2 files changed, 237 insertions, 0 deletions
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..8d9bd20
--- /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("#8b000c")
+        dot0_lab = TextMobject(r"$f(a)$", color = "#8b000c").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), ShowCreation(line))
+        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.bring_to_front(dot0)
+        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/file2_domain_range.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file2_domain_range.py
new file mode 100644
index 0000000..919e68b
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file2_domain_range.py
@@ -0,0 +1,187 @@
+# Plotting Graphs
+from manimlib.imports import *
+
+class PlotGraphs(GraphScene):
+    CONFIG = {
+    "x_min": -5,
+    "x_max": 5,
+    "y_min": 0,
+    "y_max": 4,
+    "graph_origin": ORIGIN + 2.5* DOWN,
+    "x_labeled_nums": list(range(-5, 6)),
+    "y_labeled_nums": list(range(0, 5)),
+    }
+    def construct(self):
+
+        topic = TextMobject("Domain and Range")
+        topic.scale(2)
+        topic.set_color(YELLOW)
+        self.play(Write(topic))
+        self.play(FadeOut(topic))
+        self.wait(1)
+
+        scalar_func_R = TextMobject(r"Scalar Valued Functions in $\mathbb{R}$").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)
+
+        self.setup_axes(animate = True)
+
+        graphobj = self.get_graph(lambda x :  np.sqrt(x + 4), x_min = -4, x_max = 5)
+        graph_lab = self.get_graph_label(graphobj, label = r"\sqrt{x + 4}")
+
+
+        rangeline1 = Arrow(self.graph_origin+2.2*YTD*UP+5*XTD*LEFT, self.graph_origin+4.1*YTD*UP+5*XTD*LEFT)
+        rangeline2 = Arrow(self.graph_origin+1.7*YTD*UP+5*XTD*LEFT, self.graph_origin+5*XTD*LEFT)
+        rangeline1.set_color(RED)
+        rangeline2.set_color(RED)
+
+        rangeMsg = TextMobject(r"Range: $y \geq 0$")
+        rangeMsg.move_to(self.graph_origin+2*YTD*UP+5*XTD*LEFT)
+        rangeMsg.scale(0.5)
+        rangeMsg.set_color(YELLOW)
+
+        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)
+
+        domainMsg = TextMobject(r"Domain: $x \geq -4$")
+        domainMsg.move_to(self.graph_origin+0.6*YTD*DOWN)
+        domainMsg.scale(0.5)
+        domainMsg.set_color(GREEN)
+
+        domain_subset = TextMobject(r"Domain $\subset \mathbb{R}$", color = PURPLE).scale(0.7).move_to(self.graph_origin+3.5*YTD*UP+2*XTD*RIGHT)
+    
+        
+        self.play(ShowCreation(graphobj))
+        self.play(ShowCreation(graph_lab))
+        self.wait(1)
+        self.play(GrowArrow(rangeline1))
+        self.play(GrowArrow(rangeline2))
+        self.play(Write(rangeMsg))
+        self.wait(1)
+        self.play(GrowArrow(domainline1))
+        self.play(GrowArrow(domainline2))
+        self.play(Write(domainMsg), Write(domain_subset))
+        self.wait(3)
+
+
+
+
+class PlotSineGraphs(GraphScene):
+    CONFIG = {
+    "x_min": -8,
+    "x_max": 8,
+    "y_min": -1,
+    "y_max": 1,
+    "graph_origin": ORIGIN,
+    "x_labeled_nums": list(range(-8, 9)),
+    "y_labeled_nums": list(range(-1, 2)),
+    }
+    def construct(self):
+        
+
+
+        XTD = self.x_axis_width/(self.x_max- self.x_min)
+        YTD = self.y_axis_height/(self.y_max- self.y_min)
+
+        self.setup_axes(animate = True)
+
+        sineobj = self.get_graph(lambda x :  np.sin(x), x_min = -7, x_max = 8)
+        sine_lab = self.get_graph_label(sineobj, label = "\\sin(x)")
+
+
+        rangeline1 = Arrow(8*XTD*LEFT,1*YTD*UP+8*XTD*LEFT, buff = 0)
+        rangeline2 = Arrow(8*XTD*LEFT,1*YTD*DOWN+8*XTD*LEFT, buff = 0)
+        rangeline1.set_color(RED)
+        rangeline2.set_color(RED)
+
+        rangeMsg = TextMobject(r"Range: $-1 \leq y \leq  1$")
+        rangeMsg.move_to(1.1*YTD*UP+8.5*XTD*LEFT)
+        rangeMsg.scale(0.5)
+        rangeMsg.set_color(YELLOW)
+
+
+        domainline1 = Arrow(1.1*YTD*DOWN+2*XTD*LEFT, 1.1*YTD*DOWN + 8.5*XTD*LEFT)
+        domainline2 = Arrow(1.1*YTD*DOWN+2*XTD*RIGHT, 1.1*YTD*DOWN + 8.5*XTD*RIGHT)
+        domainline1.set_color(PINK)
+        domainline2.set_color(PINK)
+
+        domainMsg = TextMobject(r"Domain: $[-\infty, \infty]$")
+        domainMsg.move_to(1.1*YTD*DOWN)
+        domainMsg.scale(0.5)
+        domainMsg.set_color(GREEN)
+
+        domain_subset = TextMobject(r"Domain $\subseteq \mathbb{R}$", color = PURPLE).scale(0.7).move_to(self.graph_origin+0.8*YTD*UP+4.5*XTD*RIGHT)
+
+        self.play(ShowCreation(sineobj))
+        self.play(ShowCreation(sine_lab))
+        self.wait(1)
+        self.play(GrowArrow(rangeline1))
+        self.play(GrowArrow(rangeline2))
+        self.play(Write(rangeMsg))
+        self.wait(1)
+        self.play(GrowArrow(domainline1))
+        self.play(GrowArrow(domainline2))
+        self.play(Write(domainMsg), Write(domain_subset))
+        self.wait(3)
+
+
+        
+
+        
+class Paraboloid(ThreeDScene):
+    def construct(self):
+
+        scalar_func_R2 = TextMobject(r"Scalar Valued Functions in $\mathbb{R}^2$").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"$Domain: \mathbb{R}^2$", 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