_D, RED_E],

-            resolution=(15, 32)).scale(2)

-

-

-

-        #self.set_camera_orientation(phi=0 * DEGREES,theta=270*DEGREES)

-

-        text3d = TextMobject(r"$f(x,y) \rightarrow Point(x,y,z)$")

-        text3d1 = TextMobject(r"$f(x,y) \rightarrow Point(x,y, 1 - x^2 - y^2)$")

-        self.add_fixed_in_frame_mobjects(text3d)

-        text3d.scale(0.7)

-        text3d1.scale(0.7)

-        text3d.to_corner(UL)

-        text3d1.to_corner(UL)

-        text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

-        text3d1.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) 

-        self.play(Write(text3d))

-        self.wait(1)

-        

-        self.play(Transform(text3d,text3d1))

-        self.add_fixed_in_frame_mobjects(text3d1)

-        self.play(FadeOut(text3d))

-

-        

-        self.set_camera_orientation(phi=75 * DEGREES)

-        self.begin_ambient_camera_rotation(rate=0.3)

-

-

-        self.add(axes)

-        self.play(Write(sphere))

-        self.wait(5)
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_sphere.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_sphere.py
new file mode 100644
index 0000000..86239ae
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file3_sphere.py
@@ -0,0 +1,177 @@
+from manimlib.imports import *

+

+class Sphere(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() # creates a 3D Axis

+

+        text3d = TextMobject(r"$f(x,y) \rightarrow Point(x,y,z)$")

+        text3d1 = TextMobject(r"$f(x,y) \rightarrow Point(x,y, \sqrt{r^2 - x^2 - y^2})$")

+        self.add_fixed_in_frame_mobjects(text3d)

+        text3d.scale(0.7)

+        text3d1.scale(0.7)

+        text3d.to_corner(UL)

+        text3d1.to_corner(UL)

+        text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

+        text3d1.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE) 

+        self.play(Write(text3d))

+        self.wait(1)

+        

+        self.play(Transform(text3d,text3d1))

+        self.add_fixed_in_frame_mobjects(text3d1)

+        self.play(FadeOut(text3d))

+

+        sphere = ParametricSurface(

+            lambda u, v: np.array([

+                2*np.sin(u)*np.cos(v),

+                2*np.sin(u)*np.sin(v),

+                2*np.cos(u)

+            ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI,checkerboard_colors=[RED_D, RED_E],

+            resolution=(15, 32)).scale(1)

+

+

+        #Experiment with circles by changing difference value of u and v

+        '''

+        sphere_points = [np.array([2*np.sin(u*DEGREES)*np.cos(v*DEGREES), 2*np.sin(u*DEGREES)*np.sin(v*DEGREES), 2*np.cos(u*DEGREES)]) for u in range(0, 185, 5) for v in range(0, 365, 5)]

+

+        sphere_spheres = [Dot().move_to(pts) for pts in sphere_points]

+

+        sphere = VGroup(*sphere_spheres)

+        '''

+        

+        self.set_camera_orientation(phi=75 * DEGREES, theta = 45*DEGREES)

+

+        self.add(axes)

+

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(np.array([0,0,3.7]))

+

+        self.add_fixed_orientation_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1]) 

+

+        dot_x_y1 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([-1,1,0]))

+        dot_x_y_z1 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([-1,1,1.414]))

+        dot_x_y_z_1 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([-1,1,-1.414]))

+        line1 = DashedLine(np.array([-1,1,-1.414]), np.array([-1,1,1.414]), color = YELLOW_C)

+

+        point_x_y1 = TexMobject("(-1,1,0)").set_color(BLUE_C).move_to(np.array([-1.5,1.5,0])).scale(0.5)

+        point_x_y_z1 = TexMobject("(-1,1,\\sqrt{r^2 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)

+        point_x_y_z1_2 = TexMobject("(-1,1,\\sqrt{4 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)

+        point_x_y_z1_3 = TexMobject("(-1,1,\\sqrt{4 - 1 - 1})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)

+        point_x_y_z1_4 = TexMobject("(-1,1,\\sqrt{2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)

+        point_x_y_z1_5 = TexMobject("(-1,1,1.414)").set_color(BLUE_C).move_to(np.array([-1.5,1.5,1.414])).scale(0.5)

+

+        point_x_y_z_1 = TexMobject("(-1,1,\\sqrt{r^2 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)

+        point_x_y_z_1_2 = TexMobject("(-1,1,\\sqrt{4 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)

+        point_x_y_z_1_3 = TexMobject("(-1,1,\\sqrt{4 - 1 - 1})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)

+        point_x_y_z_1_4 = TexMobject("(-1,1,\\sqrt{2})").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)

+        point_x_y_z_1_5 = TexMobject("(-1,1,-1.414)").set_color(BLUE_C).move_to(np.array([-1.5,1.5,-1.414])).scale(0.5)

+

+        

+        self.play(ShowCreation(dot_x_y1))

+        self.add_fixed_orientation_mobjects(point_x_y1)

+        self.play(ShowCreation(dot_x_y_z1), ShowCreation(dot_x_y_z_1), ShowCreation(line1))

+        self.add_fixed_orientation_mobjects(point_x_y_z1, point_x_y_z_1)

+        self.wait(0.5)

+        self.play(ReplacementTransform(point_x_y_z1,point_x_y_z1_2), ReplacementTransform(point_x_y_z_1,point_x_y_z_1_2))

+        self.add_fixed_orientation_mobjects(point_x_y_z1_2, point_x_y_z_1_2)

+

+        self.wait(0.5)

+        self.play(ReplacementTransform(point_x_y_z1_2,point_x_y_z1_3), ReplacementTransform(point_x_y_z_1_2,point_x_y_z_1_3))

+        self.add_fixed_orientation_mobjects(point_x_y_z1_3, point_x_y_z_1_3)

+        self.wait(0.5)

+        self.play(ReplacementTransform(point_x_y_z1_3,point_x_y_z1_4), ReplacementTransform(point_x_y_z_1_3,point_x_y_z_1_4))

+        self.add_fixed_orientation_mobjects(point_x_y_z1_4, point_x_y_z_1_4)

+        self.wait(0.5)

+        self.play(ReplacementTransform(point_x_y_z1_4,point_x_y_z1_5), ReplacementTransform(point_x_y_z_1_4,point_x_y_z_1_5))

+        self.add_fixed_orientation_mobjects(point_x_y_z1_5, point_x_y_z_1_5)

+        

+

+

+        dot_x_y2 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([0.5,-0.5,0]))

+        dot_x_y_z2 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([0.5,-0.5,1.87]))

+        dot_x_y_z_2 = Dot().scale(0.75).set_fill(RED_C).move_to(np.array([0.5,-0.5,-1.87]))

+        line2 = DashedLine(np.array([0.5,-0.5,-1.87]), np.array([0.5,-0.5,1.87]), color = YELLOW_C)

+

+        point_x_y2 = TexMobject("(0.5,-0.5,0)").set_color(BLUE_C).move_to(np.array([1.5,-1.5,0])).scale(0.5)

+        point_x_y_z2 = TexMobject("(0.5,-0.5,\\sqrt{r^2 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)

+        point_x_y_z2_2 = TexMobject("(0.5,-0.5,\\sqrt{4 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)

+        point_x_y_z2_3 = TexMobject("(0.5,-0.5,\\sqrt{4 - 0.25 - 0.25})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)

+        point_x_y_z2_4 = TexMobject("(0.5,-0.5,\\sqrt{3.5})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)

+        point_x_y_z2_5 = TexMobject("(0.5,-0.5,1.87)").set_color(BLUE_C).move_to(np.array([1.5,-1.5,1.87])).scale(0.5)

+

+        point_x_y_z_2 = TexMobject("(0.5,-0.5,\\sqrt{r^2 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)

+        point_x_y_z_2_2 = TexMobject("(0.5,-0.5,\\sqrt{4 - x^2 - y^2})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)

+        point_x_y_z_2_3 = TexMobject("(0.5,-0.5,\\sqrt{4 - 0.25 - 0.25})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)

+        point_x_y_z_2_4 = TexMobject("(0.5,-0.5,\\sqrt{3.5})").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)

+        point_x_y_z_2_5 = TexMobject("(0.5,-0.5,-1.87)").set_color(BLUE_C).move_to(np.array([1.5,-1.5,-1.87])).scale(0.5)

+

+        

+        self.play(ShowCreation(dot_x_y2))

+        self.add_fixed_orientation_mobjects(point_x_y2)

+        self.play(ShowCreation(dot_x_y_z2), ShowCreation(dot_x_y_z_2), ShowCreation(line2))

+        self.add_fixed_orientation_mobjects(point_x_y_z2, point_x_y_z_2)

+        self.wait(0.5)

+        self.play(ReplacementTransform(point_x_y_z2,point_x_y_z2_2), ReplacementTransform(point_x_y_z_2,point_x_y_z_2_2))

+        self.add_fixed_orientation_mobjects(point_x_y_z2_2, point_x_y_z_2_2)

+

+        self.wait(0.5)

+        self.play(ReplacementTransform(point_x_y_z2_2,point_x_y_z2_3), ReplacementTransform(point_x_y_z_2_2,point_x_y_z_2_3))

+        self.add_fixed_orientation_mobjects(point_x_y_z2_3, point_x_y_z_2_3)

+        self.wait(0.5)

+        self.play(ReplacementTransform(point_x_y_z2_3,point_x_y_z2_4), ReplacementTransform(point_x_y_z_2_3,point_x_y_z_2_4))

+        self.add_fixed_orientation_mobjects(point_x_y_z2_4, point_x_y_z_2_4)

+        self.wait(0.5)

+        self.play(ReplacementTransform(point_x_y_z2_4,point_x_y_z2_5), ReplacementTransform(point_x_y_z_2_4,point_x_y_z_2_5))

+        self.add_fixed_orientation_mobjects(point_x_y_z2_5, point_x_y_z_2_5)

+

+        self.play(FadeOut(point_x_y1), FadeOut(point_x_y_z1_5), FadeOut(point_x_y_z_1_5), FadeOut(dot_x_y1), FadeOut(dot_x_y_z1), FadeOut(dot_x_y_z_1), FadeOut(line1))

+        self.play(FadeOut(point_x_y2), FadeOut(point_x_y_z2_5), FadeOut(point_x_y_z_2_5), FadeOut(dot_x_y2), FadeOut(dot_x_y_z2), FadeOut(dot_x_y_z_2), FadeOut(line2))

+        

+

+

+

+        sphere_final = []

+    

+        for u in range(0, 180, 15): 

+            sphere_points1 = [np.array([2*np.sin(u*DEGREES)*np.cos(v*DEGREES), 2*np.sin(u*DEGREES)*np.sin(v*DEGREES), 2*np.cos(u*DEGREES)]) for v in range(0, 370, 10)]

+            sphere_dots1 = [Dot().scale(0.75).set_fill(RED_C).move_to(pts) for pts in sphere_points1]

+

+            sphere_points2 = [np.array([2*np.sin((u+5)*DEGREES)*np.cos(v*DEGREES), 2*np.sin((u+5)*DEGREES)*np.sin(v*DEGREES), 2*np.cos((u+5)*DEGREES)]) for v in range(0, 370, 10)]

+            sphere_dots2 = [Dot().scale(0.75).set_fill(RED_C).move_to(pts) for pts in sphere_points2]

+

+            sphere_points3 = [np.array([2*np.sin((u+10)*DEGREES)*np.cos(v*DEGREES), 2*np.sin((u+10)*DEGREES)*np.sin(v*DEGREES), 2*np.cos((u+10)*DEGREES)]) for v in range(0, 370, 10)]

+            sphere_dots3 = [Dot().scale(0.75).set_fill(RED_C).move_to(pts) for pts in sphere_points3]

+

+            sphere_final = sphere_final + sphere_dots1 + sphere_dots2 + sphere_dots3

+

+            sphere_dots = sphere_dots1 + sphere_dots2 + sphere_dots3

+   

+            sphere_with_dots = VGroup(*sphere_dots)

+            self.play(ShowCreation(sphere_with_dots))

+

+        sphere_final_with_dots = VGroup(*sphere_final)

+        

+        

+        self.begin_ambient_camera_rotation(rate=0.5)

+        self.wait(3)

+        self.play(ReplacementTransform(sphere_final_with_dots, sphere))

+        self.wait(5)

+        

+

+

+

+

+

+

+        

+

+

+

+

+        

+        

+

+        

diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_vectorvf_helix.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_vectorvf_helix.py
new file mode 100644
index 0000000..fc151ac
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_vectorvf_helix.py
@@ -0,0 +1,92 @@
+from manimlib.imports import *

+

+class Helix(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() # creates a 3D Axis

+

+        helix1=ParametricFunction(

+                lambda u : np.array([

+                1.5*np.cos(u),

+                1.5*np.sin(u),

+                u/4

+            ]),color=PURPLE,t_min=-TAU,t_max=TAU,

+            )

+

+        helix2=ParametricFunction(

+                lambda u : np.array([

+                2*np.cos(u),

+                2*np.sin(u),

+                u/2

+            ]),color=GREEN_C,t_min=-TAU,t_max=TAU,

+            )

+

+        function = TexMobject("f(", "r", ",", "\\theta", ")", "=", "[", "r", "\\cos", "\\theta", ",", "r", "\\sin" ,"\\theta", ",", "h" ,"\\theta", "]" ).scale(0.6).to_corner(UL)

+        function.set_color_by_tex(r"\theta", BLUE_C)

+        function.set_color_by_tex(r"r", RED_C)

+        function.set_color_by_tex(r"\cos", GREEN_C)

+        function.set_color_by_tex(r"\sin", YELLOW_C)

+        function[0].set_color(ORANGE)

+        function[4].set_color(ORANGE)

+

+

+        self.add_fixed_in_frame_mobjects(function)

+

+        self.set_camera_orientation(phi=60*DEGREES, theta = 45*DEGREES)

+

+        self.add(axes)

+

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(np.array([0,0,3.7]))

+

+        self.add_fixed_orientation_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1])

+

+

+        dot1 = Dot().rotate(PI/2).set_color(RED_C)

+        alpha1 = ValueTracker(0)

+        vector1 = self.get_vector(alpha1.get_value(),helix1)

+        dot1.add_updater(lambda m: m.move_to(vector1.get_end()))

+        self.play(

+            ShowCreation(helix1),

+            GrowFromCenter(dot1),

+            GrowArrow(vector1)

+            )

+        vector1.add_updater(

+            lambda m: m.become(

+                    self.get_vector(alpha1.get_value()%1,helix1)

+                )

+            )

+        self.add(vector1,dot1)

+        self.play(alpha1.increment_value, 1, run_time=10, rate_func=linear)

+        

+

+        self.play(FadeOut(vector1), FadeOut(dot1))

+        self.play(ReplacementTransform(helix1, helix2))

+

+

+        dot2 = Dot().rotate(PI/2).set_color(RED_C)

+        alpha2 = ValueTracker(0)

+        vector2 = self.get_vector(alpha2.get_value(),helix2)

+        dot2.add_updater(lambda m: m.move_to(vector2.get_end()))

+        self.play(

+            ShowCreation(helix2),

+            GrowFromCenter(dot2),

+            GrowArrow(vector2)

+            )

+        vector2.add_updater(

+            lambda m: m.become(

+                    self.get_vector(alpha2.get_value()%1,helix2)

+                )

+            )

+        self.add(vector2,dot2)

+        self.play(alpha2.increment_value, 1, run_time=10, rate_func=linear)

+        self.wait()

+

+

+

+    def get_vector(self, proportion, curve):

+        vector = Line(np.array([0,0,0]), curve.point_from_proportion(proportion), color = YELLOW_C, buff=0)

+        return vector
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_derivative_vectorvf.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file6_derivative_vectorvf.py
index 466e389..466e389 100644
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file5_derivative_vectorvf.py
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/file6_derivative_vectorvf.py
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivar_func_examples.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivar_func_examples.gif
new file mode 100644
index 0000000..43c3a42
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivar_func_examples.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivariable_func_respresentation.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivariable_func_respresentation.gif
deleted file mode 100644
index a173bda..0000000
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file1_multivariable_func_respresentation.gif
+++ /dev/null
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_examples.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_examples.gif
deleted file mode 100644
index 11f66f1..0000000
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_examples.gif
+++ /dev/null
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_respresentation.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_respresentation.gif
new file mode 100644
index 0000000..40add0f
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file2_multivariable_func_respresentation.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_plot_sphere.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_plot_sphere.gif
deleted file mode 100644
index ad7582c..0000000
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_plot_sphere.gif
+++ /dev/null
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_sphere.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_sphere.gif
new file mode 100644
index 0000000..3e35ec8
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file3_sphere.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file5_vectorvf_helix.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file5_vectorvf_helix.gif
new file mode 100644
index 0000000..c3d37f6
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file5_vectorvf_helix.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file5_derivative_vectorvf.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file6_derivative_vectorvf.gif
index a94de90..a94de90 100644
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file5_derivative_vectorvf.gif
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-functions/gifs/file6_derivative_vectorvf.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/Limits_and_Continuity_of_Multivariable_Function_Quiz.pdf b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/Limits_and_Continuity_of_Multivariable_Function_Quiz.pdf
index 99918e5..99918e5 100644
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/Limits_and_Continuity_of_Multivariable_Function_Quiz.pdf
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/Limits_and_Continuity_of_Multivariable_Function_Quiz.pdf
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file1_epsilon_delta_defn.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file1_epsilon_delta_defn.py
new file mode 100644
index 0000000..803c122
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file1_epsilon_delta_defn.py
@@ -0,0 +1,179 @@
+from manimlib.imports import *

+

+class EpsilonDelta(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() # creates a 3D Axis

+        

+

+        sphere = ParametricSurface(

+            lambda u, v: np.array([

+                3*np.sin(u)*np.cos(v),

+                3*np.sin(u)*np.sin(v),

+                3*np.cos(u)

+            ]),u_min=0,u_max=PI/4,v_min=PI/2,v_max=PI,checkerboard_colors=[RED_D, RED_E],

+            resolution=(15, 32)).scale(1)

+        

+

+        cylinder_z = ParametricSurface(

+            lambda u, v: np.array([

+                0.25*np.cos(TAU * v),

+                1.8* (1 - u),

+                0.25*np.sin(TAU * v)

+                

+            ]),

+            checkerboard_colors=[YELLOW_C, YELLOW_E], resolution=(6, 32)).fade(0.2).rotate(PI/4).move_to(np.array([-0.65,0.65,2.54]))

+

+

+        cylinder_x = ParametricSurface(

+            lambda u, v: np.array([

+                0.3*np.cos(TAU * v)-1,

+                0.3*np.sin(TAU * v)+1,

+                2.6*(1 - u)

+            ]),

+            checkerboard_colors=[BLUE_C, BLUE_E], resolution=(6, 32)).fade(0.2)

+        

+

+        delta_circle = Circle(radius= 0.3, color = BLACK).shift(1*LEFT+1*UP).set_fill(GREEN_E, opacity = 0.5)

+

+        epsilon_circle = [np.array([0.25*np.cos(i*DEGREES),0,0.25*np.sin(i*DEGREES)]) for i in range(361)]

+

+        epsilon_circle_polygon = Polygon(*epsilon_circle, color = RED_E, fill_color = RED_E, fill_opacity = 0.5).rotate(PI/4).move_to(np.array([0,0,2.54]))

+

+

+        dot_circle = Dot().move_to(np.array([-1,1,0])).set_fill("#000080")

+        

+        dot_surface = Dot().rotate(-PI/4).scale(1.5).move_to(np.array([-1.2,1.2,2.7])).set_fill("#000080")

+

+        dot_L_epsilon1 = Polygon(*[np.array([0.05*np.cos(i*DEGREES),0,0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#000080", fill_color = "#000080", fill_opacity = 1).rotate(PI/4).move_to(np.array([0,0,2.3]))

+

+        dot_L_epsilon2 = Polygon(*[np.array([0.05*np.cos(i*DEGREES),0,0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#000080", fill_color = "#000080", fill_opacity = 1).rotate(PI/4).move_to(np.array([0,0,2.8]))

+        

+        dot_L = Polygon(*[np.array([0.05*np.cos(i*DEGREES),0,0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#006400", fill_color = "#006400", fill_opacity = 1).rotate(PI/4).move_to(np.array([0,0,2.54]))

+

+        

+    

+        self.add(axes)

+

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(np.array([0,0,3.7]))

+

+        self.add_fixed_orientation_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1]) 

+

+        self.set_camera_orientation(phi=75*DEGREES,theta=135*DEGREES)

+        #self.set_camera_orientation(phi=80*DEGREES,theta=45*DEGREES)

+

+

+        self.play(ShowCreation(sphere),ShowCreation(delta_circle), ShowCreation(dot_circle)) 

+

+        temp_circle_center = TextMobject(r"$(a,b,0)$").scale(0.6).set_color(BLUE_C).move_to(1.7*LEFT+1.1*UP)

+        self.add_fixed_orientation_mobjects(temp_circle_center)

+        self.wait()

+

+        delta_lab = TextMobject(r"$\delta$", r"$-$", "disk").scale(0.5).move_to(0.6*LEFT+1.7*UP)

+        delta_lab[0].set_color(PINK).scale(1.3)

+        delta_lab[1].set_color(ORANGE)

+        delta_lab[2].set_color(GREEN_E)

+

+        self.add_fixed_orientation_mobjects(delta_lab)

+

+        self.play(ShowCreation(dot_surface))

+

+        temp_curve_circle_center = TextMobject(r"$(a,b,L)$").scale(0.6).set_color("#006400").move_to(np.array([-2,1,2.7]))

+        self.add_fixed_orientation_mobjects(temp_curve_circle_center)

+

+

+        self.wait()

+        self.play(ShowCreation(cylinder_x), FadeOut(dot_surface))

+        self.wait()

+        

+        self.move_camera(phi=0* DEGREES,theta=135*DEGREES)

+        self.wait()

+

+        self.move_camera(phi=80* DEGREES,theta=225*DEGREES)

+        self.wait()

+        

+        self.play(FadeOut(delta_lab), ShowCreation(cylinder_z))

+        self.wait()

+

+        self.play(FadeOut(temp_circle_center), FadeOut(temp_curve_circle_center),ShowCreation(epsilon_circle_polygon))

+

+        self.move_camera(phi=80* DEGREES,theta=325*DEGREES)

+

+        dot_L_epsilon1_lab = TextMobject(r"$L$", r"$-$", r"$\epsilon$").scale(0.6).move_to(np.array([-0.4,-0.4,2.3]))

+        dot_L_epsilon1_lab[0].set_color("#D4108A")

+        dot_L_epsilon1_lab[1].set_color("#006400")

+        dot_L_epsilon1_lab[2].set_color("#4DC8A1").scale(1.5)

+

+        dot_L_epsilon2_lab = TextMobject(r"$L$", r"$+$", r"$\epsilon$").scale(0.6).move_to(np.array([-0.4,-0.4,2.8]))

+        dot_L_epsilon2_lab[0].set_color("#D4108A")

+        dot_L_epsilon2_lab[1].set_color("#006400")

+        dot_L_epsilon2_lab[2].set_color("#4DC8A1").scale(1.5)

+        

+        dot_L_lab = TextMobject(r"$L$").scale(0.6).set_color("#D4108A").move_to(np.array([-0.4,-0.4,2.54]))

+

+

+        self.play(ShowCreation(dot_L_epsilon1), ShowCreation(dot_L), ShowCreation(dot_L_epsilon2))

+        self.add_fixed_orientation_mobjects(dot_L_epsilon1_lab, dot_L_epsilon2_lab, dot_L_lab)

+        self.wait(4)

+

+        self.move_camera(phi=80* DEGREES,theta=45*DEGREES)

+        self.wait(2)

+

+

+        

+

+        

+

+        

+

+        

+        

+

+        

+        

+

+        '''

+        

+

+

+        

+        

+

+

+

+

+        

+

+        delta_lab = TextMobject(r"$\delta - disk$")

+        delta_lab.scale(0.5)

+        delta_lab.set_color(PINK)   

+

+        self.play(ShowCreation(circle_center))

+        self.add_fixed_in_frame_mobjects(temp_circle_center)

+        temp_circle_center.move_to(1.5*RIGHT)

+        self.play(Write(temp_circle_center))

+

+        self.play(ShowCreation(curve_circle_center))

+        self.add_fixed_in_frame_mobjects(temp_curve_circle_center)

+        temp_curve_circle_center.move_to(1.9*UP+1*RIGHT)

+        self.play(Write(temp_curve_circle_center))

+

+

+        self.add_fixed_in_frame_mobjects(delta_lab)

+        delta_lab.move_to(0.4*DOWN+1.7*RIGHT)

+        self.play(Write(delta_lab))

+

+

+

+

+

+        self.begin_ambient_camera_rotation(rate=0.2)

+        

+        self.play(ShowCreation(circle), ShowCreation(line1), ShowCreation(line2))

+        self.play(ShowCreation(line3), ShowCreation(line4))

+        self.wait(8)

+        '''
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file2_limit_approach_point.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file2_limit_approach_point.py
index 57d1d45..57d1d45 100644
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/file2_limit_approach_point.py
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file2_limit_approach_point.py
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file3_limit_approach_point_3d.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file3_limit_approach_point_3d.py
new file mode 100644
index 0000000..f1007a4
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file3_limit_approach_point_3d.py
@@ -0,0 +1,152 @@
+from manimlib.imports import *

+

+class Limit(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() 

+        

+        text3d = TextMobject(r"$f(x,y) = \frac{x - y}{x - 1}$")

+        self.add_fixed_in_frame_mobjects(text3d)

+       

+        text3d.to_corner(UL)

+      

+        text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

+

+        self.play(Write(text3d))

+        self.wait(1)

+        

+        limit_func = ParametricSurface(

+            lambda u, v: np.array([

+                3*np.sin(u)*np.cos(v),

+                3*np.sin(u)*np.sin(v),

+                (3*np.sin(u)*np.cos(v) - 3*np.sin(u)*np.sin(v))/2*(3*np.sin(u)*np.cos(v) - 1)

+            ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1,

+            resolution=(15, 32)).scale(1)

+

+        limit_y_x =ParametricFunction(

+                lambda u : np.array([

+                u,

+                u,

+                0

+            ]),color=GREEN_D,t_min=-3,t_max=3,

+            )

+

+        limit_y_1 =ParametricFunction(

+                lambda u : np.array([

+                u,

+                1,

+                1/2

+            ]),color=BLUE_D,t_min=-3,t_max=3,

+            )

+

+        limit_y_x_2 =ParametricFunction(

+                lambda u : np.array([

+                u,

+                u*u,

+                (u - u*u)/2*(u - 1)

+            ]),color=RED_D,t_min=-3,t_max=3,

+            )

+

+        limit_y_2_x =ParametricFunction(

+                lambda u : np.array([

+                u,

+                2 - u,

+                1

+            ]),color=YELLOW_D,t_min=-3,t_max=3,

+            )

+

+        plane_y_x = Polygon(np.array([-3,-3,-3]),np.array([3,3,-3]),np.array([3,3,3]),np.array([-3,-3,3]),np.array([-3,-3,-3]), color = GREEN_C, fill_color = GREEN_C, fill_opacity = 0.1)

+        plane_y_x_text = TextMobject(r"$y = x$", color = GREEN_C).move_to(np.array([5,0,3]))

+

+        plane_y_1 = Polygon(np.array([-3,1,-3]),np.array([3,1,-3]),np.array([3,1,3]),np.array([-3,1,3]),np.array([-3,1,-3]), color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1)

+        plane_y_1_text = TextMobject(r"$y = 1$", color = BLUE_C).move_to(np.array([5,0,2.5]))

+

+

+        #Creating plane y = x^2

+        ######

+        y_x_2 = []

+        y_x_2.append(np.array([2, 4, -3])) 

+        y_x_2.append(np.array([2, 4, 3])) 

+        y_x_2_1 = [np.array([i, i*i, 3]) for i in np.arange(1.9,-2.1, -0.1)]

+        

+        y_x_2 = y_x_2 + y_x_2_1

+

+        y_x_2.append(np.array([-2, 4, 3]))

+        y_x_2.append(np.array([-2, 4, -3])) 

+

+        y_x_2_2 = [np.array([i, i*i, -3]) for i in np.arange(-2,2.1, 0.1)]

+        

+        y_x_2 = y_x_2 + y_x_2_2

+        #y_x_2.append(np.array([-3, 9, 0]))

+

+        plane_y_x_2 = Polygon(*y_x_2, color = RED_C, fill_color = RED_C, fill_opacity = 0.1)

+        plane_y_x_2_text = TextMobject(r"$y = x^2$", color = RED_C).move_to(np.array([5,0,2]))

+

+        ######

+

+        plane_y_2_x = Polygon(np.array([-3,5,-3]),np.array([3,-1,-3]),np.array([3,-1,3]),np.array([-3,5,3]),np.array([-3,5,-3]), color = YELLOW_C, fill_color = YELLOW_C, fill_opacity = 0.1)

+        plane_y_2_x_text = TextMobject(r"$y = 2 - x$", color = YELLOW_C).move_to(np.array([5,0,1.5]))

+

+        line_1_1 = Line(np.array([1,1,-3]), np.array([1,1,3]), color = PINK)

+

+        point = Polygon(*[np.array([0.05*np.cos(i*DEGREES),0,0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#000080", fill_color = "#000080", fill_opacity = 1).move_to(np.array([1,1,0]))

+        point_text = TextMobject(r"$(1,1,0)$", color = WHITE).scale(0.7).move_to(np.array([1.8,1,0]))

+

+

+

+

+        self.set_camera_orientation(phi=70 * DEGREES, theta = -95*DEGREES)

+        

+

+        self.add(axes)

+        

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(3.7*UP)

+

+        self.add_fixed_in_frame_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1])

+

+        self.play(ShowCreation(limit_func))

+        self.wait(2)

+

+        self.play(ShowCreation(plane_y_x))

+        self.add_fixed_orientation_mobjects(plane_y_x_text)

+        self.play(ShowCreation(limit_y_x))

+        self.wait()

+ 

+        self.play(ShowCreation(plane_y_1))

+        self.add_fixed_orientation_mobjects(plane_y_1_text)

+        self.play(ShowCreation(limit_y_1))

+        self.wait()

+        

+        self.play(ShowCreation(plane_y_x_2))

+        self.add_fixed_orientation_mobjects(plane_y_x_2_text)

+        self.play(ShowCreation(limit_y_x_2))

+        self.wait()

+       

+        self.play(ShowCreation(plane_y_2_x))

+        self.add_fixed_orientation_mobjects(plane_y_2_x_text)

+        self.play(ShowCreation(limit_y_2_x))

+        self.wait()

+

+        self.play(ShowCreation(line_1_1))

+        self.wait()

+

+        self.play(ShowCreation(point))

+        self.add_fixed_orientation_mobjects(point_text)

+        self.wait()

+

+        self.play(FadeOut(plane_y_x_text), FadeOut(plane_y_1_text), FadeOut(plane_y_x_2_text), FadeOut(plane_y_2_x_text))

+

+        self.move_camera(phi=0* DEGREES,theta=-95*DEGREES)

+        self.wait(2)

+        self.play(FadeOut(plane_y_x), FadeOut(plane_y_1), FadeOut(plane_y_x_2), FadeOut(plane_y_2_x))

+        self.wait(3)

+

+        self.move_camera(phi=75* DEGREES,theta=-95*DEGREES)

+        self.wait(3)

+

+

+    
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file4_limit_different_point.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file4_limit_different_point.py
new file mode 100644
index 0000000..0a43def
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file4_limit_different_point.py
@@ -0,0 +1,115 @@
+from manimlib.imports import *

+

+class DifferentPoint(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() 

+        

+        text3d = TextMobject(r"$f(x,y) = \frac{x^2 - y^2}{x^2 + y^2}$")

+        self.add_fixed_in_frame_mobjects(text3d)

+       

+        text3d.to_corner(UL)

+      

+        text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

+

+        self.play(Write(text3d))

+        self.wait(1)

+        

+        limit_func = ParametricSurface(

+            lambda u, v: np.array([

+                3*np.sin(u)*np.cos(v),

+                3*np.sin(u)*np.sin(v),

+                (np.cos(v)*np.cos(v) - np.sin(v)*np.sin(v))

+            ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E],

+            resolution=(15, 32)).scale(1)

+

+        limit_func_copy1 = limit_func.copy()

+        limit_func_copy2 = limit_func.copy()

+

+        limit_func_x = ParametricSurface(

+            lambda u, v: np.array([

+                3*np.sin(u)*np.cos(v),

+                3*np.sin(u)*np.sin(v),

+                (np.cos(v)*np.cos(v) - np.sin(v)*np.sin(v))

+            ]),u_min=0,u_max=PI,v_min=PI,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E],

+            resolution=(15, 32)).scale(1)

+

+        limit_func_y = ParametricSurface(

+            lambda u, v: np.array([

+                3*np.sin(u)*np.cos(v),

+                3*np.sin(u)*np.sin(v),

+                (np.cos(v)*np.cos(v) - np.sin(v)*np.sin(v))

+            ]),u_min=0,u_max=PI,v_min=PI/2,v_max=3*PI/2,checkerboard_colors=[YELLOW_C, YELLOW_E],

+            resolution=(15, 32)).scale(1)

+

+        limit_x =ParametricFunction(

+                lambda u : np.array([

+                u,

+                0,

+                1

+            ]),color="#006400",t_min=-3,t_max=3,

+            )

+

+        limit_y =ParametricFunction(

+                lambda u : np.array([

+                0,

+                u,

+                -1

+            ]),color="#000080",t_min=-3,t_max=3,

+            )

+

+        plane_x = Polygon(np.array([-3,0,-2]),np.array([3,0,-2]),np.array([3,0,2]),np.array([-3,0,2]),np.array([-3,0,-2]), color = GREEN, fill_color = GREEN, fill_opacity = 0.2)

+        plane_x_text = TextMobject(r"$y = 0$", color = GREEN_C).move_to(1.7*UP + 3.8*RIGHT)

+

+        plane_y = Polygon(np.array([0,-3,-2]),np.array([0,3,-2]),np.array([0,3,2]),np.array([0,-3,2]),np.array([0,-3,-2]), color = BLUE, fill_color = BLUE, fill_opacity = 0.2)

+        plane_y_text = TextMobject(r"$x = 0$", color = BLUE_C).move_to(1.7*UP + 3.8*RIGHT)

+

+        origin_x = Polygon(*[np.array([0.05*np.cos(i*DEGREES),0,0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#000080", fill_color = "#000080", fill_opacity = 1).move_to(np.array([0,0,0]))

+        origin_x_text = TextMobject(r"$(0,0,0)$", color = RED_C).scale(0.7).move_to(np.array([-0.6,0,-0.5]))

+

+        origin_y = Polygon(*[np.array([0,0.05*np.cos(i*DEGREES),0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#000080", fill_color = "#000080", fill_opacity = 1).move_to(np.array([0,0,0]))

+        origin_y_text = TextMobject(r"$(0,0,0)$", color = RED_C).scale(0.7).move_to(np.array([0,-0.6,-0.5]))

+

+        self.set_camera_orientation(phi=80 * DEGREES, theta = 0*DEGREES)

+        

+

+        self.add(axes)

+

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(3.7*UP)

+

+        self.add_fixed_in_frame_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1])

+

+        self.play(ShowCreation(limit_func))

+

+        self.move_camera(phi=80* DEGREES,theta=105*DEGREES)

+

+        self.play(ShowCreation(plane_x))

+        self.add_fixed_in_frame_mobjects(plane_x_text)

+        self.wait()

+        self.play(ReplacementTransform(limit_func, limit_func_x))

+        self.play(FadeOut(plane_x), FadeOut(plane_x_text), ShowCreation(origin_x))

+        self.add_fixed_orientation_mobjects(origin_x_text)

+        self.play(ShowCreation(limit_x))

+

+        self.move_camera(phi=80* DEGREES,theta=15*DEGREES)

+        self.wait(3)

+

+        self.play(FadeOut(origin_x), FadeOut(origin_x_text), FadeOut(limit_x), ReplacementTransform(limit_func_x, limit_func_copy1))

+        self.play(ShowCreation(plane_y))

+        self.add_fixed_in_frame_mobjects(plane_y_text)

+        self.wait()

+        self.play(ReplacementTransform(limit_func_copy1, limit_func_y))

+        self.play(FadeOut(plane_y), FadeOut(plane_y_text), ShowCreation(origin_y))

+        self.add_fixed_orientation_mobjects(origin_y_text)

+        self.play(ShowCreation(limit_y))

+

+        self.move_camera(phi=80* DEGREES,theta=75*DEGREES)

+        self.wait(3)

+

+        self.play(FadeOut(origin_y), FadeOut(origin_y_text), FadeOut(limit_y), ReplacementTransform(limit_func_y, limit_func_copy2))

+        self.wait(2)

+        
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file5_continuity_func.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file5_continuity_func.py
new file mode 100644
index 0000000..99159a4
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/file5_continuity_func.py
@@ -0,0 +1,115 @@
+from manimlib.imports import *

+

+class Continuity(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() 

+        

+        text3d = TextMobject(r"$f(x,y) = \frac{3x^2y}{x^2 + y^2}$")

+        self.add_fixed_in_frame_mobjects(text3d)

+       

+        text3d.to_corner(UL)

+      

+        text3d.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

+

+        self.play(Write(text3d))

+        self.wait(1)

+        

+

+        continuity_func = ParametricSurface(

+            lambda u, v: np.array([

+                3*np.sin(u)*np.cos(v),

+                3*np.sin(u)*np.sin(v),

+                9*np.sin(u)*np.cos(v)*np.cos(v)*np.sin(v)

+            ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E],

+            resolution=(15, 32)).scale(1)

+

+        continuity_func_copy1 = continuity_func.copy()

+        continuity_func_copy2 = continuity_func.copy()

+

+        continuity_func_x = ParametricSurface(

+            lambda u, v: np.array([

+                3*np.sin(u)*np.cos(v),

+                3*np.sin(u)*np.sin(v),

+                9*np.sin(u)*np.cos(v)*np.cos(v)*np.sin(v)

+            ]),u_min=0,u_max=PI,v_min=PI,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E],

+            resolution=(15, 32)).scale(1)

+

+        continuity_func_y = ParametricSurface(

+            lambda u, v: np.array([

+                3*np.sin(u)*np.cos(v),

+                3*np.sin(u)*np.sin(v),

+                9*np.sin(u)*np.cos(v)*np.cos(v)*np.sin(v)

+            ]),u_min=0,u_max=PI,v_min=PI/2,v_max=3*PI/2,checkerboard_colors=[YELLOW_C, YELLOW_E],

+            resolution=(15, 32)).scale(1)

+

+        continuity_x =ParametricFunction(

+                lambda u : np.array([

+                u,

+                0,

+                0

+            ]),color="#006400",t_min=-3,t_max=3,

+            )

+

+        continuity_y =ParametricFunction(

+                lambda u : np.array([

+                0,

+                u,

+                0

+            ]),color="#000080",t_min=-3,t_max=3,

+            )

+    

+        plane_x = Polygon(np.array([-3,0,-3]),np.array([3,0,-3]),np.array([3,0,3]),np.array([-3,0,3]),np.array([-3,0,-3]), color = GREEN, fill_color = GREEN, fill_opacity = 0.2)

+        plane_x_text = TextMobject(r"$y = 0$", color = GREEN_C).move_to(1.7*UP + 3.8*RIGHT)

+

+        plane_y = Polygon(np.array([0,-3,-3]),np.array([0,3,-3]),np.array([0,3,3]),np.array([0,-3,3]),np.array([0,-3,-3]), color = BLUE, fill_color = BLUE, fill_opacity = 0.2)

+        plane_y_text = TextMobject(r"$x = 0$", color = BLUE_C).move_to(1.7*UP + 3.8*RIGHT)

+

+        origin_x = Polygon(*[np.array([0.05*np.cos(i*DEGREES),0,0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#000080", fill_color = "#000080", fill_opacity = 1).move_to(np.array([0,0,0]))

+        origin_x_text = TextMobject(r"$(0,0,0)$", color = RED_C).scale(0.7).move_to(np.array([-0.6,0,-0.5]))

+

+        origin_y = Polygon(*[np.array([0,0.05*np.cos(i*DEGREES),0.05*np.sin(i*DEGREES)]) for i in range(361)], color = "#006400", fill_color = "#006400", fill_opacity = 1).move_to(np.array([0,0,0]))

+        origin_y_text = TextMobject(r"$(0,0,0)$", color = RED_C).scale(0.7).move_to(np.array([0,-0.6,-0.5]))

+

+        self.set_camera_orientation(phi=80 * DEGREES, theta = 0*DEGREES)

+        

+

+        self.add(axes)

+

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(3.7*UP)

+

+        self.add_fixed_in_frame_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1])

+

+        self.play(ShowCreation(continuity_func))

+

+        self.move_camera(phi=80* DEGREES,theta=105*DEGREES)

+

+        self.play(ShowCreation(plane_x))

+        self.add_fixed_in_frame_mobjects(plane_x_text)

+        self.wait()

+        self.play(ReplacementTransform(continuity_func, continuity_func_x))

+        self.play(FadeOut(plane_x), FadeOut(plane_x_text))

+        self.play(ShowCreation(continuity_x), ShowCreation(origin_x))

+        self.add_fixed_orientation_mobjects(origin_x_text)

+

+        self.move_camera(phi=80* DEGREES,theta=15*DEGREES)

+        self.wait(3)

+

+        self.play(FadeOut(origin_x), FadeOut(origin_x_text), FadeOut(continuity_x), ReplacementTransform(continuity_func_x, continuity_func_copy1))

+        self.play(ShowCreation(plane_y))

+        self.add_fixed_in_frame_mobjects(plane_y_text)

+        self.wait()

+        self.play(ReplacementTransform(continuity_func_copy1, continuity_func_y))

+        self.play(FadeOut(plane_y), FadeOut(plane_y_text))

+        self.play(ShowCreation(continuity_y), ShowCreation(origin_y))

+        self.add_fixed_orientation_mobjects(origin_y_text)

+

+        self.move_camera(phi=80* DEGREES,theta=75*DEGREES)

+        self.wait(3)

+

+        self.play(FadeOut(origin_y), FadeOut(origin_y_text), FadeOut(continuity_y), ReplacementTransform(continuity_func_y, continuity_func_copy2))

+        self.wait(2)
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file1_epsilon_delta_defn.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file1_epsilon_delta_defn.gif
new file mode 100644
index 0000000..2378bcf
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file1_epsilon_delta_defn.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file2_limit_approach_point.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file2_limit_approach_point.gif
index 830b6f1..830b6f1 100644
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/limits-and-continuity-of-multivariable-functions/gifs/file2_limit_approach_point.gif
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file2_limit_approach_point.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file3_limit_approach_point_3d.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file3_limit_approach_point_3d.gif
new file mode 100644
index 0000000..4bccf8c
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file3_limit_approach_point_3d.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file4_limit_different_point.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file4_limit_different_point.gif
new file mode 100644
index 0000000..9a831e4
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file4_limit_different_point.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file5_continuity_func.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file5_continuity_func.gif
new file mode 100644
index 0000000..2a0a61f
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/multivariable-limits-and-continuity/gifs/file5_continuity_func.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file1_partial_deriv_gas_law.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file1_partial_deriv_gas_law.py
new file mode 100644
index 0000000..3d35c97
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file1_partial_deriv_gas_law.py
@@ -0,0 +1,88 @@
+from manimlib.imports import *

+

+class GasLaw(Scene):

+    def construct(self):

+        gas_law = TextMobject(r"$P$", r"$V$", r"=", r"$n$", r"$R$", r"$T$").scale(1.5)

+        gas_law[0].set_color(BLUE_C)

+        gas_law[1].set_color(GREEN_C)

+        gas_law[3].set_color(RED_C)

+        gas_law[4].set_color(ORANGE)

+        gas_law[5].set_color(YELLOW_C)

+

+        gas_law_trans = TexMobject("V", "=", "{n", "R", "T", "\\over", "P}").scale(1.5)

+        gas_law_trans[0].set_color(GREEN_C)

+        gas_law_trans[2].set_color(RED_C)

+        gas_law_trans[3].set_color(ORANGE)

+        gas_law_trans[4].set_color(YELLOW_C)

+        gas_law_trans[6].set_color(BLUE_C)

+

+        gas_law_func = TexMobject("V", "=", "f(", "n", ",", "T", ",", "P", ")").scale(1.5)

+        gas_law_func[0].set_color(GREEN_C)

+        gas_law_func[2].set_color(ORANGE)

+        gas_law_func[3].set_color(RED_C)

+        gas_law_func[5].set_color(YELLOW_C)

+        gas_law_func[7].set_color(BLUE_C)

+        gas_law_func[8].set_color(ORANGE)

+

+        partial_gas_law_func = TexMobject("{\\partial", "V","\\over", "\\partial", "P}", r"=", "{\\partial", "\\over", "\\partial", "P}", "f(", r"n", ",", r"T", ",", r"P", r")").scale(1.5)

+        partial_gas_law_func.set_color_by_tex("\\partial", PINK)

+        partial_gas_law_func.set_color_by_tex("P}", BLUE_C)

+

+        partial_gas_law_func[1].set_color(GREEN_C)

+        partial_gas_law_func[10].set_color(ORANGE)

+        partial_gas_law_func[11].set_color(RED_C)

+        partial_gas_law_func[13].set_color(YELLOW_C)

+        partial_gas_law_func[15].set_color(BLUE_C)

+        partial_gas_law_func[16].set_color(ORANGE)

+

+        partial_gas_law_trans = TexMobject("{\\partial", "V","\\over", "\\partial", "P}", r"=", "{\\partial", "\\over", "\\partial", "P}", "{n", "R", "T", "\\over", "P}").scale(1.5)

+        partial_gas_law_trans.set_color_by_tex("\\partial", PINK)

+        partial_gas_law_trans.set_color_by_tex("P}", BLUE_C)

+

+        partial_gas_law_trans[1].set_color(GREEN_C)

+        partial_gas_law_trans[10].set_color(RED_C)

+        partial_gas_law_trans[11].set_color(ORANGE)

+        partial_gas_law_trans[12].set_color(YELLOW_C)

+

+        partial_gas_law_trans2 = TexMobject("{\\partial", "V","\\over", "\\partial", "P}", r"=", "n", "R", "T", "{\\partial", "\\over", "\\partial", "P}", "P^{-1}",).scale(1.5)

+        partial_gas_law_trans2.set_color_by_tex("\\partial", PINK)

+        partial_gas_law_trans2.set_color_by_tex("P}", BLUE_C)

+

+        partial_gas_law_trans2[1].set_color(GREEN_C)

+        partial_gas_law_trans2[6].set_color(RED_C)

+        partial_gas_law_trans2[7].set_color(ORANGE)

+        partial_gas_law_trans2[8].set_color(YELLOW_C)

+        partial_gas_law_trans2[-1].set_color(BLUE_C)

+

+        partial_gas_law_trans3 = TexMobject("{\\partial", "V","\\over", "\\partial", "P}", r"=", "n", "R", "T", "P^{-2}",).scale(1.5)

+        partial_gas_law_trans3.set_color_by_tex("\\partial", PINK)

+        partial_gas_law_trans3.set_color_by_tex("P}", BLUE_C)

+

+        partial_gas_law_trans3[1].set_color(GREEN_C)

+        partial_gas_law_trans3[6].set_color(RED_C)

+        partial_gas_law_trans3[7].set_color(ORANGE)

+        partial_gas_law_trans3[8].set_color(YELLOW_C)

+        partial_gas_law_trans3[9].set_color(BLUE_C)

+

+        framebox = SurroundingRectangle(partial_gas_law_trans3, color = PURPLE, buff = 0.3)

+

+

+

+        self.play(Write(gas_law))

+        self.wait()

+        self.play(Transform(gas_law, gas_law_trans))

+        self.wait()

+        self.play(Transform(gas_law, gas_law_func))

+        self.wait()

+        self.play(Transform(gas_law, gas_law_trans))

+        self.wait()

+        self.play(Transform(gas_law, partial_gas_law_func))

+        self.wait()

+        self.play(Transform(gas_law, partial_gas_law_trans))

+        self.wait()

+        self.play(Transform(gas_law, partial_gas_law_trans2))

+        self.wait()

+        self.play(Transform(gas_law, partial_gas_law_trans3))

+        self.wait()

+        self.play(ShowCreation(framebox))

+        self.wait()
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file2_partial_deriv_hill.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file2_partial_deriv_hill.py
new file mode 100644
index 0000000..bfb7687
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file2_partial_deriv_hill.py
@@ -0,0 +1,122 @@
+from manimlib.imports import *

+

+class Hill(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() 

+

+        function = ParametricSurface(

+            lambda u, v: np.array([

+                1.2*np.sin(u)*np.cos(v),

+                1.2*np.sin(u)*np.sin(v),

+                -1.2*1.2*np.sin(u)*np.sin(u)*(1+0.5*np.sin(v)*np.sin(v))+2

+            ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[GREEN_C, GREEN_E],

+            resolution=(15, 32)).scale(1)

+

+        func_x =ParametricFunction(

+                lambda u : np.array([

+                u,

+                0,

+                2 - u*u

+            ]),color=RED_E,t_min=-1.2,t_max=1.2,

+            )

+    

+        func_y =ParametricFunction(

+                lambda u : np.array([

+                0,

+                u,

+                2 - 1.5*u*u

+            ]),color=PINK,t_min=-1.2,t_max=1.2,

+            )

+

+        self.set_camera_orientation(phi=60 * DEGREES, theta = 0*DEGREES)

+        #self.set_camera_orientation(phi=45 * DEGREES, theta = -20*DEGREES)

+

+        self.add(axes)

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(np.array([0,0,3.7]))

+

+        self.add_fixed_orientation_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1])

+

+        self.play(ShowCreation(function))

+        self.wait()

+

+        self.move_camera(phi=60 * DEGREES, theta = 45*DEGREES)

+        #self.play(ShowCreation(func_x))

+

+        text_x = TextMobject("Slope of the hill along", r"$x$", "axis", color = YELLOW_C).scale(0.6).move_to(2.7*UP + 3.5*RIGHT)

+        text_x[1].set_color(PINK)

+

+

+        slope_text_x = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "x}").scale(0.6).move_to(2*UP + 3.5*RIGHT)

+        slope_text_x[0].set_color(BLUE_E)

+        slope_text_x.set_color_by_tex("\\partial",YELLOW_C)

+        slope_text_x.set_color_by_tex("f",RED_E)

+        slope_text_x[5].set_color(PINK)

+

+        self.add_fixed_in_frame_mobjects(text_x, slope_text_x)

+

+        dot_x = Dot().rotate(PI/2).set_color(YELLOW_E)

+        alpha_x = ValueTracker(0)

+        vector_x = self.get_tangent_vector(alpha_x.get_value(),func_x,scale=1.5)

+        dot_x.add_updater(lambda m: m.move_to(vector_x.get_center()))

+        self.play(

+            ShowCreation(func_x),

+            GrowFromCenter(dot_x),

+            GrowArrow(vector_x)

+            )

+        vector_x.add_updater(

+            lambda m: m.become(

+                    self.get_tangent_vector(alpha_x.get_value()%1,func_x,scale=1.5)

+                )

+            )

+        

+        self.add(vector_x,dot_x)

+        

+        self.play(alpha_x.increment_value, 1, run_time=10, rate_func=linear)

+

+        #self.move_camera(phi=60 * DEGREES, theta = 0*DEGREES)

+        self.play(FadeOut(vector_x), FadeOut(dot_x), FadeOut(func_x), FadeOut(text_x), FadeOut(slope_text_x))

+

+        text_y = TextMobject("Slope of the hill along", r"$y$", "axis", color = YELLOW_C).scale(0.6).move_to(2.7*UP + 3.5*RIGHT)

+        text_y[1].set_color(RED_C)

+

+

+        slope_text_y = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "x}").scale(0.6).move_to(2*UP + 3.5*RIGHT)

+        slope_text_y[0].set_color(BLUE_E)

+        slope_text_y.set_color_by_tex("\\partial",YELLOW_C)

+        slope_text_y.set_color_by_tex("f",PINK)

+        slope_text_y[5].set_color(RED_C)

+

+        self.add_fixed_in_frame_mobjects(text_y, slope_text_y)

+

+        dot_y = Dot().rotate(PI/2).set_color(BLUE_E)

+        alpha_y = ValueTracker(0)

+        vector_y = self.get_tangent_vector(alpha_y.get_value(),func_y,scale=1.5)

+        dot_y.add_updater(lambda m: m.move_to(vector_y.get_center()))

+        self.play(

+            ShowCreation(func_y),

+            GrowFromCenter(dot_y),

+            GrowArrow(vector_y)

+            )

+        vector_y.add_updater(

+            lambda m: m.become(

+                    self.get_tangent_vector(alpha_y.get_value()%1,func_y,scale=1.5)

+                )

+            )

+

+        self.add(vector_y,dot_y)

+        self.play(alpha_y.increment_value, 1, run_time=10, rate_func=linear)

+        self.play(FadeOut(vector_y), FadeOut(dot_y), FadeOut(func_y), FadeOut(text_y), FadeOut(slope_text_y))

+        self.wait(2)

+

+    def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1):

+        coord_i = curve.point_from_proportion(proportion)

+        coord_f = curve.point_from_proportion(proportion + dx)

+        reference_line = Line(coord_i,coord_f)

+        unit_vector = reference_line.get_unit_vector() * scale

+        vector = Line(coord_i - unit_vector, coord_i + unit_vector, color = ORANGE, buff=0)

+        return vector       
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file3_partial_deriv_defn.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file3_partial_deriv_defn.py
new file mode 100644
index 0000000..a25ca56
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file3_partial_deriv_defn.py
@@ -0,0 +1,218 @@
+from manimlib.imports import *

+

+class PartialDeriv(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() 

+

+        paraboloid = ParametricSurface(

+            lambda u, v: np.array([

+                2*np.sin(u)*np.cos(v),

+                2*np.sin(u)*np.sin(v),

+                -2*2*np.sin(u)*np.sin(u)+2

+            ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[PINK, PURPLE],

+            resolution=(15, 32)).scale(1)

+

+        paraboloid_copy1 = paraboloid.copy()

+        paraboloid_copy2 = paraboloid.copy()

+

+        paraboloid_x = ParametricSurface(

+            lambda u, v: np.array([

+                2*np.sin(u)*np.cos(v),

+                2*np.sin(u)*np.sin(v),

+                -2*2*np.sin(u)*np.sin(u)+2

+            ]),u_min=0,u_max=PI/2,v_min=PI,v_max=2*PI,checkerboard_colors=[PINK, PURPLE],

+            resolution=(15, 32)).scale(1)

+

+        paraboloid_x_copy = paraboloid_x.copy()

+

+        paraboloid_y = ParametricSurface(

+            lambda u, v: np.array([

+                2*np.sin(u)*np.cos(v),

+                2*np.sin(u)*np.sin(v),

+                -2*2*np.sin(u)*np.sin(u)+2

+            ]),u_min=0,u_max=PI/2,v_min=PI/2,v_max=3*PI/2,checkerboard_colors=[PINK, PURPLE],

+            resolution=(15, 32)).scale(1)

+

+        parabola1 =ParametricFunction(

+                lambda u : np.array([

+                u,

+                0,

+                -(u*u) + 2

+            ]),color="#006400",t_min=-2,t_max=2,

+            )

+        parabola2 =ParametricFunction(

+                lambda u : np.array([

+                0,

+                u,

+                -(u*u) + 2

+            ]),color=BLUE_C,t_min=-2,t_max=2,

+            )

+

+        plane1 = Polygon(np.array([-2.2,0,-2.5]),np.array([2.2,0,-2.5]),np.array([2.2,0,2.5]),np.array([-2.2,0,2.5]),np.array([-2.2,0,-2.5]), color = GREEN, fill_color = GREEN, fill_opacity = 0.2)

+        plane1_text = TextMobject(r"$y = 0$", color = GREEN_C).move_to(2*UP + 3.3*RIGHT)

+

+        plane2 = Polygon(np.array([0,-2.2,-2.5]),np.array([0,2.2,-2.5]),np.array([0,2.2,2.5]),np.array([0,-2.2,2.5]),np.array([0,-2.2,-2.5]), color = BLUE, fill_color = BLUE, fill_opacity = 0.2)

+        plane2_text = TextMobject(r"$x = 0$", color = BLUE_C).move_to(2*UP + 3.2*RIGHT)

+

+        surface_eqn = TextMobject("Surface", r"$z = 2- x^2 -y^2$", color = YELLOW_C).scale(0.6).move_to(np.array([3*LEFT +3*UP]))

+        surface_eqn[0].set_color(PINK)

+

+        dot1 =Sphere(radius=0.08).move_to(np.array([-1,0,1]))

+        dot1.set_fill(RED)

+        line1 = Line(np.array([-1.55, 0,0]), np.array([-0.4, 0,2.2]), color = RED)

+        lab_x = TextMobject(r"$f(x_0,y_0)$", color = RED).scale(0.7)

+        para_lab_x = TextMobject(r"$f(x,y_0)$", color = "#006400").scale(0.7)

+        tangent_line_x = TextMobject("Tangent Line", color = RED_C, buff = 0.4).scale(0.6).move_to(np.array([1.7*RIGHT +1.8*UP]))

+

+

+        text1 = TextMobject(r"$\frac{\partial f}{\partial x}\vert_{(x_0,y_0)} = \frac{d}{dx}$", r"$f(x,y_0)$", r"$\vert_{x=x_0}$").scale(0.6)

+        brace1 = Brace(text1[1], DOWN, buff = SMALL_BUFF, color = GREEN)

+        t1 = brace1.get_text("Just depends on x")

+        t1.scale(0.6)

+        t1.set_color(GREEN)

+        

+

+        dot2 =Sphere(radius=0.08).move_to(np.array([0,1,1]))

+        dot2.set_fill(RED)

+        line2 = Line(np.array([0, 1.55,0]), np.array([0, 0.4,2.2]), color = RED)

+        lab_y = TextMobject(r"$f(x_0,y_0)$", color = RED).scale(0.7)

+        para_lab_y = TextMobject(r"$f(x_0,y)$", color = BLUE_C).scale(0.7)

+        tangent_line_y = TextMobject("Tangent Line", color = RED_C, buff = 0.4).scale(0.6).move_to(np.array([1.7*RIGHT +1.8*UP]))

+

+        text2 = TextMobject(r"$\frac{\partial f}{\partial y}\vert_{(x_0,y_0)} = \frac{d}{dy}$", r"$f(x_0,y)$", r"$\vert_{y=y_0}$").scale(0.6)

+        brace2 = Brace(text2[1], DOWN, buff = SMALL_BUFF, color = GREEN)

+        t2 = brace2.get_text("Just depends on y")

+        t2.scale(0.6)

+        t2.set_color(GREEN)

+

+        text3 = TextMobject(r"$= \lim_{h \to 0} \frac{f(x_0+h,y_0) - f(x_0,y_0)}{h}$").scale(0.6)

+

+        dot3 =Sphere(radius=0.08).move_to(np.array([-1.22,0,0.5]))

+        dot3.set_fill(YELLOW_C)

+        line3 = Line(np.array([-1.44,0,0]), np.array([-0.6,0,2.2]), color = YELLOW_C)

+        lab_line3 = TextMobject(r"$f(x_0+h,y_0)$", color = YELLOW_C).scale(0.7)

+        

+

+        self.set_camera_orientation(phi=80 * DEGREES, theta = 0*DEGREES)

+        #self.set_camera_orientation(phi=80 * DEGREES, theta = 20*DEGREES)

+        #self.begin_ambient_camera_rotation(rate=0.3)

+

+

+        self.add(axes)

+

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(3.7*UP)

+

+        self.add_fixed_in_frame_mobjects(axis[2])

+        #self.add_fixed_orientation_mobjects(axis[2])

+        

+        self.play(Write(paraboloid))

+

+        self.add_fixed_in_frame_mobjects(surface_eqn)

+        #self.move_camera(phi=80* DEGREES,theta=110*DEGREES)

+        self.move_camera(phi=80* DEGREES,theta=45*DEGREES)

+        

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1])

+        self.play(ShowCreation(plane1))

+        self.add_fixed_in_frame_mobjects(plane1_text)

+        self.wait()

+        self.play(ReplacementTransform(paraboloid, paraboloid_x))

+

+        lab_x.move_to(np.array([1.8*RIGHT +1.15*UP]))

+        para_lab_x.move_to(np.array([1.3*LEFT +1.6*UP]))

+        self.wait()

+        self.play(FadeOut(plane1), FadeOut(plane1_text))

+        self.play(ShowCreation(parabola1))

+        self.add_fixed_in_frame_mobjects(para_lab_x)

+        self.play(ShowCreation(dot1))

+        self.add_fixed_in_frame_mobjects(lab_x)

+        #self.play(ShowCreation(dot1))

+        self.wait()

+        self.play(ShowCreation(line1))

+        self.add_fixed_in_frame_mobjects(tangent_line_x)

+        self.wait()

+   

+        self.add_fixed_in_frame_mobjects(text1, brace1, t1)

+        grp1 = VGroup(text1, brace1, t1)

+        grp1.move_to(3*UP+3*RIGHT)

+        self.play(Write(text1),GrowFromCenter(brace1), FadeIn(t1))

+        self.wait()

+        self.play(FadeOut(parabola1), FadeOut(line1), FadeOut(lab_x), FadeOut(para_lab_x), FadeOut(dot1), FadeOut(tangent_line_x),FadeOut(grp1))

+        

+        

+

+        

+        #self.move_camera(phi=80* DEGREES,theta=20*DEGREES)

+        

+        self.play(ReplacementTransform(paraboloid_x, paraboloid_copy1))

+        self.wait()

+        self.play(ShowCreation(plane2))

+        self.add_fixed_in_frame_mobjects(plane2_text)

+        self.wait()

+        self.play(ReplacementTransform(paraboloid_copy1, paraboloid_y))

+        

+        lab_y.move_to(np.array([1.8*RIGHT +1.15*UP]))

+        para_lab_y.move_to(np.array([1.3*LEFT +1.6*UP]))

+        self.wait()

+        self.play(FadeOut(plane2), FadeOut(plane2_text))

+        self.play(ShowCreation(parabola2))

+        self.add_fixed_in_frame_mobjects(para_lab_y)

+        self.play(ShowCreation(dot2))

+        self.add_fixed_in_frame_mobjects(lab_y)

+        self.wait()

+        self.play(ShowCreation(line2))

+        self.add_fixed_in_frame_mobjects(tangent_line_y)

+        self.wait()

+   

+        self.add_fixed_in_frame_mobjects(text2, brace2, t2)

+        grp2 = VGroup(text2, brace2, t2)

+        grp2.move_to(3*UP+3*RIGHT)

+        self.play(Write(text2),GrowFromCenter(brace2), FadeIn(t2))

+        self.wait()

+        self.play(FadeOut(parabola2), FadeOut(line2), FadeOut(lab_y), FadeOut(para_lab_y), FadeOut(dot2), FadeOut(tangent_line_y), FadeOut(grp2))

+        self.wait()

+

+        

+        #self.move_camera(phi=80* DEGREES,theta=105*DEGREES)

+        self.play(ReplacementTransform(paraboloid_y, paraboloid_copy2))

+        self.wait()

+

+        

+        self.play(ShowCreation(plane1))

+        self.add_fixed_in_frame_mobjects(plane1_text)

+        self.wait()

+        self.play(ReplacementTransform(paraboloid_copy2, paraboloid_x_copy))

+        

+        lab_x.move_to(np.array([1.8*RIGHT +1.15*UP]))

+        para_lab_x.move_to(np.array([1.3*LEFT +1.6*UP]))

+        lab_line3.move_to(np.array([2.4*RIGHT +0.5*UP]))

+        self.wait()

+        self.play(FadeOut(plane1), FadeOut(plane1_text))

+        self.play(ShowCreation(parabola1))

+        self.add_fixed_in_frame_mobjects(para_lab_x)

+        self.play(ShowCreation(dot1))

+        self.add_fixed_in_frame_mobjects(lab_x)

+        self.play(ShowCreation(dot3))

+        self.add_fixed_in_frame_mobjects(lab_line3)

+        self.wait()

+        self.play(ShowCreation(line1))

+        self.add_fixed_in_frame_mobjects(tangent_line_x)

+        self.play(ShowCreation(line3))

+        self.wait()

+        

+        

+        self.add_fixed_in_frame_mobjects(text1,text3)

+        text1.move_to(3*UP+3*RIGHT)

+        text3.next_to(text1, DOWN)

+        self.play(Write(text1),Write(text3))

+        self.wait()

+        self.play(FadeOut(parabola1), FadeOut(line1), FadeOut(lab_x), FadeOut(line3), FadeOut(lab_line3), FadeOut(para_lab_x), FadeOut(dot1), FadeOut(dot3), FadeOut(tangent_line_x), FadeOut(text1), FadeOut(text3))

+        self.wait()

+        

+

+

+

+

diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py
new file mode 100644
index 0000000..5712a62
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py
@@ -0,0 +1,246 @@
+from manimlib.imports import *

+

+class PartialDerivX(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() 

+

+        paraboloid = ParametricSurface(

+            lambda u, v: np.array([

+                2*np.sin(u)*np.cos(v),

+                2*np.sin(u)*np.sin(v),

+                -2*2*np.sin(u)*np.sin(u)+2

+            ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[PINK, PURPLE],

+            resolution=(15, 32)).scale(1)

+

+        paraboloid_copy = paraboloid.copy()

+

+ 

+        paraboloid_x = ParametricSurface(

+            lambda u, v: np.array([

+                2*np.sin(u)*np.cos(v),

+                2*np.sin(u)*np.sin(v),

+                -2*2*np.sin(u)*np.sin(u)+2

+            ]),u_min=0,u_max=PI/2,v_min=PI,v_max=2*PI,checkerboard_colors=[PINK, PURPLE],

+            resolution=(15, 32)).scale(1)

+

+

+        parabola =ParametricFunction(

+                lambda u : np.array([

+                u,

+                0,

+                -(u*u) + 2

+            ]),color="#006400",t_min=-2,t_max=2,

+            )

+        

+        plane = Polygon(np.array([-2.2,0,-2.5]),np.array([2.2,0,-2.5]),np.array([2.2,0,2.5]),np.array([-2.2,0,2.5]),np.array([-2.2,0,-2.5]), color = GREEN, fill_color = GREEN, fill_opacity = 0.2)

+        plane_text = TextMobject(r"$y = 0$", color = GREEN_C).move_to(2*UP + 3*RIGHT)

+

+        surface_eqn = TextMobject("Surface", r"$z = 2- x^2 -y^2$", color = PINK).scale(0.6).move_to(np.array([3*LEFT +3*UP]))

+        surface_eqn[0].set_color(BLUE_C)

+

+        line = Line(np.array([-2,0,0]), np.array([2,0,0]), color = RED_C)

+        

+ 

+        self.add(axes)

+

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(3.7*UP)

+

+        self.add_fixed_in_frame_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1])

+

+

+        self.set_camera_orientation(phi=80 * DEGREES, theta = 0*DEGREES)

+

+        self.play(Write(paraboloid))

+

+        self.add_fixed_in_frame_mobjects(surface_eqn)

+        #self.move_camera(phi=80* DEGREES,theta=95*DEGREES)

+        self.move_camera(phi=80* DEGREES,theta=45*DEGREES)

+        self.play(ShowCreation(plane))

+        self.add_fixed_in_frame_mobjects(plane_text)

+        self.wait()

+        self.play(ReplacementTransform(paraboloid, paraboloid_x))

+        self.play(FadeOut(plane), FadeOut(plane_text))

+        self.play(ShowCreation(parabola), ShowCreation(line))

+

+        text1 = TextMobject("Moving small", r"$dx$", r"steps").scale(0.6).move_to(3*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, BLUE, PURPLE)

+    

+        text2 = TextMobject("Observing change in function, keeping", r"$y$", r"constant").scale(0.6).move_to(2.6*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

+        

+        slope_text = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "x}").scale(0.6).move_to(2*UP + 3.5*RIGHT)

+        slope_text[0].set_color(BLUE_E)

+        slope_text.set_color_by_tex("\\partial",PINK)

+        slope_text.set_color_by_tex("f","#006400")

+        slope_text[5].set_color(RED_C)

+

+        self.add_fixed_in_frame_mobjects(text1, text2)

+        self.wait()

+        self.add_fixed_in_frame_mobjects(slope_text)

+        #add_fixed_orientation_mobjects

+        

+        

+        dot = Dot().rotate(PI/2).set_color(RED_C)

+        alpha = ValueTracker(0)

+        vector = self.get_tangent_vector(alpha.get_value(),parabola,scale=1.5)

+        dot.add_updater(lambda m: m.move_to(vector.get_center()))

+        self.play(

+            ShowCreation(parabola),

+            GrowFromCenter(dot),

+            GrowArrow(vector)

+            )

+        vector.add_updater(

+            lambda m: m.become(

+                    self.get_tangent_vector(alpha.get_value()%1,parabola,scale=1.5)

+                )

+            )

+        self.add(vector,dot)

+        self.play(alpha.increment_value, 1, run_time=10, rate_func=linear)

+        self.wait()

+

+

+        '''

+        for i in np.arange(-2,2,0.2):

+        	self.play(ReplacementTransform(Line(np.array([i,0,0]), np.array([i,0,-i*i + 2]), color = GREEN_C), Line(np.array([i+0.2,0,0]), np.array([i+0.2,0,-(i+0.2)**2 + 2]), color = GREEN_C)))

+            #self.wait()

+        '''

+

+        self.wait()

+        self.play(FadeOut(parabola), FadeOut(line), FadeOut(vector), FadeOut(dot), FadeOut(text1), FadeOut(text2), FadeOut(slope_text),FadeOut(surface_eqn))

+

+        #self.move_camera(phi=80* DEGREES,theta= 0*DEGREES)

+        self.play(ReplacementTransform(paraboloid_x, paraboloid_copy))

+        self.wait()

+

+

+    def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1):

+        coord_i = curve.point_from_proportion(proportion)

+        coord_f = curve.point_from_proportion(proportion + dx)

+        reference_line = Line(coord_i,coord_f)

+        unit_vector = reference_line.get_unit_vector() * scale

+        vector = Line(coord_i - unit_vector, coord_i + unit_vector, color = BLUE_E, buff=0)

+        return vector

+

+

+class PartialDerivY(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() 

+

+        paraboloid = ParametricSurface(

+            lambda u, v: np.array([

+                2*np.sin(u)*np.cos(v),

+                2*np.sin(u)*np.sin(v),

+                -2*2*np.sin(u)*np.sin(u)+2

+            ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[PINK, PURPLE],

+            resolution=(15, 32)).scale(1)

+

+        paraboloid_copy = paraboloid.copy()

+

+ 

+        paraboloid_y = ParametricSurface(

+            lambda u, v: np.array([

+                2*np.sin(u)*np.cos(v),

+                2*np.sin(u)*np.sin(v),

+                -2*2*np.sin(u)*np.sin(u)+2

+            ]),u_min=0,u_max=PI/2,v_min=PI/2,v_max=3*PI/2,checkerboard_colors=[PINK, PURPLE],

+            resolution=(15, 32)).scale(1)

+

+

+        parabola =ParametricFunction(

+                lambda u : np.array([

+                0,

+                u,

+                -(u*u) + 2

+            ]),color=YELLOW_C,t_min=-2,t_max=2,

+            )

+        

+        plane = Polygon(np.array([0,-2.2,-2.5]),np.array([0,2.2,-2.5]),np.array([0,2.2,2.5]),np.array([0,-2.2,2.5]),np.array([0,-2.2,-2.5]), color = BLUE, fill_color = BLUE, fill_opacity = 0.2)

+        plane_text = TextMobject(r"$x = 0$", color = BLUE_C).move_to(2*UP + 3*RIGHT)

+

+        surface_eqn = TextMobject("Surface", r"$z = 2- x^2 -y^2$", color = PINK).scale(0.6).move_to(np.array([3*LEFT +3*UP]))

+        surface_eqn[0].set_color(BLUE_C)

+        

+        line = Line(np.array([0,-2,0]), np.array([0,2,0]), color = RED_C)

+ 

+        self.add(axes)

+

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(3.7*UP)

+

+        self.add_fixed_in_frame_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1])

+

+        self.set_camera_orientation(phi=80 * DEGREES, theta = 45*DEGREES)

+

+        self.play(Write(paraboloid))

+

+        self.add_fixed_in_frame_mobjects(surface_eqn)

+        #self.move_camera(phi=80* DEGREES,theta=5*DEGREES)

+        self.play(ShowCreation(plane))

+        self.add_fixed_in_frame_mobjects(plane_text)

+        self.wait()

+        self.play(ReplacementTransform(paraboloid, paraboloid_y))

+        self.play(FadeOut(plane), FadeOut(plane_text))

+        self.play(ShowCreation(parabola), ShowCreation(line))

+

+        text1 = TextMobject("Moving small", r"$dy$", r"steps").scale(0.6).move_to(3*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, BLUE, PURPLE)

+        

+        text2 = TextMobject("Observing change in function, keeping", r"$x$", r"constant").scale(0.6).move_to(2.6*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

+        

+        slope_text = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "y}").scale(0.6).move_to(2*UP + 3.5*RIGHT)

+        slope_text[0].set_color("#006400")

+        slope_text.set_color_by_tex("\\partial",PINK)

+        slope_text.set_color_by_tex("f",YELLOW_C)

+        slope_text[5].set_color(RED_C)

+

+        self.add_fixed_in_frame_mobjects(text1, text2)

+        self.wait()

+        self.add_fixed_in_frame_mobjects(slope_text)

+

+        dot = Dot().rotate(PI/2).set_color(RED_C)

+        alpha = ValueTracker(0)

+        vector = self.get_tangent_vector(alpha.get_value(),parabola,scale=1.5)

+        dot.add_updater(lambda m: m.move_to(vector.get_center()))

+        self.play(

+            ShowCreation(parabola),

+            GrowFromCenter(dot),

+            GrowArrow(vector)

+            )

+        vector.add_updater(

+            lambda m: m.become(

+                    self.get_tangent_vector(alpha.get_value()%1,parabola,scale=1.5)

+                )

+            )

+        self.add(vector,dot)

+        self.play(alpha.increment_value, 1, run_time=10, rate_func=linear)

+        self.wait()

+        

+        '''

+        for i in np.arange(-2,2,0.2):

+        	self.play(ReplacementTransform(Line(np.array([0,i,0]), np.array([0,i,-i*i + 2]), color = BLUE_C), Line(np.array([0,i+0.2,0]), np.array([0,i+0.2,-(i+0.2)**2 + 2]), color = BLUE_C)))

+            #self.wait()

+        '''

+

+

+        self.wait()

+        self.play(FadeOut(parabola), FadeOut(line), FadeOut(vector), FadeOut(dot), FadeOut(text1), FadeOut(text2), FadeOut(slope_text),FadeOut(surface_eqn))

+

+        #self.move_camera(phi=80* DEGREES,theta= 90*DEGREES)

+        self.play(ReplacementTransform(paraboloid_y, paraboloid_copy))

+        self.wait()   

+

+    def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1):

+        coord_i = curve.point_from_proportion(proportion)

+        coord_f = curve.point_from_proportion(proportion + dx)

+        reference_line = Line(coord_i,coord_f)

+        unit_vector = reference_line.get_unit_vector() * scale

+        vector = Line(coord_i - unit_vector, coord_i + unit_vector, color = "#006400", buff=0)

+        return vector         

+

+        
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file5_partial_deriv_func_2maximas.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file5_partial_deriv_func_2maximas.py
new file mode 100644
index 0000000..7bbb9a7
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file5_partial_deriv_func_2maximas.py
@@ -0,0 +1,227 @@
+from manimlib.imports import *

+

+class MaximaMinima(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() 

+       

+        paraboloid = ParametricSurface(

+            lambda u, v: np.array([

+                3.5*np.sin(u)*np.cos(v),

+                3.5*np.sin(u)*np.sin(v),

+                3.5*3.5*np.sin(u)*np.sin(u)*(1+2*np.sin(v)*np.sin(v))*np.exp(1 - 3.5*3.5*np.sin(u)*np.sin(u) ) 

+            ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1,

+            resolution=(15, 32)).scale(1)

+

+        paraboloid_copy1 = paraboloid.copy()

+        paraboloid_copy2 = paraboloid.copy()

+

+        paraboloid_x = ParametricSurface(

+            lambda u, v: np.array([

+                3.5*np.sin(u)*np.cos(v),

+                3.5*np.sin(u)*np.sin(v),

+                3.5*3.5*np.sin(u)*np.sin(u)*(1+2*np.sin(v)*np.sin(v))*np.exp(1 - 3.5*3.5*np.sin(u)*np.sin(u) ) 

+            ]),u_min=0,u_max=PI,v_min=PI,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1,

+            resolution=(15, 32)).scale(1)

+

+        paraboloid_y = ParametricSurface(

+            lambda u, v: np.array([

+                3.5*np.sin(u)*np.cos(v),

+                3.5*np.sin(u)*np.sin(v),

+                3.5*3.5*np.sin(u)*np.sin(u)*(1+2*np.sin(v)*np.sin(v))*np.exp(1 - 3.5*3.5*np.sin(u)*np.sin(u) ) 

+            ]),u_min=0,u_max=PI,v_min=PI/2,v_max=3*PI/2, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1,

+            resolution=(15, 32)).scale(1)

+        

+        parabola_x_out =ParametricFunction(

+                lambda u : np.array([

+                u,

+                0,

+                (u*u )*np.exp(1-u*u)

+            ]),color=RED_E,t_min=-3.5,t_max=3.5,

+            )

+    

+        parabola_y_out =ParametricFunction(

+                lambda u : np.array([

+                0,

+                u,

+                (3*u*u)*np.exp(1-u*u)

+            ]),color=PINK,t_min=-3.5,t_max=3.5,

+            )

+

+        plane1 = Polygon(np.array([-3.5,0,-3]),np.array([3.5,0,-3]),np.array([3.5,0,3]),np.array([-3.5,0,3]),np.array([-3.5,0,-3]), color = RED_C, fill_color = RED_C, fill_opacity = 0.2)

+        plane_text_x = TextMobject(r"$y = 0$", color = RED_C).move_to(2*UP + 4.5*RIGHT)

+

+        plane2 = Polygon(np.array([0,-3.5,-3]),np.array([0,3.5,-3]),np.array([0,3.5,3]),np.array([0,-3.5,3]),np.array([0,-3.5,-3]), color = PINK, fill_color = PINK, fill_opacity = 0.2)

+        plane_text_y = TextMobject(r"$x = 0$", color = PINK).move_to(2*UP + 4.5*RIGHT)

+

+        surface_eqn = TextMobject("Surface", r"$z = (x^2 + 3y^2)e^{(1 - x^2 - y^2)}$", color = YELLOW_C).scale(0.6).move_to(np.array([3.5*LEFT +3.5*UP]))

+        surface_eqn[0].set_color(BLUE_C)

+

+        self.set_camera_orientation(phi=60 * DEGREES, theta = 45*DEGREES)

+

+        self.add(axes)

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(np.array([0,0,3.7]))

+

+        self.add_fixed_orientation_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1])

+

+        self.play(ShowCreation(paraboloid))

+

+

+        #self.move_camera(phi=60 * DEGREES, theta = 45*DEGREES,run_time=3)

+

+        

+        plane_x = Polygon(np.array([-3.5,2,-3]),np.array([3.5,2,-3]),np.array([3.5,2,3]),np.array([-3.5,2,3]),np.array([-3.5,2,-3]), color = YELLOW_C, fill_color = YELLOW_A, fill_opacity = 0.2)

+        

+        plane_y = Polygon(np.array([2,-3.5,-3]),np.array([2,3.5,-3]),np.array([2,3.5,3]),np.array([2,-3.5,3]),np.array([2,-3.5,-3]), color = GREEN_C, fill_color = GREEN_A, fill_opacity = 0.2) 

+        

+        text_x = TextMobject(r"$x$", "is fixed on this" ,"plane").scale(0.7).to_corner(UL)

+        text_y = TextMobject(r"$y$", "is fixed on this" ,"plane").scale(0.7).to_corner(UR)

+             

+        text_x[0].set_color(RED_C)

+        text_y[0].set_color(PINK)

+        text_x[1].set_color(BLUE_C)

+        text_y[1].set_color(BLUE_C)

+        text_x[2].set_color(GREEN_C)

+        text_y[2].set_color(YELLOW_C)

+

+        self.add_fixed_in_frame_mobjects(text_x, text_y)

+        

+        for i in range(2,-4,-1):

+            

+            parabola_x =ParametricFunction(lambda u : np.array([u,i,(u*u + 3*i*i)*np.exp(1- u*u - i*i)]),color=RED_C,t_min=-3.5,t_max=3.5,)

+

+            parabola_y =ParametricFunction(lambda u : np.array([i,u,(i*i + 3*u*u)*np.exp(1-  u*u - i*i)]),color=PINK,t_min=-3.5,t_max=3.5,)

+

+            if(i==2):

+             self.play(ShowCreation(plane_x), ShowCreation(plane_y))

+             parabola_copy_x = parabola_x.copy()

+             parabola_copy_y = parabola_y.copy()

+

+

+             self.play(ShowCreation(parabola_copy_x), ShowCreation(parabola_copy_y))

+             self.wait()

+             self.play(FadeOut(parabola_copy_x), FadeOut(parabola_copy_y))

+

+            else:

+             self.play(ApplyMethod(plane_x.move_to, np.array([0,i,0])),ReplacementTransform(parabola_copy_x, parabola_x),ApplyMethod(plane_y.move_to, np.array([i,0,0])),ReplacementTransform(parabola_copy_y, parabola_y))

+             self.play(FadeOut(parabola_x), FadeOut(parabola_y))

+             self.wait()

+            

+            parabola_copy_x = parabola_x.copy()

+            parabola_copy_y = parabola_y.copy()

+            

+        self.play(FadeOut(plane_x), FadeOut(plane_y), FadeOut(text_x), FadeOut(text_y))

+        

+

+        self.add_fixed_in_frame_mobjects(surface_eqn)

+

+        self.move_camera(phi=80 * DEGREES, theta = 95*DEGREES)

+

+        self.play(ShowCreation(plane1))

+        self.add_fixed_in_frame_mobjects(plane_text_x)

+        self.wait()

+        self.play(ReplacementTransform(paraboloid, paraboloid_x))

+        self.play(FadeOut(plane1), FadeOut(plane_text_x))

+

+        line_x = Line(np.array([-3.5,0,0]), np.array([3.5,0,0]), color = YELLOW_E)

+

+        self.play(ShowCreation(parabola_x_out), ShowCreation(line_x))

+

+        slope_text_x = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "x}").scale(0.6).move_to(2*UP + 3.5*RIGHT)

+        slope_text_x[0].set_color(ORANGE)

+        slope_text_x.set_color_by_tex("\\partial",GREEN_E)

+        slope_text_x.set_color_by_tex("f",RED_E)

+        slope_text_x[5].set_color(YELLOW_E)

+

+        self.add_fixed_in_frame_mobjects(slope_text_x)

+

+

+        dot_x = Dot().rotate(PI/2).set_color(YELLOW_E)

+        alpha_x = ValueTracker(0)

+        vector_x = self.get_tangent_vector(alpha_x.get_value(),parabola_x_out,scale=1.5)

+        dot_x.add_updater(lambda m: m.move_to(vector_x.get_center()))

+        self.play(

+            ShowCreation(parabola_x_out),

+            GrowFromCenter(dot_x),

+            GrowArrow(vector_x)

+            )

+        vector_x.add_updater(

+            lambda m: m.become(

+                    self.get_tangent_vector(alpha_x.get_value()%1,parabola_x_out,scale=1.5)

+                )

+            )

+        self.add(vector_x,dot_x)

+        self.play(alpha_x.increment_value, 1, run_time=10, rate_func=linear)

+

+        self.wait(2)

+        self.play(FadeOut(parabola_x_out), FadeOut(line_x), FadeOut(vector_x), FadeOut(dot_x), FadeOut(slope_text_x))

+

+        self.move_camera(phi=80* DEGREES,theta= 5*DEGREES)

+        self.play(ReplacementTransform(paraboloid_x, paraboloid_copy1))

+        self.wait()

+

+        

+

+        self.play(ShowCreation(plane2))

+        self.add_fixed_in_frame_mobjects(plane_text_y)

+        self.wait()

+        self.play(ReplacementTransform(paraboloid_copy1, paraboloid_y))

+        self.play(FadeOut(plane2), FadeOut(plane_text_y))

+

+        line_y = Line(np.array([0,-3.5,0]), np.array([0,3.5,0]), color = GREEN_E)

+

+        self.play(ShowCreation(parabola_y_out), ShowCreation(line_y))

+

+        slope_text_y = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "y}").scale(0.6).move_to(2*UP + 3.5*RIGHT)

+        slope_text_y[0].set_color(ORANGE)

+        slope_text_y.set_color_by_tex("\\partial",YELLOW_E)

+        slope_text_y.set_color_by_tex("f",PINK)

+        slope_text_y[5].set_color(GREEN_E)

+

+        self.add_fixed_in_frame_mobjects(slope_text_y)

+

+

+        dot_y = Dot().rotate(PI/2).set_color(GREEN_E)

+        alpha_y = ValueTracker(0)

+        vector_y = self.get_tangent_vector(alpha_y.get_value(),parabola_y_out,scale=1.5)

+        dot_y.add_updater(lambda m: m.move_to(vector_y.get_center()))

+        self.play(

+            ShowCreation(parabola_y_out),

+            GrowFromCenter(dot_y),

+            GrowArrow(vector_y)

+            )

+        vector_y.add_updater(

+            lambda m: m.become(

+                    self.get_tangent_vector(alpha_y.get_value()%1,parabola_y_out,scale=1.5)

+                )

+            )

+        self.add(vector_y,dot_y)

+        self.play(alpha_y.increment_value, 1, run_time=10, rate_func=linear)

+

+        self.wait(2)

+        self.play(FadeOut(parabola_y_out), FadeOut(line_y), FadeOut(vector_y), FadeOut(dot_y), FadeOut(slope_text_y))

+

+        self.move_camera(phi=60* DEGREES,theta= 45*DEGREES)

+        self.play(ReplacementTransform(paraboloid_y, paraboloid_copy2))

+        self.wait()

+

+

+

+

+

+

+

+        

+

+    def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1):

+        coord_i = curve.point_from_proportion(proportion)

+        coord_f = curve.point_from_proportion(proportion + dx)

+        reference_line = Line(coord_i,coord_f)

+        unit_vector = reference_line.get_unit_vector() * scale

+        vector = Line(coord_i - unit_vector , coord_i + unit_vector, color = ORANGE, buff=0)

+        return vector    

+

diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file6_clariant_rule.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file6_clariant_rule.py
new file mode 100644
index 0000000..b79f77c
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file6_clariant_rule.py
@@ -0,0 +1,64 @@
+from manimlib.imports import *

+

+class ClariantRule(Scene):

+    def construct(self):

+        derivatives = TextMobject(r"$cos(x)y^3$",r"$-sin(x)y^3$", r"$3cos(x)y^2$", r"$-cos(x)y^3$", r"$-3sin(x)y^2$", r"$-3sin(x)y^2$", r"$6cos(x)y$")

+

+        partial_derivatives = TextMobject(r"$\frac{\partial}{\partial x}$", r"$\frac{\partial}{\partial y}$")

+

+        

+        derivatives[0].move_to(2*UP).set_color(PURPLE)

+        derivatives[1].move_to(3*LEFT).set_color(YELLOW_C)

+        derivatives[2].move_to(3*RIGHT).set_color(BLUE_C)

+        

+        arrrow_1 = Arrow(derivatives[0].get_bottom(), derivatives[1].get_top())

+        arrrow_1_lab = partial_derivatives[0].copy().scale(0.7)  

+        arrrow_1_lab.move_to(2.5*LEFT+ 1.3*UP)

+

+        arrrow_2 = Arrow(derivatives[0].get_bottom(), derivatives[2].get_top())

+        arrrow_2_lab = partial_derivatives[1].copy().scale(0.7)  

+        arrrow_2_lab.move_to(2.5*RIGHT+ 1.3*UP)

+

+        self.play(Write(derivatives[0]))

+        self.play(GrowArrow(arrrow_1), GrowArrow(arrrow_2), Write(arrrow_1_lab), Write(arrrow_2_lab))

+

+        self.play(Write(derivatives[1]))

+        self.play(Write(derivatives[2]))

+

+        derivatives[3].move_to(2*DOWN + 4.5*LEFT).set_color(GREEN_C)

+        derivatives[4].move_to(2*DOWN + 1.5*LEFT).set_color(PINK)

+        derivatives[5].move_to(2*DOWN + 1.5*RIGHT).set_color(PINK)

+        derivatives[6].move_to(2*DOWN + 4.5*RIGHT).set_color(ORANGE)

+

+        arrrow_3 = Arrow(derivatives[1].get_bottom(), derivatives[3].get_top())

+        arrrow_3_lab = partial_derivatives[0].copy().scale(0.7) 

+        arrrow_3_lab.move_to(4.3*LEFT+ 0.8*DOWN)

+

+        arrrow_4 = Arrow(derivatives[1].get_bottom(), derivatives[4].get_top())

+        arrrow_4_lab = partial_derivatives[1].copy().scale(0.7)  

+        arrrow_4_lab.move_to(1.6*LEFT+ 0.8*DOWN)

+

+        arrrow_5 = Arrow(derivatives[2].get_bottom(), derivatives[5].get_top())

+        arrrow_5_lab = partial_derivatives[0].copy().scale(0.7)  

+        arrrow_5_lab.move_to(1.6*RIGHT+ 0.8*DOWN)

+

+        arrrow_6 = Arrow(derivatives[2].get_bottom(), derivatives[6].get_top())

+        arrrow_6_lab = partial_derivatives[1].copy().scale(0.7)  

+        arrrow_6_lab.move_to(4.3*RIGHT+ 0.8*DOWN)

+

+        self.play(GrowArrow(arrrow_3), GrowArrow(arrrow_4), Write(arrrow_3_lab), Write(arrrow_4_lab))

+        self.play(Write(derivatives[3]), Write(derivatives[4]))

+

+        self.play(GrowArrow(arrrow_5), GrowArrow(arrrow_6), Write(arrrow_5_lab), Write(arrrow_6_lab))

+        self.play(Write(derivatives[5]), Write(derivatives[6]))

+        

+        brace1 = Brace(derivatives[4:6], DOWN, buff = SMALL_BUFF, color = RED_C)

+        brace_t1 = brace1.get_text("Mixed partial derivatives are the same!")

+        brace_t1.set_color(RED_C)

+

+        self.play(GrowFromCenter(brace1), FadeIn(brace_t1))

+        

+        self.wait()

+

+

+

diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file7_partial_deriv_clariant_rule.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file7_partial_deriv_clariant_rule.py
new file mode 100644
index 0000000..313c6cd
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file7_partial_deriv_clariant_rule.py
@@ -0,0 +1,108 @@
+from manimlib.imports import *

+

+class ClariantRule(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() 

+       

+        function = ParametricSurface(

+            lambda u, v: np.array([

+                3.5*np.sin(u)*np.cos(v),

+                3.5*np.sin(u)*np.sin(v),

+                3.5*3.5*np.sin(u)*np.sin(u)*(1+2*np.sin(v)*np.sin(v))*np.exp(1 - 3.5*3.5*np.sin(u)*np.sin(u) ) 

+            ]),u_min=0,u_max=PI,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1,

+            resolution=(15, 32)).scale(1)

+

+        

+        function_copy1 = function.copy()

+        function_copy2 = function.copy()

+        

+        func_x =ParametricFunction(

+                lambda u : np.array([

+                u,

+                -1,

+                (u*u )*np.exp(1-u*u)

+            ]),color=RED_E,t_min=-3.5,t_max=3.5,

+            )

+    

+        func_y =ParametricFunction(

+                lambda u : np.array([

+                0,

+                u,

+                (3*u*u)*np.exp(1-u*u)

+            ]),color=PINK,t_min=-3.5,t_max=3.5,

+            )

+       

+        plane_x = Polygon(np.array([-3.5,-1,-3]),np.array([3.5,-1,-3]),np.array([3.5,-1,3]),np.array([-3.5,-1,3]),np.array([-3.5,-1,-3]), color = YELLOW_E, fill_color = YELLOW_B, fill_opacity = 0.1)

+        plane_text_x = TextMobject(r"$y = -1$", color = YELLOW_C).move_to(np.array([5,0,2.7])).scale(0.7)

+

+        plane_y = Polygon(np.array([0,-3.5,-3]),np.array([0,3.5,-3]),np.array([0,3.5,3]),np.array([0,-3.5,3]),np.array([0,-3.5,-3]), color = GREEN_E, fill_color = GREEN_B, fill_opacity = 0.1)

+        plane_text_y = TextMobject(r"$x = 0$", color = GREEN_C).move_to(np.array([0,4,2.7])).scale(0.7)

+        

+        surface_eqn = TextMobject("Surface", r"$z = (x^2 + 3y^2)e^{(1 - x^2 - y^2)}$", color = YELLOW_C).scale(0.6).move_to(np.array([4.6*LEFT+3.5*UP]))

+        surface_eqn[0].set_color(BLUE_C)

+

+        self.set_camera_orientation(phi=60 * DEGREES, theta = 45*DEGREES)

+

+        self.add(axes)

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(np.array([0,0,3.7]))

+

+        self.add_fixed_orientation_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1])

+

+        self.play(ShowCreation(function))

+

+        self.add_fixed_in_frame_mobjects(surface_eqn)

+

+        self.play(ShowCreation(plane_x), ShowCreation(plane_y))

+        self.add_fixed_orientation_mobjects(plane_text_x, plane_text_y)

+

+        self.play(ShowCreation(func_x), ShowCreation(func_y))

+        

+        dot_x = Dot().rotate(PI/2).set_color(YELLOW_E)

+        alpha_x = ValueTracker(0)

+        vector_x = self.get_tangent_vector(alpha_x.get_value(),func_x,scale=1.5)

+        dot_x.add_updater(lambda m: m.move_to(vector_x.get_center()))

+        self.play(

+            ShowCreation(func_x),

+            GrowFromCenter(dot_x),

+            GrowArrow(vector_x)

+            )

+        vector_x.add_updater(

+            lambda m: m.become(

+                    self.get_tangent_vector(alpha_x.get_value()%1,func_x,scale=1.5)

+                )

+            )

+        dot_y = Dot().rotate(PI/2).set_color(GREEN_E)

+        alpha_y = ValueTracker(0)

+        vector_y = self.get_tangent_vector(alpha_y.get_value(),func_y,scale=1.5)

+        dot_y.add_updater(lambda m: m.move_to(vector_y.get_center()))

+        self.play(

+            ShowCreation(func_y),

+            GrowFromCenter(dot_y),

+            GrowArrow(vector_y)

+            )

+        vector_y.add_updater(

+            lambda m: m.become(

+                    self.get_tangent_vector(alpha_y.get_value()%1,func_y,scale=1.5)

+                )

+            )

+        self.add(vector_x,dot_x)

+        

+        self.play(alpha_x.increment_value, 1, run_time=10, rate_func=linear)

+

+        self.add(vector_y,dot_y)

+        self.play(alpha_y.increment_value, 1, run_time=10, rate_func=linear)

+

+        self.wait(2)

+       

+

+       

+

+

+            

+

+

diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file8_chain_rule.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file8_chain_rule.py
new file mode 100644
index 0000000..f50d2d1
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file8_chain_rule.py
@@ -0,0 +1,60 @@
+from manimlib.imports import *

+

+class ChainRule(Scene):

+    def construct(self):

+

+        chain_rule = TextMobject(r"$\frac{dw}{dt}$", r"=", r"$\frac{\partial w}{\partial x}$", r"$\frac{dx}{dt}$", r"+", r"$\frac{\partial w}{\partial y}$", r"$\frac{dy}{dt}$").move_to(4*RIGHT).scale(0.8)

+        

+        chain_rule[0].set_color(ORANGE)

+        chain_rule[2].set_color(GREEN_C)

+        chain_rule[3].set_color(RED_C)

+        chain_rule[5].set_color(YELLOW_C)

+        chain_rule[6].set_color(BLUE_C)

+        

+        functions = TextMobject(r"$w =f(x,y)$",r"$x$", r"$y$", r"$t$")

+

+        functions[0].move_to(3.3*UP+1*LEFT).set_color(ORANGE)

+        functions[1].move_to(3.3*LEFT).set_color(PURPLE)

+        functions[2].move_to(1.3*RIGHT).set_color(PURPLE)

+        functions[3].move_to(3.3*DOWN+1*LEFT).set_color(WHITE)

+

+        partial_derivatives = TextMobject(r"$\frac{\partial w}{\partial x}$", r"$\frac{\partial w}{\partial y}$")

+

+        partial_derivatives[0].move_to(1.5*UP+3*LEFT).set_color(GREEN_C)

+        partial_derivatives[1].move_to(1.5*UP+1*RIGHT).set_color(YELLOW_C)

+

+        derivatives = TextMobject(r"$\frac{dx}{dt}$", r"$\frac{dy}{dt}$")

+

+        derivatives[0].move_to(1.5*DOWN+3*LEFT).set_color(RED_C)

+        derivatives[1].move_to(1.5*DOWN+1*RIGHT).set_color(BLUE_C)

+

+        line_f_x = Line(np.array([-1,3,0]), np.array([-3,0,0]), color = BLUE_C)

+        line_f_y = Line(np.array([-1,3,0]), np.array([1,0,0]), color = BLUE_C)

+        line_x_t = Line(np.array([-3,0,0]), np.array([-1,-3,0]), color = BLUE_C)

+        line_y_t = Line(np.array([1,0,0]), np.array([-1,-3,0]), color = BLUE_C)

+

+        dot_f = Dot().shift(np.array([-1,3,0])).set_color(BLUE_C)

+        dot_x = Dot().shift(np.array([-3,0,0])).set_color(BLUE_C)

+        dot_y = Dot().shift(np.array([1,0,0])).set_color(BLUE_C)

+        dot_t = Dot().shift(np.array([-1,-3,0])).set_color(BLUE_C)

+

+        variables = TextMobject("Dependent Variable","Intermediate Variables", "Dependent Variable").set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE).scale(0.7)

+        variables[0].move_to(3.3*UP+3.5*RIGHT)

+        variables[1].move_to(3.5*RIGHT)

+        variables[2].move_to(3.3*DOWN+3.5*RIGHT)

+

+        self.play(ShowCreation(dot_f), Write(functions[0]))

+        self.play(ShowCreation(dot_x), ShowCreation(line_f_x), Write(functions[1]), ShowCreation(dot_y), ShowCreation(line_f_y), Write(functions[2]))

+        self.play(Write(partial_derivatives[0]), Write(partial_derivatives[1]))

+        self.wait()

+

+        self.play(ShowCreation(dot_t), ShowCreation(line_x_t), ShowCreation(line_y_t), Write(functions[3]))

+        self.play(Write(derivatives[0]), Write(derivatives[1]))

+        self.wait()

+

+        self.play(Write(variables[0]), Write(variables[1]), Write(variables[2]))

+

+        self.play(FadeOut(variables))

+        self.play(Write(chain_rule))

+        self.wait()

+ 
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file1_partial_deriv_gas_law.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file1_partial_deriv_gas_law.gif
new file mode 100644
index 0000000..560a7c0
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file1_partial_deriv_gas_law.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file2_partial_deriv_hill.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file2_partial_deriv_hill.gif
new file mode 100644
index 0000000..f4c3f49
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file2_partial_deriv_hill.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file3_partial_deriv_defn.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file3_partial_deriv_defn.gif
new file mode 100644
index 0000000..e0e42db
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file3_partial_deriv_defn.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file4_partial_deriv_example.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file4_partial_deriv_example.gif
new file mode 100644
index 0000000..30682cb
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file4_partial_deriv_example.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file5_partial_deriv_func_2maximas.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file5_partial_deriv_func_2maximas.gif
new file mode 100644
index 0000000..aa74437
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file5_partial_deriv_func_2maximas.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file6_clariant_rule.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file6_clariant_rule.gif
new file mode 100644
index 0000000..8377827
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file6_clariant_rule.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file7_partial_deriv_clariant_rule.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file7_partial_deriv_clariant_rule.gif
new file mode 100644
index 0000000..ecef499
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file7_partial_deriv_clariant_rule.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file8_chain_rule.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file8_chain_rule.gif
new file mode 100644
index 0000000..596b08d
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/gifs/file8_chain_rule.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/README.md b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/README.md
new file mode 100644
index 0000000..4339c30
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/README.md
@@ -0,0 +1,20 @@
+**file1_scalar_function**
+![file1_scalar_function](https://github.com/nishanpoojary/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file1_scalar_functions.gif)
+
+**file2_domain_range**
+![file2_domain_range](https://github.com/nishanpoojary/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file2_domain_range.gif)
+
+**file3_parabola_example**
+![file3_parabola_example](https://github.com/nishanpoojary/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file3_parabola_example.gif)
+
+**file4_level_curves**
+![file4_non_rect_region](https://github.com/nishanpoojary/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file4_level_curves.gif)
+
+**file5_level_surface**
+![file5_level_surface](https://github.com/nishanpoojary/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file5_level_surface.gif)
+
+**file6_scalar_function_application**
+![file6_scalar_function_application](https://github.com/nishanpoojary/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file6_scalar_function_application.gif)
+
+**file7_neural_nets**
+![file7_neural_nets](https://github.com/nishanpoojary/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file7_neural_nets.gif)
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file1_scalar_functions.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file1_scalar_functions.py
new file mode 100644
index 0000000..1a6f4ed
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file1_scalar_functions.py
@@ -0,0 +1,50 @@
+from manimlib.imports import *

+

+class ScalarFunction(Scene):

+    def construct(self):

+        circle = Circle(radius = 1.5, color = BLUE_E, fill_color = BLUE_C, fill_opacity = 0.1).move_to(2*LEFT)

+        dot_circle = Dot().shift(np.array([-1.5,0,0])).set_color(BLUE_E)

+        dot_circle_lab = TextMobject(r"$a$", color = BLUE_E).next_to(dot_circle, DOWN)

+

+        arrow = Arrow(np.array([3,-3,0]),np.array([3,3,0]))

+        line = Line(np.array([3,-1.5,0]),np.array([3,1.5,0]), color = RED_C)

+

+        dot0 = Dot().shift(np.array([3,0,0])).set_color(RED_E)

+        dot0_lab = TextMobject(r"$f(a)$", color = RED_E).scale(0.8).next_to(dot0, RIGHT)

+

+        dot1 = Dot().shift(np.array([3,-1.5,0])).set_color(RED_C)

+

+        dot2 = Dot().shift(np.array([3,1.5,0])).set_color(RED_C)

+        dot2_lab = TextMobject(r"$f(A)$", color = RED_C).scale(0.8).next_to(dot2, RIGHT)

+

+        arrow_f = Arrow(np.array([-1.5,0,0]),np.array([3,0,0]), color = YELLOW_C, buff = 0.1)

+

+        R = TextMobject(r"$\mathbb{R}$", color = WHITE).move_to(np.array([3,-3.3,0]))

+

+        A = TextMobject(r"$A$", color = BLUE_E).move_to(np.array([-2.5,-3.3,0]))

+

+        F = TextMobject(r"$f$", color = GREY).move_to(np.array([0,-2.9,0]))

+

+        F_center = TextMobject(r"$f$", color = YELLOW_C).move_to(np.array([0.8,0.5,0]))

+

+        arrow_R_A = Arrow(np.array([-2.3,-3.3,0]),np.array([2.7,-3.3,0]), color = GREY, buff = 0.1)

+

+        scalar_function = TextMobject(r"Scalar Valued Function", r"$f: A \rightarrow \mathbb{R}$", color = PURPLE).move_to(np.array([0,3.5,0]))

+        scalar_function[1].set_color(GREEN_C)

+

+

+

+        self.play(ShowCreation(circle))

+        self.play(ShowCreation(arrow))

+

+        

+        self.play(ShowCreation(dot1), ShowCreation(dot2))

+        self.play(ShowCreation(dot_circle))

+        self.play(ShowCreation(dot_circle_lab),  ShowCreation(dot2_lab))

+        self.play(ShowCreation(A), ShowCreation(R))

+        self.play(GrowArrow(arrow_f), ShowCreation(dot0), ShowCreation(dot0_lab), ShowCreation(F_center), GrowArrow(arrow_R_A), ShowCreation(F), Transform(circle.copy(), line.copy()))

+

+        self.play(Write(scalar_function))

+

+

+        self.wait(2)
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file1_domain_range.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file2_domain_range.py
index 9b1ca7b..1b54cb6 100644
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file1_domain_range.py
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file2_domain_range.py
@@ -20,6 +20,11 @@ class PlotGraphs(GraphScene):
         self.play(FadeOut(topic))

         self.wait(1)

 

+        scalar_func_R = TextMobject(r"Scalar Valued Functions in $R$").scale(1.5).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

+        self.play(Write(scalar_func_R))

+        self.play(FadeOut(scalar_func_R))

+        self.wait(1)

+

 

         XTD = self.x_axis_width/(self.x_max- self.x_min)

         YTD = self.y_axis_height/(self.y_max- self.y_min)

@@ -40,8 +45,8 @@ class PlotGraphs(GraphScene):
         rangeMsg.scale(0.5)

         rangeMsg.set_color(YELLOW)

 

-        domainline1 = Line(self.graph_origin+0.6*YTD*DOWN+1.2*XTD*LEFT, self.graph_origin+0.6*YTD*DOWN + 4*XTD*LEFT)

-        domainline2 = Arrow(self.graph_origin+0.6*YTD*DOWN+1.1*XTD*RIGHT, self.graph_origin+0.6*YTD*DOWN + 5.3*XTD*RIGHT)

+        domainline1 = Arrow(self.graph_origin+0.6*YTD*DOWN+1.2*XTD*LEFT, self.graph_origin+0.6*YTD*DOWN + 4*XTD*LEFT, buff = 0.1)

+        domainline2 = Arrow(self.graph_origin+0.6*YTD*DOWN+1.1*XTD*RIGHT, self.graph_origin+0.6*YTD*DOWN + 5.3*XTD*RIGHT, buff = 0.1)

         domainline1.set_color(PINK)

         domainline2.set_color(PINK)

 

@@ -128,5 +133,58 @@ class PlotSineGraphs(GraphScene):
         self.play(Write(domainMsg))

         self.wait(3)

 

+    

+

+        

+class Paraboloid(ThreeDScene):

+    def construct(self):

+

+        scalar_func_R2 = TextMobject(r"Scalar Valued Functions in $R^2$").scale(1.5).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

+        self.play(Write(scalar_func_R2))

+        self.play(FadeOut(scalar_func_R2))

+        self.wait(1)

+

+        axes = ThreeDAxes() 

+

+        paraboloid = ParametricSurface(

+            lambda u, v: np.array([

+                2*np.sin(u)*np.cos(v),

+                2*np.sin(u)*np.sin(v),

+                2*2*np.sin(u)*np.sin(u)

+            ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[GREEN_C, GREEN_E],

+            resolution=(15, 32)).scale(1)

+

+        domain = Polygon(np.array([-5,-5,0]),np.array([5,-5,0]),np.array([5,5,0]),np.array([-5,5,0]),np.array([-5,-5,0]), color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.2)

+        domain_lab = TextMobject(r"$Domain: R^2$", color = YELLOW_C).scale(0.7).move_to(1*DOWN + 2*LEFT)

+        

+        rangef = Line(np.array([0, 0,0]), np.array([0, 0,5]), color = RED_C)

+        rangef_lab = TextMobject(r"$Range: z \geq 0$", color = RED_C).scale(0.7).move_to(2*UP + 1.5*RIGHT)

+

+        func = TextMobject(r"$z = f(x,y) = x^2+y^2$").scale(0.7).move_to(3*UP + 4*LEFT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

+        

+        self.set_camera_orientation(phi=60 * DEGREES, theta = 0*DEGREES)

+        self.begin_ambient_camera_rotation(rate=0.3)

+

+        self.add(axes)

+

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(np.array([0,0,3.7]))

+

+        self.add_fixed_orientation_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1]) 

+

+

+

+        self.add_fixed_in_frame_mobjects(func)

+        self.play(Write(paraboloid))

+        self.play(ShowCreation(domain))

+        self.add_fixed_in_frame_mobjects(domain_lab)

+        self.wait()

+        self.play(ShowCreation(rangef))

+        self.add_fixed_in_frame_mobjects(rangef_lab)

+        self.wait(5)

 

     
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file3_parabola_example.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file3_parabola_example.py
index 74dc063..63c16b3 100644
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file3_parabola_example.py
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file3_parabola_example.py
@@ -9,11 +9,10 @@ class Parabola(ThreeDScene):
                 2*np.cosh(u)*np.cos(v),

                 2*np.cosh(u)*np.sin(v),

                 2*np.sinh(u)

-            ]),v_min=0,v_max=TAU,u_min=0,u_max=2,checkerboard_colors=[YELLOW_D, YELLOW_E],

+            ]),v_min=0,v_max=TAU,u_min=0,u_max=2,checkerboard_colors=[YELLOW_D, YELLOW_E],#

             resolution=(15, 32))

 

-        text3d = TextMobject(r"Plot of $f: \mathbb{R}^2 \rightarrow \mathbb{R}$", "z = f(x,y)")

-        self.add_fixed_in_frame_mobjects(text3d) 

+        text3d = TextMobject(r"Plot of $f: \mathbb{R}^2 \rightarrow \mathbb{R}$", r"$z = f(x,y) = \sqrt{x^2 + y^2 - 4}$") 

         text3d[0].move_to(4*LEFT+2*DOWN)

         text3d[1].next_to(text3d[0], DOWN)

         text3d[0].set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

@@ -21,8 +20,21 @@ class Parabola(ThreeDScene):
 

         #self.set_camera_orientation(phi=0 * DEGREES,theta=270*DEGREES)

         self.move_camera(phi=110* DEGREES,theta=45*DEGREES)

+

         self.add(axes)

+

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(np.array([0,0,3.7]))

+

+        self.add_fixed_orientation_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1]) 

+

+

         self.play(ShowCreation(paraboloid))

+        self.add_fixed_in_frame_mobjects(text3d)

         self.play(Write(text3d[0]))

         self.play(Write(text3d[1]))

         self.begin_ambient_camera_rotation(rate=0.2)

diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_level_curves.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_level_curves.py
new file mode 100644
index 0000000..2b6f719
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_level_curves.py
@@ -0,0 +1,118 @@
+from manimlib.imports import *

+

+class LevelCurves(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() 

+

+        paraboloid = ParametricSurface(

+            lambda u, v: np.array([

+                u*np.cos(v),

+                u*np.sin(v),

+                -u*u+2

+            ]),u_min=-1.414,u_max=1.414,v_min=0,v_max=2*PI, color = BLUE_C, fill_color = BLUE_C, fill_opacity = 0.1,

+            resolution=(15, 32)).scale(1)

+        

+        plane_0 = Polygon(np.array([2,-2,0]),np.array([2,2,0]),np.array([-2,2,0]),np.array([-2,-2,0]),np.array([2,-2,0]), color = BLUE_E, fill_color = BLUE_E, fill_opacity = 0.3)

+        plane_0_lab = TextMobject("C = 0").move_to(0.4*UP+3.2*RIGHT).set_color(BLUE_E).scale(0.6)

+        circle_0 = Circle(radius = 1.414 , color = BLUE_E)

+        circle_0_lab = TextMobject("0").move_to(1.1*DOWN+1.1*RIGHT).set_color(BLUE_E).scale(0.6)

+

+        plane_0_5 = Polygon(np.array([2,-2,0.5]),np.array([2,2,0.5]),np.array([-2,2,0.5]),np.array([-2,-2,0.5]),np.array([2,-2,0.5]), color = GREEN_C, fill_color = GREEN_C, fill_opacity = 0.3)

+        plane_0_5_lab = TextMobject("C = 0.5").move_to(0.8*UP+3.4*RIGHT).set_color(GREEN_C).scale(0.6)

+        circle_0_5 = Circle(radius = 1.224 , color = GREEN_C)

+        circle_0_5_lab = TextMobject("0.5").move_to(0.9*DOWN+0.9*RIGHT).set_color(GREEN_C).scale(0.6)

+        circle_0_5_copy = circle_0_5.copy().move_to(np.array([0,0,0.5]))

+

+        plane_1 = Polygon(np.array([2,-2,1]),np.array([2,2,1]),np.array([-2,2,1]),np.array([-2,-2,1]),np.array([2,-2,1]), color = YELLOW_C, fill_color = YELLOW_C, fill_opacity = 0.3)

+        plane_1_lab = TextMobject("C = 1").move_to(1.2*UP+3.3*RIGHT).set_color(YELLOW_C).scale(0.6)

+        circle_1 = Circle(radius = 1 , color = YELLOW_C)

+        circle_1_lab = TextMobject("1").move_to(0.7*DOWN+0.7*RIGHT).set_color(YELLOW_C).scale(0.6)

+        circle_1_copy = circle_1.copy().move_to(np.array([0,0,1]))

+

+        plane_1_5 = Polygon(np.array([2,-2,1.5]),np.array([2,2,1.5]),np.array([-2,2,1.5]),np.array([-2,-2,1.5]),np.array([2,-2,1.5]), color = ORANGE, fill_color = ORANGE, fill_opacity = 0.3)

+        plane_1_5_lab = TextMobject("C = 1.5").move_to(1.7*UP+3.4*RIGHT).set_color(ORANGE).scale(0.6)

+        circle_1_5 = Circle(radius = 0.707 , color = ORANGE)

+        circle_1_5_lab = TextMobject("1.5").move_to(0.5*DOWN+0.5*RIGHT).set_color(ORANGE).scale(0.6)

+        circle_1_5_copy = circle_1_5.copy().move_to(np.array([0,0,1.5]))

+

+        plane_2 = Polygon(np.array([2,-2,2]),np.array([2,2,2]),np.array([-2,2,2]),np.array([-2,-2,2]),np.array([2,-2,2]), color = RED_C, fill_color = RED_C, fill_opacity = 0.3)

+        plane_2_lab = TextMobject("C = 2").move_to(2.1*UP+3.3*RIGHT).set_color(RED_C).scale(0.6)

+        dot_2 = Dot().set_fill(RED_C)

+        circle_2_lab = TextMobject("2").move_to(0.2*DOWN+0.2*RIGHT).set_color(RED_C).scale(0.6)

+        dot_2_copy = dot_2.copy().move_to(np.array([0,0,2]))

+

+        level_curves_line1 = DashedLine(np.array([0,-1.414,0]),np.array([0,-2,1]), color = WHITE)

+        level_curves_line2 = DashedLine(np.array([0,-1.224,0.5]),np.array([0,-2,1]), color = WHITE)

+        level_curves_line3 = DashedLine(np.array([0,-1,1]),np.array([0,-2,1]), color = WHITE)

+        level_curves_line4 = DashedLine(np.array([0,-0.707,1.5]),np.array([0,-2,1]), color = WHITE)

+        level_curves_line5 = DashedLine(np.array([0,0,2]),np.array([0,-2,1]), color = WHITE)

+

+        level_curves = TextMobject("Level Curves").move_to(1.4*UP+3*LEFT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE).scale(0.8)

+

+

+        contour_line1 = DashedLine(np.array([0,-1.414,0]),np.array([0,-2,1]), color = WHITE)

+        contour_line2 = DashedLine(np.array([0,-1.224,0]),np.array([0,-2,1]), color = WHITE)

+        contour_line3 = DashedLine(np.array([0,-1,0]),np.array([0,-2,1]), color = WHITE)

+        contour_line4 = DashedLine(np.array([0,-0.707,0]),np.array([0,-2,1]), color = WHITE)

+        contour_line5 = DashedLine(np.array([0,0,0]),np.array([0,-2,1]), color = WHITE)

+

+        contours = TextMobject("Contours").move_to(1.4*UP+2.7*LEFT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE).scale(0.8)

+

+        

+        topic = TextMobject("Contour Plot").move_to(3*UP+3*LEFT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE).scale(0.8)

+

+        self.set_camera_orientation(phi=80 * DEGREES, theta = 0*DEGREES)

+        #self.set_camera_orientation(phi=0 * DEGREES, theta = 0*DEGREES)

+

+        self.add(axes)

+

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(np.array([0,0,3.7]))

+

+        self.add_fixed_orientation_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1])

+        

+        self.play(Write(paraboloid))

+        self.wait()

+        self.play(ShowCreation(plane_0), ShowCreation(circle_0))

+        self.add_fixed_in_frame_mobjects(plane_0_lab)

+        self.wait()

+        self.play(ShowCreation(plane_0_5), ShowCreation(circle_0_5_copy), ShowCreation(circle_0_5))

+        self.add_fixed_in_frame_mobjects(plane_0_5_lab)

+        self.wait()

+        self.play(ShowCreation(plane_1), ShowCreation(circle_1_copy), ShowCreation(circle_1))

+        self.add_fixed_in_frame_mobjects(plane_1_lab)

+        self.wait()

+        self.play(ShowCreation(plane_1_5), ShowCreation(circle_1_5_copy), ShowCreation(circle_1_5))

+        self.add_fixed_in_frame_mobjects(plane_1_5_lab)

+        self.wait()

+        self.play(ShowCreation(plane_2), ShowCreation(dot_2_copy), ShowCreation(dot_2))

+        self.add_fixed_in_frame_mobjects(plane_2_lab)

+        self.wait()

+

+        self.move_camera(phi=60 * DEGREES, theta = 30*DEGREES,run_time=3)

+        self.play(FadeOut(plane_0), FadeOut(plane_0_lab), FadeOut(plane_0_5), FadeOut(plane_0_5_lab), FadeOut(plane_1), FadeOut(plane_1_lab), FadeOut(plane_1_5), FadeOut(plane_1_5_lab), FadeOut(plane_2), FadeOut(plane_2_lab))

+        

+        self.play(GrowArrow(level_curves_line1), GrowArrow(level_curves_line2), GrowArrow(level_curves_line3), GrowArrow(level_curves_line4), GrowArrow(level_curves_line5))

+        self.add_fixed_in_frame_mobjects(level_curves)

+        self.wait()

+        self.play(FadeOut(level_curves_line1), FadeOut(level_curves_line2), FadeOut(level_curves_line3), FadeOut(level_curves_line4), FadeOut(level_curves_line5), FadeOut(level_curves))

+        self.play(FadeOut(circle_0_5_copy), FadeOut(circle_1_copy), FadeOut(circle_1_5_copy), FadeOut(dot_2_copy))

+        self.wait()

+

+        self.play(GrowArrow(contour_line1), GrowArrow(contour_line2), GrowArrow(contour_line3), GrowArrow(contour_line4), GrowArrow(contour_line5))

+        self.add_fixed_in_frame_mobjects(contours)

+        self.wait()

+        self.play(FadeOut(contour_line1), FadeOut(contour_line2), FadeOut(contour_line3), FadeOut(contour_line4), FadeOut(contour_line5), FadeOut(contours))

+        

+

+        self.move_camera(phi=0 * DEGREES, theta = 0*DEGREES,run_time=3)

+        self.play(FadeOut(paraboloid))

+        self.wait()

+

+        self.add_fixed_in_frame_mobjects(circle_0_lab, circle_0_5_lab, circle_1_lab, circle_1_5_lab,circle_2_lab)

+        self.add_fixed_in_frame_mobjects(topic)

+        self.wait(3)
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file5_level_surface.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file5_level_surface.py
new file mode 100644
index 0000000..8052676
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file5_level_surface.py
@@ -0,0 +1,78 @@
+from manimlib.imports import *

+

+class LevelSurface(ThreeDScene):

+    def construct(self):

+        axes = ThreeDAxes() 

+

+        surface_0 = ParametricSurface(

+            lambda u, v: np.array([

+                u*np.cos(v),

+                u*np.sin(v),

+                (u*u*np.cos(v)*np.cos(v))-(u*np.sin(v)/5)+0

+            ]),u_min=-1,u_max=1,v_min=0,v_max=2*PI,checkerboard_colors=[RED_C, RED_E],

+            resolution=(15, 32)).scale(1)

+

+        k_0 = TextMobject("K = 0", color = RED_C).scale(0.7)

+

+        surface_1 = ParametricSurface(

+            lambda u, v: np.array([

+                u*np.cos(v),

+                u*np.sin(v),

+                (u*u*np.cos(v)*np.cos(v))-(u*np.sin(v)/5)+1

+            ]),u_min=-1,u_max=1,v_min=0,v_max=2*PI,checkerboard_colors=[GREEN_C, GREEN_E],

+            resolution=(15, 32)).scale(1)

+        

+        k_1 = TextMobject("K = 1", color = GREEN_C).scale(0.7)

+

+        surface_2 = ParametricSurface(

+            lambda u, v: np.array([

+                u*np.cos(v),

+                u*np.sin(v),

+                (u*u*np.cos(v)*np.cos(v))-(u*np.sin(v)/5)+2

+            ]),u_min=-1,u_max=1,v_min=0,v_max=2*PI,checkerboard_colors=[YELLOW_C, YELLOW_E],

+            resolution=(15, 32)).scale(1)

+

+        k_2 = TextMobject("K = 2", color = YELLOW_C).scale(0.7)

+

+        func = TextMobject(r"$w = g(x,y,z)$", r"$= z - f(x,y)$", r"$z-x^2+y/5 = K$")

+        func.set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)

+

+        self.set_camera_orientation(phi=90 * DEGREES, theta = 90*DEGREES)

+        self.begin_ambient_camera_rotation(rate=0.3)

+

+

+        self.add(axes)

+        

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(3.7*UP)

+

+        self.add_fixed_in_frame_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1])

+

+        self.play(Write(surface_0))

+        self.add_fixed_in_frame_mobjects(k_0)

+        k_0.move_to(np.array([1.4*RIGHT ]))

+

+        self.play(Write(surface_1))

+        self.add_fixed_in_frame_mobjects(k_1)

+        k_1.move_to(np.array([1.4*RIGHT + 1*UP]))

+    

+        self.play(Write(surface_2))

+        self.add_fixed_in_frame_mobjects(k_2)

+        k_2.move_to(np.array([1.4*RIGHT + 2*UP]))

+        self.wait()

+

+        self.add_fixed_in_frame_mobjects(func)

+        func[0].move_to(np.array([4.5*LEFT + 3*UP]))

+        func[1].move_to(np.array([4.5*LEFT + 2.5*UP]))

+        func[2].move_to(np.array([4.5*LEFT + 2*UP]))

+

+        self.wait(3)

+        self.move_camera(phi=60 * DEGREES,run_time=3)

+        self.wait(2)

+

+

+     
\ No newline at end of file
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file2_scalar_function_application.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file6_scalar_function_application.py
index 56b3e53..3ccfad6 100644
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file2_scalar_function_application.py
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file6_scalar_function_application.py
@@ -3,12 +3,23 @@ from manimlib.imports import *
 class ScalarApplication(ThreeDScene):

     def construct(self):

         axes = ThreeDAxes() # creates a 3D Axis

+

+        self.add(axes)

+

+        axis = TextMobject(r"X",r"Y",r"Z")

+        axis[0].move_to(6*RIGHT)

+        axis[1].move_to(6*UP)

+        axis[2].move_to(np.array([0,0,3.7]))

+

+        self.add_fixed_orientation_mobjects(axis[2])

+        self.add_fixed_orientation_mobjects(axis[0])

+        self.add_fixed_orientation_mobjects(axis[1]) 

         

         cube = Cube()

-        cube.set_fill(YELLOW_E, opacity = 0.1)

+        cube.set_fill(YELLOW_C, opacity = 0.2)

         cube.scale(2)

         self.set_camera_orientation(phi=0 * DEGREES,theta=270*DEGREES)

-        self.play(ShowCreation(cube),ShowCreation(axes))

+        self.play(ShowCreation(cube))

         

         dot = Sphere()

         dot.scale(0.1)

diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_neural_nets.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file7_neural_nets.py
index eb6bf45..eb6bf45 100644
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_neural_nets.py
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file7_neural_nets.py
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file1_domain_range.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file1_domain_range.gif
deleted file mode 100644
index d0351e5..0000000
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file1_domain_range.gif
+++ /dev/null
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file1_scalar_functions.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file1_scalar_functions.gif
new file mode 100644
index 0000000..bea9c7b
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file1_scalar_functions.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file2_domain_range.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file2_domain_range.gif
new file mode 100644
index 0000000..6801e4f
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file2_domain_range.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file2_scalar_function_application.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file2_scalar_function_application.gif
deleted file mode 100644
index 831ec8e..0000000
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file2_scalar_function_application.gif
+++ /dev/null
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file3_parabola_example.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file3_parabola_example.gif
index 3fdecf4..af9e536 100644
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file3_parabola_example.gif
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file3_parabola_example.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file4_level_curves.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file4_level_curves.gif
new file mode 100644
index 0000000..b4ac106
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file4_level_curves.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file5_level_surface.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file5_level_surface.gif
new file mode 100644
index 0000000..e4dc80d
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file5_level_surface.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file6_scalar_function_application.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file6_scalar_function_application.gif
new file mode 100644
index 0000000..8bb176a
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file6_scalar_function_application.gif
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file4_neural_nets.gif b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file7_neural_nets.gif
index 9d24688..9d24688 100644
--- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file4_neural_nets.gif
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file7_neural_nets.gif