Upload scalar-functions Folder

9 files changed, 473 insertions, 0 deletions

diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/Scalar_Function_Quiz.pdf b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/Scalar_Function_Quiz.pdf
new file mode 100644
index 0000000..6d94a2c
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/Scalar_Function_Quiz.pdf
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/file1_domain_range.py
new file mode 100644
index 0000000..9b1ca7b
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file1_domain_range.py
@@ -0,0 +1,132 @@
+# 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)

+

+

+        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 = 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.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)

+

+

+    

+        

+        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))

+        self.wait(3)

+

+        self.wait(2)

+

+

+

+

+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 = Line(8*XTD*LEFT,1*YTD*UP+8*XTD*LEFT)

+        rangeline2 = Line(8*XTD*LEFT,1*YTD*DOWN+8*XTD*LEFT)

+        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)

+

+

+

+        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))

+        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/file2_scalar_function_application.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file2_scalar_function_application.py
new file mode 100644
index 0000000..56b3e53
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file2_scalar_function_application.py
@@ -0,0 +1,129 @@
+from manimlib.imports import *

+

+class ScalarApplication(ThreeDScene):

+    def construct(self):

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

+        

+        cube = Cube()

+        cube.set_fill(YELLOW_E, opacity = 0.1)

+        cube.scale(2)

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

+        self.play(ShowCreation(cube),ShowCreation(axes))

+        

+        dot = Sphere()

+        dot.scale(0.1)

+        dot.move_to(np.array([1,0.5,1]))

+        dot.set_fill(RED)

+

+        #dot = Dot(np.array([1,0.5,1]), color = RED)

+        temp_func = TextMobject("T(x,y,z)")

+        temp_func.next_to(dot,RIGHT)

+        temp_func.set_color(RED)

+        temp_func_trans = TextMobject("T(1,0.5,1)")

+        temp_func_trans.next_to(dot,RIGHT)

+        temp_func_trans.set_color(RED)

+        temp = TextMobject(r"$36 ^\circ$")

+        temp.next_to(dot,RIGHT)

+        temp.set_color(RED_E)

+

+

+        self.play(ShowCreation(dot))

+        self.play(ShowCreation(temp_func))

+        self.play(Transform(temp_func, temp_func_trans))

+        self.wait(1)

+        self.play(Transform(temp_func, temp))

+

+

+

+

+        dot1 = Sphere()

+        dot1.scale(0.1)

+        dot1.move_to(np.array([-1,-0.8,-1.5]))

+        dot1.set_fill(BLUE_E)

+        #dot1 = Dot(np.array([-1,-0.8,-1.5]), color = BLUE)

+        temp_func1 = TextMobject("T(x,y,z)")

+        temp_func1.next_to(dot1,LEFT)

+        temp_func1.set_color(BLUE)

+        temp_func_trans1 = TextMobject("T(-1,-0.8,-1.5)")

+        temp_func_trans1.next_to(dot1,LEFT)

+        temp_func_trans1.set_color(BLUE)

+        temp1 = TextMobject(r"$24 ^\circ$")

+        temp1.next_to(dot1,LEFT)

+        temp1.set_color(BLUE)

+

+        self.play(ShowCreation(dot1))

+        self.play(ShowCreation(temp_func1))

+        self.play(Transform(temp_func1, temp_func_trans1))

+        self.wait(1)

+        self.play(Transform(temp_func1, temp1))

+

+        self.play(FadeOut(temp_func))

+        self.play(FadeOut(temp_func1))

+

+

+        self.move_camera(phi=80* DEGREES,theta=45*DEGREES,run_time=3)

+

+        self.begin_ambient_camera_rotation(rate=0.2)

+        self.wait(4)

+        self.stop_ambient_camera_rotation()

+        self.wait(2)

+        

+

+

+

+class AddTempScale(Scene):

+    def construct(self):

+        temp_scale = ImageMobject("tempscale.png")

+        temp_scale.scale(4) 

+        temp_scale.move_to(2*RIGHT) 

+        self.play(ShowCreation(temp_scale))

+

+

+        temp_func = TextMobject("T(x,y,z)")

+        temp_func.move_to(3*UP +2*LEFT)

+        temp_func.set_color(RED)

+        temp_func_trans = TextMobject("T(1,0.5,1)")

+        temp_func_trans.move_to(3*UP +2*LEFT)

+        temp_func_trans.set_color(RED)

+        temp = TextMobject(r"$36 ^\circ$")

+        temp.set_color(RED)

+        temp.move_to(3*UP +2*LEFT)

+        temp.scale(0.7)

+

+        self.play(ShowCreation(temp_func))

+        self.play(Transform(temp_func, temp_func_trans))

+        self.wait(1)

+        self.play(Transform(temp_func, temp))

+        self.play(ApplyMethod(temp_func.move_to, 1.8*UP +1.8*RIGHT))

+

+        

+        temp_func1 = TextMobject("T(x,y,z)")

+        temp_func1.move_to(2*UP +2*LEFT)

+        temp_func1.set_color(BLUE)

+        temp_func_trans1 = TextMobject("T(-1,-0.8,-1.5)")

+        temp_func_trans1.move_to(2*UP +2*LEFT)

+        temp_func_trans1.set_color(BLUE)

+        temp1 = TextMobject(r"$24 ^\circ$")

+        temp1.set_color(BLUE)

+        temp1.move_to(2*UP +2*LEFT)

+        temp1.scale(0.7)

+        

+        self.play(ShowCreation(temp_func1))

+        self.play(Transform(temp_func1, temp_func_trans1))

+        self.wait(1)

+        self.play(Transform(temp_func1, temp1))

+        self.play(ApplyMethod(temp_func1.move_to, 0.6*UP +1.8*RIGHT))

+

+

+

+        transtext = TextMobject("Scalar Function Transform:")

+        transtext.set_color(GREEN)

+        transtext1 = TextMobject(r"$\mathbb{R}^3 \rightarrow \mathbb{R}$")

+        transtext1.set_color(YELLOW_E)

+        transtext.move_to(3*UP +3*LEFT)

+        transtext1.next_to(transtext,DOWN)

+        self.play(Write(transtext))

+        self.play(Write(transtext1))

+        self.wait(2)   

+

+

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
new file mode 100644
index 0000000..74dc063
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file3_parabola_example.py
@@ -0,0 +1,35 @@
+from manimlib.imports import *

+

+class Parabola(ThreeDScene):

+    def construct(self):

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

+

+        paraboloid = ParametricSurface(

+            lambda u, v: np.array([

+                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],

+            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[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)

+        text3d[1].set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE)

+

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

+        self.move_camera(phi=110* DEGREES,theta=45*DEGREES)

+        self.add(axes)

+        self.play(ShowCreation(paraboloid))

+        self.play(Write(text3d[0]))

+        self.play(Write(text3d[1]))

+        self.begin_ambient_camera_rotation(rate=0.2)

+        self.wait(3)

+        self.move_camera(phi=0 * DEGREES,theta=180*DEGREES,run_time=3)

+        self.wait(3)

+        self.move_camera(phi=110* DEGREES,theta=90*DEGREES,run_time=3)

+        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/file4_neural_nets.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_neural_nets.py
new file mode 100644
index 0000000..eb6bf45
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/file4_neural_nets.py
@@ -0,0 +1,177 @@
+from manimlib.imports import *

+

+class SigmoidFunc(GraphScene):

+    CONFIG = {

+    "x_min": -4,

+    "x_max": 4,

+    "y_min": -1,

+    "y_max": 1,

+    "graph_origin": ORIGIN + 0.8*DOWN,

+    "x_labeled_nums": list(range(-4, 5)),

+    "y_labeled_nums": list(range(-1, 2)),

+    "y_axis_height": 4.5,

+    }

+    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)

+

+        topic = TextMobject("Sigmoid Function")

+        topic.move_to(3.2*UP)

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

+

+        self.setup_axes(animate = True)

+        sigmoid_func = self.get_graph(lambda x : (1/(1 + np.exp(-x))), x_min = -4, x_max = 4)

+        sigmoid_lab = self.get_graph_label(sigmoid_func, label = r"\frac{1}{1 + e^{-z}}")

+

+        

+

+

+        self.play(ShowCreation(sigmoid_func),Write(sigmoid_lab))

+        self.play(Write(topic))

+        self.wait(2)

+        self.play(FadeOut(sigmoid_func), FadeOut(sigmoid_lab))

+        self.wait(1)

+        

+

+

+class NeuralNet(GraphScene):

+    def construct(self):

+

+        sigmoid_exp = TextMobject(r"g(z) = g($\theta^T$ X) = $\frac{1}{1 + e^{-z}}$")

+        sigmoid_exp.move_to(3*UP + 4*LEFT)

+        sigmoid_exp.scale(0.8)

+        sigmoid_exp.set_color(BLUE)

+        sigmoid_exp1 = TextMobject(r"Predict: 'y = 1'",r"When g(z) $\geq$ 0.5, z $\geq$ 0, $\theta^T$ X  $\geq$ 0")

+        sigmoid_exp2 = TextMobject(r"Predict: 'y = 0'", r"When g(z) $\leq$ 0.5, z $\leq$ 0, $\theta^T$ X  $\leq$ 0")

+        sigmoid_exp1.scale(0.5)

+        sigmoid_exp2.scale(0.5)

+        sigmoid_exp1.set_color(PURPLE)

+        sigmoid_exp2.set_color(PURPLE)

+

+        sigmoid_exp1[0].next_to(sigmoid_exp, 1.5*DOWN)

+        sigmoid_exp1[1].next_to(sigmoid_exp1[0], DOWN)

+        sigmoid_exp2[0].next_to(sigmoid_exp1[1], 1.5*DOWN)

+        sigmoid_exp2[1].next_to(sigmoid_exp2[0], DOWN)

+

+

+        self.play(Write(sigmoid_exp))

+        self.play(Write(sigmoid_exp1[0]), Write(sigmoid_exp1[1]))

+        self.play(Write(sigmoid_exp2[0]), Write(sigmoid_exp2[1]))

+        self.wait(2)

+

+

+        neuron1 = Circle()

+        neuron1.set_fill(YELLOW_A, opacity = 0.5)

+

+        neuron2 = Circle()

+        neuron2.set_fill(ORANGE, opacity = 0.5)

+

+        neuron3 = Circle()

+        neuron3.set_fill(GREEN_E, opacity = 0.5)

+

+        neuron1.move_to(2*UP+RIGHT)

+        neuron2.move_to(2*DOWN+RIGHT)

+        neuron3.move_to(4*RIGHT)

+

+        arrow1 = Arrow(neuron1.get_right(),neuron3.get_left(),buff=0.1)

+        arrow1.set_color(RED)

+        arrow2 = Arrow(neuron2.get_right(),neuron3.get_left(),buff=0.1)

+        arrow2.set_color(RED)

+

+        arrow3 = Arrow(neuron3.get_right(),7*RIGHT,buff=0.1)

+        arrow3.set_color(RED)

+

+

+        sign1 = TextMobject("+1")

+        sign1.move_to(2*UP+RIGHT)

+        sign1.scale(2)

+        sign2 = TextMobject(r"$x_1$")

+        sign2.move_to(2*DOWN+RIGHT)

+        sign2.scale(2)

+        sign3 = TextMobject(r"$h_{\theta}(x)$")

+        sign3.move_to(6*RIGHT+0.4*DOWN)

+        sign3.scale(0.7)

+        sign4 = TextMobject(r"$= g(10 - 20x_1)$")

+        sign4.next_to(sign3,DOWN)

+        sign4.scale(0.5)

+        sign5 = TextMobject(r"$= g(10 - 20x_1)$")

+        sign5.next_to(sign3,DOWN)

+        sign5.scale(0.5)

+        sign6 = TextMobject(r"$= g(10 - 20x_1)$")

+        sign6.next_to(sign3,DOWN)

+        sign6.scale(0.5) 

+

+

+        weight1 = TextMobject("10")

+        weight1.next_to(arrow1,UP)

+        weight2 = TextMobject("-20")

+        weight2.next_to(arrow2,DOWN)

+

+        gate = TextMobject("NOT GATE")

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

+        gate.scale(1.5)

+        gate.move_to(3*RIGHT+3.5*UP)

+

+

+

+        truth_table = TextMobject(r"\begin{displaymath}\begin{array}{|c|c|} x & y\\ \hline 1 & 0 \\0 & 1 \\\end{array}\end{displaymath}")

+        truth_table.next_to(sigmoid_exp2[1], 3*DOWN)

+

+        values = TextMobject("1", "0")

+        values.scale(2)

+

+        sign4_trans1 = TextMobject(r"$= g(10 - 20(1))$")

+        sign4_trans2 = TextMobject(r"$= g(10 - 20(0))$")

+        sign4_trans1.next_to(sign3,DOWN)

+        sign4_trans2.next_to(sign3,DOWN)

+        sign4_trans1.scale(0.5)

+        sign4_trans2.scale(0.5)

+

+

+

+        output1 = TextMobject("y = 0")

+        output2 = TextMobject("y = 1")

+        output1.next_to(sign4,DOWN)

+        output2.next_to(sign4,DOWN)

+        output1.scale(1.5)

+        output2.scale(1.5)

+

+

+

+        self.play(ShowCreation(neuron1),ShowCreation(neuron2))

+        self.play(ShowCreation(neuron3))

+        self.play(ShowCreation(sign1),ShowCreation(sign2))

+        self.wait(1)

+

+        self.play(GrowArrow(arrow1))

+        self.play(GrowArrow(arrow2))

+        self.play(ShowCreation(weight1),ShowCreation(weight2))

+

+

+        

+        self.play(GrowArrow(arrow3))

+        self.play(Write(sign3),Write(sign4))

+

+        self.play(Write(gate))

+        self.play(ShowCreation(truth_table))

+

+        self.play(ApplyMethod(values[0].move_to, 2*DOWN+RIGHT))

+        self.play(FadeOut(values[0]))

+        self.play(Transform(sign4,sign4_trans1))

+        self.play(Write(output1))

+        self.wait(1)

+        self.play(FadeOut(output1))

+        self.play(Transform(sign4, sign5))

+        

+

+        self.play(ApplyMethod(values[1].move_to, 2*DOWN+RIGHT))

+        self.play(FadeOut(values[1]))

+        self.play(Transform(sign4,sign4_trans2))

+        self.play(Write(output2))

+        self.wait(1)

+        self.play(FadeOut(output2))

+        self.play(Transform(sign4, sign6))

+        

+        self.wait(2)

+

+

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
new file mode 100644
index 0000000..d0351e5
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file1_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
new file mode 100644
index 0000000..831ec8e
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/scalar-functions/gifs/file2_scalar_function_application.gif
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
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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/file4_neural_nets.gif
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