From 2fb88c2ae4a8218572ec276e80d80c3cdadd5fbb Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Sat, 27 Jun 2020 19:44:01 +0530 Subject: Update file3_Degenerate_Hessian_Matrix.py --- .../file3_Degenerate_Hessian_Matrix.py | 21 +++++---------------- 1 file changed, 5 insertions(+), 16 deletions(-) (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file3_Degenerate_Hessian_Matrix.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file3_Degenerate_Hessian_Matrix.py index 732ef4f..9310553 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file3_Degenerate_Hessian_Matrix.py +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file3_Degenerate_Hessian_Matrix.py @@ -17,22 +17,13 @@ class DegenerateHessian(ThreeDScene): lambda u, v: np.array([ u, v, - -4*u**3-v**3 - ]),u_min = -0.8, u_max = 0.8, v_min = -0.8, v_max = 0.8).set_color(TEAL).shift([0,1,0]).scale(1.3) - - #---- function f(x,y) - zoom_surface = ParametricSurface( - lambda u, v: np.array([ - u, - v, - -4*u**3-v**3 - ]),u_min = -0.8, u_max = 0.8, v_min = -0.8, v_max = 0.8).set_color(TEAL).shift([0,1,0]).scale(2.5) + -u**4-v**4 + ]),u_min = -0.8, u_max = 0.8, v_min = -0.8, v_max = 0.8).set_color(TEAL).shift([0,0,-0.5]).scale(2) f_text= TextMobject("surface of the function").to_corner(UL).scale(0.5) - d = Dot(color = "#800000").shift([0,1,0]) #---- critical point - d2 = Dot(color = "#800000").shift([0,0.7,0]) #---- critical point - plane = Rectangle(color = YELLOW,fill_opacity= 0.3).shift([0,0.6,0]).rotate(m.radians(90)).scale(0.4) + d = Dot(color = "#800000").shift([0,0,-0.5]) #---- critical point + plane = Square(color = YELLOW,fill_opacity= 0.2).shift([0,0,-0.5]).scale(1.3) self.set_camera_orientation(phi = 70*DEGREES, theta = 45*DEGREES) self.add_fixed_in_frame_mobjects(heading) @@ -49,8 +40,6 @@ class DegenerateHessian(ThreeDScene): self.add_fixed_in_frame_mobjects(f_text) self.wait(1) self.play(Write(d)) - self.wait(1) - self.play(ReplacementTransform(f_surface,zoom_surface),ReplacementTransform(d,d2)) - self.wait(2) + self.wait(1) self.play(Write(plane)) self.wait(1) -- cgit From 7d8096521d44ae96be2aac0d8c87b3eb55948185 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Sat, 27 Jun 2020 19:45:05 +0530 Subject: Delete file4_Contour_Diagram.gif --- .../file4_Contour_Diagram.gif | Bin 1150777 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.gif deleted file mode 100644 index 129fedc..0000000 Binary files a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.gif and /dev/null differ -- cgit From 5520bb3fa19ef395385c52a78cac00c286e0be6a Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Sat, 27 Jun 2020 19:45:26 +0530 Subject: Update README.md --- .../The-Second-Derivative-Test/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/README.md b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/README.md index e9cc918..daf49f2 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/README.md +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/README.md @@ -15,7 +15,7 @@ file3_Degenerate_Hessian_Matrix -![file3_Degenerate_Hessian_Matrix](https://github.com/vnb09/FSF-mathematics-python-code-archive/blob/fsf_tasks/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file3_Degenerate_Hessian_Matrix.gif?raw=true) +![file3_Degenerate_Hessian_Matrix](?raw=true)



-- cgit From 03b84adf2345c2dc1cc63eaa29021b9a7ff024be Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Sat, 27 Jun 2020 19:46:36 +0530 Subject: Delete file3_Degenerate_Hessian_Matrix.gif --- .../file3_Degenerate_Hessian_Matrix.gif | Bin 652724 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file3_Degenerate_Hessian_Matrix.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file3_Degenerate_Hessian_Matrix.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file3_Degenerate_Hessian_Matrix.gif deleted file mode 100644 index 36fd25c..0000000 Binary files a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file3_Degenerate_Hessian_Matrix.gif and /dev/null differ -- cgit From 1d4cf4cda4dc6c778c8339532e8baad5badfd9f1 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Sat, 27 Jun 2020 19:47:28 +0530 Subject: Add files via upload --- .../file3_Degenerate_Hessian_Matrix.gif | Bin 0 -> 407350 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file3_Degenerate_Hessian_Matrix.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file3_Degenerate_Hessian_Matrix.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file3_Degenerate_Hessian_Matrix.gif new file mode 100644 index 0000000..5aae300 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file3_Degenerate_Hessian_Matrix.gif differ -- cgit From 8b578d7993f33115aaa3259be85ed87ab71466cb Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Sat, 27 Jun 2020 19:48:48 +0530 Subject: Update README.md --- .../The-Second-Derivative-Test/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/README.md b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/README.md index daf49f2..e9cc918 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/README.md +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/README.md @@ -15,7 +15,7 @@ file3_Degenerate_Hessian_Matrix -![file3_Degenerate_Hessian_Matrix](?raw=true) +![file3_Degenerate_Hessian_Matrix](https://github.com/vnb09/FSF-mathematics-python-code-archive/blob/fsf_tasks/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file3_Degenerate_Hessian_Matrix.gif?raw=true)



-- cgit From c53b6cd7e1a10b0e5c4f12801412646fd17569c8 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Sun, 28 Jun 2020 02:05:21 +0530 Subject: Add files via upload --- .../file4_Contour_Diagram.gif | Bin 0 -> 1140109 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.gif new file mode 100644 index 0000000..41068e2 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.gif differ -- cgit From 7650a4ad8777a8a979c4899c1e0d852bd5111be8 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Sun, 28 Jun 2020 02:06:42 +0530 Subject: Update README.md --- .../The-Second-Derivative-Test/README.md | 6 ++++++ 1 file changed, 6 insertions(+) (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/README.md b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/README.md index e9cc918..96b32bf 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/README.md +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/README.md @@ -19,3 +19,9 @@



+file4_Contour_Diagram + +![file4_Contour_Diagram](https://github.com/vnb09/FSF-mathematics-python-code-archive/blob/fsf_tasks/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/The-Second-Derivative-Test/file4_Contour_Diagram.gif?raw=true) +

+

+ -- cgit From f78f8e6889c00cc3d9ec4e0094fb8417cdf74240 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Mon, 29 Jun 2020 00:42:54 +0530 Subject: Delete file1_Extrema_over_g(x,y)=k.gif --- .../file1_Extrema_over_g(x,y)=k.gif | Bin 499796 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.gif deleted file mode 100644 index 1e1782e..0000000 Binary files a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.gif and /dev/null differ -- cgit From a4c28a866815b0b2687e3baf2d1dbc96a7039324 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Mon, 29 Jun 2020 00:43:56 +0530 Subject: Update file1_Extrema_over_g(x,y)=k.py --- .../Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py | 15 +++++++++------ 1 file changed, 9 insertions(+), 6 deletions(-) (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py index 17f31ac..17ba858 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py @@ -1,14 +1,18 @@ from manimlib.imports import* +import math as m class firstScene(ThreeDScene): def construct(self): - axes = ThreeDAxes() + axes = ThreeDAxes().fade(0.4) + label_x = TextMobject("$x$").shift([5.5,-0.5,0]).fade(0.4) #---- x axis + label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5).fade(0.4) #---- y axis + surface = ParametricSurface( lambda u, v: np.array([ u, v, u**2+v**2+u**3-v**3 - ]),u_min=-0.5,u_max=0.5, v_min=-0.5,v_max=0.5).scale(5).shift([0,1,2.5]).set_color('#F0FFFF').fade(0.4) + ]),u_min=-0.5,u_max=0.5, v_min=-0.5,v_max=0.5).scale(5).shift([0,1,2.5]).set_color(TEAL).fade(0.4) c = Circle().set_color('#FF00FF').shift([-0.4,0,1.5]).rotate(1.9,UP).scale(0.7) @@ -26,10 +30,11 @@ class firstScene(ThreeDScene): max_text = TextMobject("maximum over $g(x,y)=k$",color = '#FFA074').shift([-1.7,0,0]).scale(0.5).shift(2.2*UP) min_text = TextMobject("minimum over $g(x,y)=k$",color = '#FFA074').shift([2.5,0.5,1]).scale(0.5).shift(0.5*UP) label_f = TextMobject("$z=f(x,y)$",color = '#8A2BE2').scale(0.5).shift(3*UP+3*RIGHT) - label_g = TextMobject("$g(x,y)=k$",color = '#8A2BE2').scale(0.5).shift(2*RIGHT) - + label_g = TextMobject("$g(x,y)=k$",color = '#8A2BE2').scale(0.5).shift(2*RIGHT) self.add(axes) + self.add(label_x) + self.add(label_y) self.set_camera_orientation(phi=75*DEGREES,theta=45*DEGREES) self.play(Write(surface)) self.add_fixed_in_frame_mobjects(label_f) @@ -49,5 +54,3 @@ class firstScene(ThreeDScene): self.play(Write(maxima_refl)) self.play(Write(minima_refl)) self.wait(1) - - -- cgit From 838dfb6f044db8a1ec2b0bfeb191632cfd60054f Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Mon, 29 Jun 2020 00:51:08 +0530 Subject: Add files via upload --- .../file1_Extrema_over_g(x,y)=k.gif | Bin 0 -> 595677 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.gif new file mode 100644 index 0000000..9d64d50 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.gif differ -- cgit From 076b497787e65f119430837acf8d8b812c82003c Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Mon, 29 Jun 2020 00:57:02 +0530 Subject: Update file1_Extrema_over_g(x,y)=k.py --- .../Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py index 17ba858..da17aac 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file1_Extrema_over_g(x,y)=k.py @@ -1,7 +1,8 @@ from manimlib.imports import* import math as m -class firstScene(ThreeDScene): +#---- optimizing funtion f(x,y) w.r.t to g(x,y) +class ConstrainedExtrema(ThreeDScene): def construct(self): axes = ThreeDAxes().fade(0.4) label_x = TextMobject("$x$").shift([5.5,-0.5,0]).fade(0.4) #---- x axis -- cgit From 7638fde966190d0cdd22d763767df7551ccd980d Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Mon, 29 Jun 2020 16:05:43 +0530 Subject: Delete file2_Geometric_Proof.gif --- .../Lagrange-Multipliers/file2_Geometric_Proof.gif | Bin 419262 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.gif deleted file mode 100644 index b22afb3..0000000 Binary files a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.gif and /dev/null differ -- cgit From 85875270cfe25fe3e5b666fe45a76eece2419452 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Mon, 29 Jun 2020 16:15:49 +0530 Subject: Update file2_Geometric_Proof.py --- .../Lagrange-Multipliers/file2_Geometric_Proof.py | 48 ++++++++++++++++------ 1 file changed, 35 insertions(+), 13 deletions(-) (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.py index 4374ff7..2c2a9de 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.py +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Lagrange-Multipliers/file2_Geometric_Proof.py @@ -1,8 +1,12 @@ from manimlib.imports import* -class firstScene(ThreeDScene): +#---- visualization of geometric proof of Lagrange multiplier +class GeometricProof(ThreeDScene): def construct(self): - axes = ThreeDAxes().scale(0.7).rotate(math.radians(180)) + axes = ThreeDAxes().scale(0.7).rotate(math.radians(180)) + label_x = TextMobject("$x$").shift(4*RIGHT).fade(0.4) #---- x axis + label_y = TextMobject("$y$").shift(3.2*DOWN+0.2*RIGHT).rotate(math.radians(180)).fade(0.4) #---- y axis + surface = ParametricSurface( lambda u, v: np.array([ 1*np.sin(u)*np.cos(v), @@ -11,15 +15,16 @@ class firstScene(ThreeDScene): ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[GREEN_C, GREEN_E]).scale(1).shift([-1.5,-1.5,0]) d = Dot([-2,-2.55,0],color = '#800000') - a_df = Arrow(color = '#00FFFF').rotate(-2).shift(3.2*DOWN+2.3*LEFT) #---- f parallel to g - a_dg = Arrow(color = '#FF00FF').scale(0.8).shift(3.2*DOWN+2.3*LEFT).rotate(-2) #---- f parallel to g + a_df = Arrow(color = '#00FFFF').rotate(-2).shift(3.2*DOWN+2.3*LEFT) #---- f parallel to g at maxima + a_dg = Arrow(color = '#FF00FF').scale(0.8).shift(3.2*DOWN+2.3*LEFT).rotate(-2) #---- g parallel to f at maxima - b_df = Arrow(color = '#00FFFF').rotate(1.1).shift(0.82*LEFT+0.15*UP) #---- f parallel to g - b_dg = Arrow(color = '#FF00FF').scale(0.6).rotate(-2).shift(1.43*LEFT+1.1*DOWN) #---- f parallel to g + b_dg = Arrow(color = '#00FFFF').rotate(1.1).shift(0.82*LEFT+0.15*UP) #---- g parallel to f at minima + b_df = Arrow(color = '#FF00FF').scale(0.6).rotate(-2).shift(1.43*LEFT+1.1*DOWN) #---- f parallel to g at minima qd = Dot(color = '#800000').shift(1.2*LEFT+0.6*DOWN) + #---- level curves l1 = Line([-1,-3.1,0],[-4,-3.1,0],color = PINK).rotate(-0.3).fade(0.6) l2 = Line([-0.9,-2.9,0],[-4,-2.9,0],color = PINK).rotate(-0.3).fade(0.6) l3= Line([-0.8,-2.7,0],[-4,-2.7,0],color = PINK).rotate(-0.3).fade(0.6) @@ -36,19 +41,36 @@ class firstScene(ThreeDScene): l14= Line([-0,-0.35,0],[-4,-0.35,0],color = PINK).rotate(-0.3).fade(0.6) l15= Line([-0.,-0.15,0],[-4,-0.15,0],color = PINK).rotate(-0.3).fade(0.6) - level_Curve = VGroup(l1,l2,l3,l4,l5,l6,l7,l8,l9,l10,l11,l12,l13,l14,l15) - rel_text = TextMobject("$\\nabla f = \\lambda \\nabla g$",color = TEAL).shift([3,3.2,0]).scale(0.5) f_text = TextMobject("$\\nabla f$",color = '#800000').shift([1,1,0]).scale(0.5) g_text = TextMobject("$\\nabla g$").shift([1.2,-0.8,0]).scale(0.5) p_text= TextMobject("$P$").shift([1.8,2.6,0]).scale(0.5) - - - self.add(axes) + #---- labelling of level curves + l1_text = TextMobject("$w=$ 17").rotate(math.radians(180)).scale(0.4).shift(2.7*DOWN+4.36*LEFT) + l2_text = TextMobject("$w=$ 16").rotate(math.radians(180)).scale(0.4).shift(2.46*DOWN+4.36*LEFT) + l3_text = TextMobject("$w=$ 15").rotate(math.radians(180)).scale(0.4).shift(2.2*DOWN+4.36*LEFT) + l4_text = TextMobject("$w=$ 14").rotate(math.radians(180)).scale(0.4).shift(1.97*DOWN+4.36*LEFT) + l5_text = TextMobject("$w=$ 13").rotate(math.radians(180)).scale(0.4).shift(1.74*DOWN+4.36*LEFT) + l6_text = TextMobject("$w=$ 12").rotate(math.radians(180)).scale(0.4).shift(1.5*DOWN+4.36*LEFT) + l7_text = TextMobject("$w=$ 11").rotate(math.radians(180)).scale(0.4).shift(1.26*DOWN+4.36*LEFT) + l8_text = TextMobject("$w=$ 10").rotate(math.radians(180)).scale(0.4).shift(1.05*DOWN+4.36*LEFT) + l9_text = TextMobject("$w=$ 9").rotate(math.radians(180)).scale(0.4).shift(0.8*DOWN+4.32*LEFT) + l10_text = TextMobject("$w=$ 8").rotate(math.radians(180)).scale(0.4).shift(0.6*DOWN+4.32*LEFT) + l11_text = TextMobject("$w=$ 7").rotate(math.radians(180)).scale(0.4).shift(0.4*DOWN+4.32*LEFT) + l12_text = TextMobject("$w=$ 6").rotate(math.radians(180)).scale(0.4).shift(0.2*DOWN+4.32*LEFT) + l13_text = TextMobject("$w=$ 5").rotate(math.radians(180)).scale(0.4).shift(-0.02*DOWN+4.32*LEFT) + l14_text = TextMobject("$w=$ 4").rotate(math.radians(180)).scale(0.4).shift(-0.23*DOWN+4.32*LEFT) + l15_text = TextMobject("$w=$ 3").rotate(math.radians(180)).scale(0.4).shift(-0.44*DOWN+4.32*LEFT) + + level_Curve = VGroup(l1,l1_text,l2,l2_text,l3,l3_text,l4,l4_text,l5,l5_text,l6,l6_text,l7,l7_text,l8,l8_text,l9,l9_text,l10,l10_text,l11,l11_text,l12,l12_text,l13,l13_text,l14,l14_text,l15,l15_text) + self.set_camera_orientation(phi=0 * DEGREES, theta = 90*DEGREES) + self.add(axes) + self.add(label_x) + self.add(label_y) self.play(Write(surface)) self.wait(1) self.play(ShowCreation(level_Curve)) @@ -61,8 +83,8 @@ class firstScene(ThreeDScene): self.play(Write(qd)) self.wait(1) self.play(ShowCreation(b_df)) - self.play(ShowCreation(b_dg)) - self.wait(1) self.add_fixed_in_frame_mobjects(f_text) + self.wait(1) + self.play(ShowCreation(b_dg)) self.add_fixed_in_frame_mobjects(g_text) self.wait(1) -- cgit From 2fc0bbf646c2aaf31d3e1f578a6427012b4a214e Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 00:39:05 +0530 Subject: Delete file1_Visualization_of_dz.gif --- .../Total-Differential/file1_Visualization_of_dz.gif | Bin 558983 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.gif deleted file mode 100644 index e00a946..0000000 Binary files a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.gif and /dev/null differ -- cgit From 1d775364041157dbe2db000676ec2e185c0ccb84 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 00:42:21 +0530 Subject: Update file1_Visualization_of_dz.py --- .../file1_Visualization_of_dz.py | 80 ++++++++++++++-------- 1 file changed, 52 insertions(+), 28 deletions(-) (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.py index a097a96..2a1a750 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.py +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.py @@ -1,53 +1,77 @@ from manimlib.imports import* - -class firstScene(ThreeDScene): - +#---- visualization of the differential dz between two points on the surface of the function +class differentialdz(ThreeDScene): def construct(self): - - axes = ThreeDAxes().rotate(1.571) + + axes = ThreeDAxes() + label_x = TextMobject("$x$").shift([5.5,-0.3,0]).fade(0.4) #---- x axis + label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5).fade(0.4) #---- y axis + surface = ParametricSurface( lambda u, v: np.array([ u, v, u**2+v**2 - ]),u_min=-1,u_max=1, v_min=-1,v_max=1).set_color("#FF69B4").fade(0.6).scale(2).shift(3*UP+1*LEFT) + ]),u_min=-1,u_max=1, v_min=-1,v_max=1).set_color("#FF69B4").shift([0,2.5,0.3]).scale(1.2) #----surface z = f(x,y) + - d = Dot([1.4,1.75,1],color = '#00FFFF').rotate(1.571,UP) - d2 = Dot([2,2,1],color = '#00FFFF').rotate(1.571,UP) + + plane = Rectangle(color = '#E6E6FA',fill_opacity = 1).scale(3).shift(-1*RIGHT+3*UP).fade(0.9) #---- x-y plane + + d = Dot([1,2,1],color = '#9400D3').rotate(1.571,UP) #---- point on the surface + d2 = Dot([2,2.9,1],color = '#9400D3').rotate(1.571,UP) #---- point on the surface p1 = TextMobject("$P_1$",color ='#ADFF2F').scale(0.6).shift(2*RIGHT+1*UP) - p2 = TextMobject("$P_2$",color = '#ADFF2F').scale(0.6).shift(2.6*RIGHT+0.9*UP) + p2 = TextMobject("$P_2$",color = '#ADFF2F').scale(0.6).shift(2.6*RIGHT+0.4*UP) - l = DashedLine(color = '#800000').rotate(1.571,UP).scale(1).shift(1.7*UP+1.6*RIGHT) - l2 = DashedLine(color = '#800000').rotate(1.571,UP).scale(0.8).shift(2.26*UP+1.2*RIGHT) - l_text = TextMobject("$(x_1,y_1)$",color = '#ADFF2F').scale(0.6).shift(2*RIGHT+1.6*DOWN) - l2_text = TextMobject("$(x_2,y_2)$",color = '#ADFF2F').scale(0.6).shift(2.7*RIGHT+1.2*DOWN) + l1 = DashedLine(color = '#00BFFF').scale(1.6).shift(3.5*UP+3.25*LEFT).rotate(1.571) + l2 = DashedLine(color = '#00BFFF').scale(1).shift(4*UP+2*LEFT).rotate(1.571) - a = Arrow(color = '#FFFACD').scale(0.7).rotate(1.38,RIGHT).shift(2.5*LEFT+3.1*UP) + label_dz= TextMobject("$dz$").scale(0.4).shift(5.3*RIGHT+0.4*UP) - a_text = TextMobject("$dz$",color='#800000').scale(0.5).shift(2.3*RIGHT+0.5*UP) - plane = Rectangle(color = '#E6E6FA',fill_opacity = 1).scale(3).shift(1*RIGHT+3*UP).fade(0.9) + l3 = Line(color = '#FFDAB9').scale(0.8).shift(1.95*UP+0.7*RIGHT).rotate(1.571,DOWN).fade(0.2) + l4 = Line(color = '#FFDAB9').scale(0.6).shift(2.86*UP+0.9*RIGHT).rotate(1.571,DOWN).fade(0.2) - label = TextMobject("$z = f(x,y)$").scale(0.6).shift(3.5*RIGHT+1.8*UP) - + line_y1 = DashedLine(color = '#00BFFF').scale(1.3).shift(0.82*UP+3.25*RIGHT).rotate(1.571) + line_y2 = DashedLine(color = '#00BFFF').scale(1.7).shift(1.2*UP+2.8*RIGHT).rotate(1.571) + + label_dy= TextMobject("$dy$").scale(0.6).shift(3*RIGHT+0.8*DOWN).rotate(math.radians(90)) + + line_x1 = DashedLine(color = '#00BFFF').scale(1.5).shift(2.2*UP+1.6*RIGHT).rotate(1.571,RIGHT) + line_x2 = DashedLine(color = '#00BFFF').scale(1.2).shift(2.9*UP+1.6*RIGHT).rotate(1.571,RIGHT) + + label_dx= TextMobject("$dx$").scale(0.4).shift(-0.4*UP+2.5*RIGHT) + + label = TextMobject("$f(x,y)$").scale(0.6).shift(4*RIGHT+3*UP) + + + self.set_camera_orientation(phi=75*DEGREES,theta=10*DEGREES) self.add(axes) - self.set_camera_orientation(phi=75*DEGREES,theta=-10*DEGREES) - self.wait(1) + self.add(label_x) + self.add(label_y) self.play(Write(plane)) - self.play(Write(surface)) + self.play(Write(surface)) self.add_fixed_in_frame_mobjects(label) self.wait(1) - self.play(ShowCreation(l),ShowCreation(l2),Write(d),Write(d2)) - self.wait(1) + self.play(Write(d),Write(d2)) self.add_fixed_in_frame_mobjects(p1) self.add_fixed_in_frame_mobjects(p2) self.wait(1) - self.add_fixed_in_frame_mobjects(l_text) - self.add_fixed_in_frame_mobjects(l2_text) - self.play(ShowCreation(a)) + self.play(Write(l1)) + self.play(Write(l2)) + self.add_fixed_in_frame_mobjects(label_dz) + self.wait(1) + self.play(Write(l3)) + self.play(Write(l4)) + self.wait(1) + self.play(Write(line_y1)) + self.play(Write(line_y2)) + self.play(ShowCreation(label_dy)) + self.wait(1) + self.play(Write(line_x1)) + self.play(Write(line_x2)) + self.add_fixed_in_frame_mobjects(label_dx) self.wait(1) - self.add_fixed_in_frame_mobjects(a_text) - self.wait(2) -- cgit From ab75cfbbfbf634b6f06f7687d8defc9ab35038b1 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 00:43:20 +0530 Subject: Delete file2_Differentials.gif --- .../Total-Differential/file2_Differentials.gif | Bin 576535 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif deleted file mode 100644 index 620b49e..0000000 Binary files a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif and /dev/null differ -- cgit From 29fdeb06d1c7c7eaf740332dbcc28e33a98bc7f8 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 00:45:13 +0530 Subject: Delete file3_Total_differential_of_z.gif --- .../file3_Total_differential_of_z.gif | Bin 732678 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file3_Total_differential_of_z.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file3_Total_differential_of_z.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file3_Total_differential_of_z.gif deleted file mode 100644 index 5aae2a1..0000000 Binary files a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file3_Total_differential_of_z.gif and /dev/null differ -- cgit From 8fcc588bd40a5d8ea4daa24d9b4056598df5c96a Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 00:46:16 +0530 Subject: Add files via upload --- .../Total-Differential/file1_Visualization_of_dz.gif | Bin 0 -> 565199 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.gif new file mode 100644 index 0000000..2e148af Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.gif differ -- cgit From 042395420527585b7880fc2690d236d607c3467f Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 00:50:51 +0530 Subject: Update file1_Visualization_of_dz.py --- .../file1_Visualization_of_dz.py | 80 +++++++++------------- 1 file changed, 31 insertions(+), 49 deletions(-) (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.py index 2a1a750..1fdd0b9 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.py +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.py @@ -1,77 +1,59 @@ from manimlib.imports import* -#---- visualization of the differential dz between two points on the surface of the function -class differentialdz(ThreeDScene): +#---- visualization of total differential dz between two points lying on the surface of the function +class differentialdz(ThreeDScene): + def construct(self): - - axes = ThreeDAxes() - label_x = TextMobject("$x$").shift([5.5,-0.3,0]).fade(0.4) #---- x axis + + axes = ThreeDAxes() + label_x = TextMobject("$x$").shift([5.5,-0.5,0]).fade(0.4) #---- x axis label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5).fade(0.4) #---- y axis - + + #---- surface of the funtion f(x,y) surface = ParametricSurface( lambda u, v: np.array([ u, v, u**2+v**2 - ]),u_min=-1,u_max=1, v_min=-1,v_max=1).set_color("#FF69B4").shift([0,2.5,0.3]).scale(1.2) #----surface z = f(x,y) - + ]),u_min=-1,u_max=1, v_min=-1,v_max=1).set_color("#FF69B4").fade(0.6).scale(2).shift(3*UP+1*LEFT) - - plane = Rectangle(color = '#E6E6FA',fill_opacity = 1).scale(3).shift(-1*RIGHT+3*UP).fade(0.9) #---- x-y plane - - d = Dot([1,2,1],color = '#9400D3').rotate(1.571,UP) #---- point on the surface - d2 = Dot([2,2.9,1],color = '#9400D3').rotate(1.571,UP) #---- point on the surface + d = Dot([1.4,1.75,1],color = '#00FFFF').rotate(1.571,UP) #---- point on the surface + d2 = Dot([2,2,1],color = '#00FFFF').rotate(1.571,UP) #---- point on the surface p1 = TextMobject("$P_1$",color ='#ADFF2F').scale(0.6).shift(2*RIGHT+1*UP) - p2 = TextMobject("$P_2$",color = '#ADFF2F').scale(0.6).shift(2.6*RIGHT+0.4*UP) - - - l1 = DashedLine(color = '#00BFFF').scale(1.6).shift(3.5*UP+3.25*LEFT).rotate(1.571) - l2 = DashedLine(color = '#00BFFF').scale(1).shift(4*UP+2*LEFT).rotate(1.571) + p2 = TextMobject("$P_2$",color = '#ADFF2F').scale(0.6).shift(2.6*RIGHT+0.9*UP) - label_dz= TextMobject("$dz$").scale(0.4).shift(5.3*RIGHT+0.4*UP) + l = DashedLine(color = '#800000').rotate(1.571,UP).scale(1).shift(1.7*UP+1.6*RIGHT) + l2 = DashedLine(color = '#800000').rotate(1.571,UP).scale(0.8).shift(2.26*UP+1.2*RIGHT) + l_text = TextMobject("$(x_1,y_1)$",color = '#ADFF2F').scale(0.6).shift(2*RIGHT+1.6*DOWN) + l2_text = TextMobject("$(x_2,y_2)$",color = '#ADFF2F').scale(0.6).shift(2.7*RIGHT+1.2*DOWN) - l3 = Line(color = '#FFDAB9').scale(0.8).shift(1.95*UP+0.7*RIGHT).rotate(1.571,DOWN).fade(0.2) - l4 = Line(color = '#FFDAB9').scale(0.6).shift(2.86*UP+0.9*RIGHT).rotate(1.571,DOWN).fade(0.2) + a = Arrow(color = '#FFFACD').scale(0.7).rotate(1.38,RIGHT).shift(2.5*LEFT+3.1*UP) - line_y1 = DashedLine(color = '#00BFFF').scale(1.3).shift(0.82*UP+3.25*RIGHT).rotate(1.571) - line_y2 = DashedLine(color = '#00BFFF').scale(1.7).shift(1.2*UP+2.8*RIGHT).rotate(1.571) + a_text = TextMobject("$dz$",color='#800000').scale(0.5).shift(2.3*RIGHT+0.5*UP) - label_dy= TextMobject("$dy$").scale(0.6).shift(3*RIGHT+0.8*DOWN).rotate(math.radians(90)) + plane = Rectangle(color = '#E6E6FA',fill_opacity = 1).scale(3).shift(1*RIGHT+3*UP).fade(0.9) - line_x1 = DashedLine(color = '#00BFFF').scale(1.5).shift(2.2*UP+1.6*RIGHT).rotate(1.571,RIGHT) - line_x2 = DashedLine(color = '#00BFFF').scale(1.2).shift(2.9*UP+1.6*RIGHT).rotate(1.571,RIGHT) - - label_dx= TextMobject("$dx$").scale(0.4).shift(-0.4*UP+2.5*RIGHT) - - label = TextMobject("$f(x,y)$").scale(0.6).shift(4*RIGHT+3*UP) - - - self.set_camera_orientation(phi=75*DEGREES,theta=10*DEGREES) + label = TextMobject("$z = f(x,y)$").scale(0.6).shift(3.5*RIGHT+1.8*UP) + + self.set_camera_orientation(phi=75*DEGREES,theta=-10*DEGREES) self.add(axes) self.add(label_x) self.add(label_y) + self.wait(1) self.play(Write(plane)) - self.play(Write(surface)) + self.play(Write(surface)) self.add_fixed_in_frame_mobjects(label) self.wait(1) - self.play(Write(d),Write(d2)) + self.play(ShowCreation(l),ShowCreation(l2),Write(d),Write(d2)) + self.wait(1) self.add_fixed_in_frame_mobjects(p1) self.add_fixed_in_frame_mobjects(p2) self.wait(1) - self.play(Write(l1)) - self.play(Write(l2)) - self.add_fixed_in_frame_mobjects(label_dz) - self.wait(1) - self.play(Write(l3)) - self.play(Write(l4)) - self.wait(1) - self.play(Write(line_y1)) - self.play(Write(line_y2)) - self.play(ShowCreation(label_dy)) - self.wait(1) - self.play(Write(line_x1)) - self.play(Write(line_x2)) - self.add_fixed_in_frame_mobjects(label_dx) + self.add_fixed_in_frame_mobjects(l_text) + self.add_fixed_in_frame_mobjects(l2_text) + self.play(ShowCreation(a)) self.wait(1) + self.add_fixed_in_frame_mobjects(a_text) + self.wait(2) -- cgit From 50e24a7c48bb2ce318b66d8690776258f54224fe Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 00:52:47 +0530 Subject: Update file2_Differentials.py --- .../Total-Differential/file2_Differentials.py | 31 +++++++++++++--------- 1 file changed, 18 insertions(+), 13 deletions(-) (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.py index b40be70..1025210 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.py +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.py @@ -1,16 +1,21 @@ from manimlib.imports import* - -class firstScene(ThreeDScene): - +#---- visualization of the differentials along the axes +class differentials(ThreeDScene): def construct(self): - axes = ThreeDAxes() + axes = ThreeDAxes() + label_x = TextMobject("$x$").shift([5.5,-0.3,0]).fade(0.4) #---- x axis + label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5).fade(0.4) #---- y axis - s = Rectangle(color = '#00FF7F',fill_opacity=0.3).shift(2.3*UP+3.9*LEFT).scale(1).rotate(0.2,UP) #----surface z = f(x,y) + surface = ParametricSurface( + lambda u, v: np.array([ + u, + v, + u**2+v**2 + ]),u_min=-1,u_max=1, v_min=-1,v_max=1).set_color("#FF69B4").shift([0,2.5,0.3]).scale(1.2) #----surface z = f(x,y) - label_y = TextMobject("$y$").shift(5*RIGHT+0.4*DOWN).rotate(1.571) - label_x = TextMobject("$x$").shift(-0.1*UP+5.6*RIGHT).scale(0.5) + plane = Rectangle(color = '#E6E6FA',fill_opacity = 1).scale(3).shift(-1*RIGHT+3*UP).fade(0.9) @@ -27,8 +32,8 @@ class firstScene(ThreeDScene): label_dz= TextMobject("$dz$").scale(0.4).shift(5.3*RIGHT+0.4*UP) - l3 = Line(color = '#FFDAB9').scale(0.8).shift(1.95*UP+0.7*RIGHT).rotate(1.571,DOWN).fade(0.7) - l4 = Line(color = '#FFDAB9').scale(0.6).shift(2.86*UP+0.9*RIGHT).rotate(1.571,DOWN).fade(0.7) + l3 = Line(color = '#FFDAB9').scale(0.8).shift(1.95*UP+0.7*RIGHT).rotate(1.571,DOWN).fade(0.2) + l4 = Line(color = '#FFDAB9').scale(0.6).shift(2.86*UP+0.9*RIGHT).rotate(1.571,DOWN).fade(0.2) line_y1 = DashedLine(color = '#00BFFF').scale(1.3).shift(0.82*UP+3.25*RIGHT).rotate(1.571) line_y2 = DashedLine(color = '#00BFFF').scale(1.7).shift(1.2*UP+2.8*RIGHT).rotate(1.571) @@ -43,12 +48,12 @@ class firstScene(ThreeDScene): label = TextMobject("$f(x,y)$").scale(0.6).shift(4*RIGHT+3*UP) - self.add(axes) self.set_camera_orientation(phi=75*DEGREES,theta=10*DEGREES) + self.add(axes) + self.add(label_x) + self.add(label_y) self.play(Write(plane)) - self.play(ShowCreation(label_y)) - self.add_fixed_in_frame_mobjects(label_x) - self.play(Write(s)) + self.play(Write(surface)) self.add_fixed_in_frame_mobjects(label) self.wait(1) self.play(Write(d),Write(d2)) -- cgit From 6f6d931675d33a7a6e2b70c929f644d154dce847 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 00:55:01 +0530 Subject: Add files via upload --- .../Total-Differential/file2_Differentials.gif | Bin 0 -> 725835 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif new file mode 100644 index 0000000..29207e3 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif differ -- cgit From 8f060d75dd518f8d2c235837962daa67e45e40d7 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 00:55:57 +0530 Subject: Add files via upload --- .../file3_Total_differential_of_z.gif | Bin 0 -> 1444924 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file3_Total_differential_of_z.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file3_Total_differential_of_z.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file3_Total_differential_of_z.gif new file mode 100644 index 0000000..a54d2da Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file3_Total_differential_of_z.gif differ -- cgit From 3a42ab7ee6ebce1ad7c97b4f466ce26d11c0506c Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 01:02:18 +0530 Subject: Create README.md --- .../Total-Differential/README.md | 32 ++++++++++++++++++++++ 1 file changed, 32 insertions(+) create mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/README.md (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/README.md b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/README.md new file mode 100644 index 0000000..51768b6 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/README.md @@ -0,0 +1,32 @@ +

SubTopic: Total Differential

+

+ +file1_Visualization_of_dz + +![file1_Visualization_of_dz](https://github.com/vnb09/FSF-mathematics-python-code-archive/blob/fsf_tasks/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file1_Visualization_of_dz.gif?raw=true) +

+

+ +file2_Differentials + +![file2_Differentials](https://github.com/vnb09/FSF-mathematics-python-code-archive/blob/fsf_tasks/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif?raw=true) +

+

+ +file3_Total_differential_of_z + +![file3_Total_differential_of_z](https://github.com/vnb09/FSF-mathematics-python-code-archive/blob/fsf_tasks/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file3_Total_differential_of_z.gif?raw=true) +

+

+ +file4_total_differential_change + +![file4_total_differential_change](https://github.com/vnb09/FSF-mathematics-python-code-archive/blob/fsf_tasks/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file4_total_differential_change.gif?raw=true) +

+

+ +file5_Total_differential_approximation + +![file5_Total_differential_approximation](https://github.com/vnb09/FSF-mathematics-python-code-archive/blob/fsf_tasks/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif?raw=true) +

+

-- cgit From 2c18d3645c579576f7cc5caf2a0989d8a35510d6 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 01:14:41 +0530 Subject: Update file5_Total_differential_approximation.py --- .../file5_Total_differential_approximation.py | 14 +++++++++----- 1 file changed, 9 insertions(+), 5 deletions(-) (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.py index 83017ed..e7b39bb 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.py +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.py @@ -1,11 +1,14 @@ from manimlib.imports import* - -class firstScene(ThreeDScene): +#---- approximation value of function between two points using total differentials +class approximation(ThreeDScene): def construct(self): - axes = ThreeDAxes().rotate(1.571) + axes = ThreeDAxes() + label_x = TextMobject("$x$").shift([5.5,-0.3,0]).fade(0.4) #---- x axis + label_y = TextMobject("$y$").shift([-0.5,5.5,0]).rotate(-4.5).fade(0.4) #---- y axis + surface = ParametricSurface( lambda u, v: np.array([ np.sin(u), @@ -29,9 +32,10 @@ class firstScene(ThreeDScene): label = TextMobject("$z = f(x,y)$").scale(0.6).shift(4*RIGHT+3*UP) - - self.add(axes) self.set_camera_orientation(phi=75*DEGREES,theta=-10*DEGREES) + self.add(axes) + self.add(label_x) + self.add(label_y) self.wait(1) self.play(Write(plane)) self.wait(1) -- cgit From 96d2742303391c0005c59f2317a16c1850da449a Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 01:15:42 +0530 Subject: Delete file5_Total_differential_approximation.gif --- .../file5_Total_differential_approximation.gif | Bin 423652 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif deleted file mode 100644 index 4f4627d..0000000 Binary files a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif and /dev/null differ -- cgit From e29f7549016c88960601bf0dfcee31bd1eabde3f Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 01:15:56 +0530 Subject: Update README.md --- .../approximations-and-optimizations/Total-Differential/README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/README.md b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/README.md index 51768b6..089ecd3 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/README.md +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/README.md @@ -27,6 +27,6 @@ file5_Total_differential_approximation -![file5_Total_differential_approximation](https://github.com/vnb09/FSF-mathematics-python-code-archive/blob/fsf_tasks/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif?raw=true) +![file5_Total_differential_approximation](?raw=true)



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-- cgit From fe28c4c821cdc250beb6582f2f439e73b064daef Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 01:20:12 +0530 Subject: Add files via upload --- .../file5_Total_differential_approximation.gif | Bin 0 -> 423246 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif new file mode 100644 index 0000000..ebbf240 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif differ -- cgit From b4d09c2c9fd0f5488fcffa7b747db1582af97521 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 01:20:44 +0530 Subject: Delete file5_Total_differential_approximation.gif --- .../file5_Total_differential_approximation.gif | Bin 423246 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif deleted file mode 100644 index ebbf240..0000000 Binary files a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif and /dev/null differ -- cgit From e4cde6e13778391e5fae623573d8656290b09988 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 01:21:47 +0530 Subject: Update README.md --- .../approximations-and-optimizations/Total-Differential/README.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/README.md b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/README.md index e51ede3..3987542 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/README.md +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/README.md @@ -9,7 +9,7 @@ file2_Differentials -![file2_Differentials](https://github.com/vnb09/FSF-mathematics-python-code-archive/blob/fsf_tasks/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif?raw=true) +



@@ -27,6 +27,6 @@ file5_Total_differential_approximation -![file5_Total_differential_approximation] +



-- cgit From d8ed52c1d3c09890c12c88e299aa0bfab66d2113 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 01:23:52 +0530 Subject: Add files via upload --- .../file5_Total_differential_approximation.gif | Bin 0 -> 423246 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif new file mode 100644 index 0000000..ebbf240 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif differ -- cgit From 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729982 -> 0 bytes 1 file changed, 0 insertions(+), 0 deletions(-) delete mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif deleted file mode 100644 index 6baf271..0000000 Binary files a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif and /dev/null differ -- cgit From ce5466c5fa13951701a1737b84582cfe5cb61b53 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 01:27:44 +0530 Subject: Add files via upload --- .../Total-Differential/file2_Differentials.gif | Bin 0 -> 729982 bytes 1 file changed, 0 insertions(+), 0 deletions(-) create mode 100644 FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif new file mode 100644 index 0000000..6baf271 Binary files /dev/null and b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif differ -- cgit From 96159e5ec9a939dea4a7d1adaa1fb729fa85fadd Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 01:29:58 +0530 Subject: Update README.md --- .../approximations-and-optimizations/Total-Differential/README.md | 2 ++ 1 file changed, 2 insertions(+) (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/README.md b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/README.md index 3987542..ce4da11 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/README.md +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/README.md @@ -9,6 +9,7 @@ file2_Differentials +![file2_Differentials](https://github.com/vnb09/FSF-mathematics-python-code-archive/blob/fsf_tasks/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file2_Differentials.gif?raw=true)



@@ -27,6 +28,7 @@ file5_Total_differential_approximation + ![file5_Total_differential_approximation](https://github.com/vnb09/FSF-mathematics-python-code-archive/blob/fsf_tasks/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file5_Total_differential_approximation.gif?raw=true)



-- cgit From 6eaafd2b199661ba0b2221ed8f75bfc4c5e18514 Mon Sep 17 00:00:00 2001 From: Vaishnavi Date: Tue, 30 Jun 2020 01:34:49 +0530 Subject: Update file3_Total_differential_of_z.py --- .../file3_Total_differential_of_z.py | 23 +++++++++++++++------- 1 file changed, 16 insertions(+), 7 deletions(-) (limited to 'FSF-2020') diff --git a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file3_Total_differential_of_z.py b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file3_Total_differential_of_z.py index b29a7a3..b8d6f96 100644 --- a/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file3_Total_differential_of_z.py +++ b/FSF-2020/calculus-of-several-variables/approximations-and-optimizations/Total-Differential/file3_Total_differential_of_z.py @@ -1,8 +1,16 @@ from manimlib.imports import* -class firstScene(ThreeDScene): +#---- visualization of total differential definition +class totaldifferential(ThreeDScene): def construct(self): axes = ThreeDAxes().fade(0.5) + surface = ParametricSurface( + lambda u, v: np.array([ + u, + v, + u**2+v**2 + ]),u_min=-1,u_max=1, v_min=-1,v_max=1).set_color("#FF69B4").fade(0.6).shift([1,0.8,1.5]).scale(2) + plane = Rectangle(color = '#E6E6FA',fill_opacity = 1).scale(3).shift(-1*RIGHT+3*UP).fade(0.9) label_x = TextMobject("$x$").shift(5*RIGHT+0.4*DOWN).rotate(1.571) label_y = TextMobject("$y$").shift(0.3*DOWN+5.6*RIGHT).scale(0.5) @@ -57,17 +65,19 @@ class firstScene(ThreeDScene): self.add_fixed_in_frame_mobjects(label_y) self.add_fixed_in_frame_mobjects(label_z) self.wait(1) + self.play(Write(surface)) + self.play(ShowCreation(d1)) + self.add_fixed_in_frame_mobjects(d1_text) + self.play(ShowCreation(d2)) + self.add_fixed_in_frame_mobjects(d2_text) + self.wait(1) self.play(Write(s2)) self.wait(1) self.play(Write(l1),Write(l2),Write(l3)) self.wait(1) self.play(Write(s1)) self.wait(1) - self.play(ShowCreation(d1)) - self.add_fixed_in_frame_mobjects(d1_text) - self.play(ShowCreation(d2)) - self.add_fixed_in_frame_mobjects(d2_text) - self.wait(1) + self.play(FadeOut(surface)) self.play(ShowCreation(d3)) self.add_fixed_in_frame_mobjects(d3_text) self.play(ShowCreation(m1_line)) @@ -88,4 +98,3 @@ class firstScene(ThreeDScene): self.play(ShowCreation(delx)) self.add_fixed_in_frame_mobjects(delx_text) self.wait(1) - -- cgit