diff options
Diffstat (limited to 'FSF-2020')
16 files changed, 384 insertions, 238 deletions
diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/README.md b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/README.md index e69de29..17fcde0 100644 --- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/README.md +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/README.md @@ -0,0 +1,4 @@ +**file1_flux@_various_points.py**
+
+**file2_different_valuesof_Div.py**
+
diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file1_flux@_various_points.gif b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file1_flux@_various_points.gif Binary files differnew file mode 100644 index 0000000..6c32b94 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file1_flux@_various_points.gif diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file1_flux@_various_points.py b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file1_flux@_various_points.py new file mode 100644 index 0000000..6727982 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file1_flux@_various_points.py @@ -0,0 +1,60 @@ +from manimlib.imports import * +def pendulum_vector_field_func(point): + #theta, omega = point[:2] + return np.array([ + 5*point[0]+point[1], + 3*point[1]+3*point[1], + 0, + ]) +class SF(Scene): + CONFIG = { + #"func": cylinder_flow_vector_field, + "flow_time": 5, + } + def initialize_vector_field(self): + self.vector_field = VectorField( + pendulum_vector_field_func, + ) + self.vector_field.sort(get_norm) + def construct(self): + # plane = NumberPlane(color=RED) + # plane.add(plane.get_axis_labels()) + # self.add(plane) + + A=TextMobject("The net flux through the green circular region is zero",tex_to_color_map={"green": GREEN}) + B=TextMobject("The net flux through the blue circular region is non-zero",tex_to_color_map={"blue": BLUE}) + + c1=Circle(color=GREEN, radius=1.5) + c1.shift(4*LEFT+2.2*UP) + c2=Circle(color=BLUE, radius=1.5) + + + + + self.play(ShowCreation(A)) + self.wait(0.5) + self.play(ApplyMethod(A.shift, (0.8*UP+0.2*LEFT))) + self.play(ShowCreation(B)) + # self.play(ApplyMethod(B.shift, (2*UP))) + self.wait(2) + self.play(FadeOut(A),FadeOut(B)) + self.initialize_vector_field() + field = self.vector_field + self.play(ShowCreation(field), run_time=4) + self.play(ShowCreation(c1)) + self.play(ShowCreation(c2)) + self.wait(1) + lines = StreamLines( + pendulum_vector_field_func, + virtual_time=3, + min_magnitude=0, + max_magnitude=2, + ) + self.add(AnimatedStreamLines( + lines, + line_anim_class=ShowPassingFlash + )) + self.wait(2) + phase_point = VectorizedPoint(1*UP+1*RIGHT) + self.add(move_along_vector_field(phase_point, pendulum_vector_field_func)) + self.wait(2) diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file2_different_valuesof_Div.gif b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file2_different_valuesof_Div.gif Binary files differnew file mode 100644 index 0000000..477c311 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file2_different_valuesof_Div.gif diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file2_different_valuesof_Div.py b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file2_different_valuesof_Div.py new file mode 100644 index 0000000..921047d --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/divergence-gauss-theorem/file2_different_valuesof_Div.py @@ -0,0 +1,91 @@ +from manimlib.imports import * +class Div(Scene): + def construct(self): + one=TextMobject(r"Div$ \vec{F} < 0$ ").set_color(RED) + two=TextMobject(r"Div$ \vec{F} = 0$ ").set_color(BLUE) + three=TextMobject(r"Div$ \vec{F} > 0$ ").set_color(YELLOW) + + one.shift(2.3*DOWN) + two.shift(2.3*DOWN) + three.shift(2.3*DOWN) + + + a=Dot(color=RED) + a.shift(0.1*LEFT) + b=Dot(color=BLUE) + b.shift(0.1*LEFT) + c=Dot(color=YELLOW) + c.shift(0.1*LEFT) + + rot=[0*DEGREES,45*DEGREES,90*DEGREES,135*DEGREES,180*DEGREES,225*DEGREES,270*DEGREES,315*DEGREES] + rot2=[180*DEGREES,180*DEGREES,180*DEGREES,180*DEGREES,180*DEGREES,180*DEGREES,180*DEGREES,180*DEGREES] + shift=[RIGHT,0.7*RIGHT+0.7*UP,UP,0.7*LEFT+0.7*UP,LEFT,0.7*LEFT+0.7*DOWN,DOWN,0.7*RIGHT+0.7*DOWN] + shift2=[RIGHT,RIGHT+UP,RIGHT+DOWN,UP,DOWN,LEFT,LEFT+UP,LEFT+DOWN] + + + + u=[Vector(color=RED),Vector(color=RED),Vector(color=RED),Vector(color=RED), + Vector(color=RED),Vector(color=RED),Vector(color=RED),Vector(color=RED)] + + + [u[i].rotate(rot[i]) for i in range(8) ] + [u[i].rotate(rot2[i]) for i in range(8) ] + [u[i].shift(shift[i]) for i in range(8) ] + + + divone=VGroup(*u) + divone.shift(0.6*LEFT) + + + v=[Vector(color=BLUE),Vector(color=BLUE),Vector(color=BLUE),Vector(color=BLUE), + Vector(color=BLUE),Vector(color=BLUE),Vector(color=BLUE),Vector(color=BLUE)] + + + [v[i].rotate(45*DEGREES) for i in range(8)] + [v[i].shift(shift2[i]) for i in range(8) ] + + divtwo=VGroup(*v) + divtwo.shift(0.6*LEFT) + + + w=[Vector(color=YELLOW),Vector(color=YELLOW),Vector(color=YELLOW),Vector(color=YELLOW), + Vector(color=YELLOW),Vector(color=YELLOW),Vector(color=YELLOW),Vector(color=YELLOW)] + + + [w[i].rotate(rot[i]) for i in range(8)] + [w[i].shift(shift[i]) for i in range(8) ] + + + divthree=VGroup(*w) + divthree.shift(0.6*LEFT) + + + + + self.play(ShowCreation(a),ShowCreation(divone)) + self.play(ShowCreation(one)) + self.wait(1) + self.play(FadeOut(a),FadeOut(divone),FadeOut(one)) + + self.play(ShowCreation(b),ShowCreation(divtwo)) + self.play(ShowCreation(two)) + self.wait(1) + self.play(FadeOut(b),FadeOut(divtwo),FadeOut(two)) + + + self.play(ShowCreation(c),ShowCreation(divthree)) + self.play(ShowCreation(three)) + self.wait(1) + self.play(FadeOut(c),FadeOut(divthree),FadeOut(three)) + self.wait(0.5) + + + + + + + + + + + diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/README.md b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/README.md index 0af7aa1..97d6d10 100644 --- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/README.md +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/README.md @@ -1,7 +1,5 @@ -**file1_flux_through_sphere.py** - -**file2_mobius_strip.py** - +**file1_flux_through_circle.py** + **file3_normal_vector.py**  **file4_cube_surface.py** diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_circle.gif b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_circle.gif Binary files differnew file mode 100644 index 0000000..c00076b --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_circle.gif diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_circle.py b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_circle.py new file mode 100644 index 0000000..e418a96 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_circle.py @@ -0,0 +1,43 @@ +from manimlib.imports import * +def pendulum_vector_field_func(point): + #theta, omega = point[:2] + return np.array([ + point[0], + point[1], + point[2], + ]) +class F2D(Scene): + CONFIG = { + # "func": cylinder_flow_vec or_field, + "flow_time": 5, + } + def initialize_vector_field(self): + self.vector_field = VectorField( + pendulum_vector_field_func, + ) + self.vector_field.sort(get_norm) + def construct(self): + # plane = NumberPlane(color=RED) + # plane.add(plane.get_axis_labels()) + # self.add(plane) + self.initialize_vector_field() + + field = self.vector_field + c1=Circle(radius=3,color=BLUE) + self.play(ShowCreation(field), run_time=7) + self.play(ShowCreation(c1)) + self.wait(3) + lines = StreamLines( + pendulum_vector_field_func, + virtual_time=3, + min_magnitude=0, + max_magnitude=2, + ) + self.add(AnimatedStreamLines( + lines, + line_anim_class=ShowPassingFlash + )) + self.wait(2) + phase_point = VectorizedPoint(1*UP+1*RIGHT) + self.add(move_along_vector_field(phase_point, pendulum_vector_field_func)) + self.wait(2) diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_sphere.gif b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_sphere.gif Binary files differdeleted file mode 100644 index 43327bf..0000000 --- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_sphere.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_sphere.py b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_sphere.py deleted file mode 100644 index e07715e..0000000 --- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file1_flux_through_sphere.py +++ /dev/null @@ -1,50 +0,0 @@ -from manimlib.imports import * -class fluxsphere(ThreeDScene): - - - def construct(self): - s = Sphere(checkerboard_colors=[BLUE_D,BLUE_D]) - s.scale(2.3) - - n = VGroup( - *[self.n(*self.func(u, v)) - for u in np.arange(0, PI, 0.4) - for v in np.arange(0, TAU, 0.8)] - ) - - - - self.move_camera(0.8 * PI / 2, -0.45 * PI) - self.play(Write(s)) - # self.play(Write(f)) - self.play(ShowCreation(n), run_time=4) - # self.add(n) - self.begin_ambient_camera_rotation(rate=0.1) - self.wait(5) - - - def func(self, u, v): - return [ - np.cos(v) * np.sin(u), - np.sin(v) * np.sin(u), - np.cos(u) - ] - - def vect(self, x, y, z): - return np.array([ - x, y, z - ]) - - def n(self, x, y, z): - vect = np.array([ - x, - y, - z - ]) - - mag = math.sqrt(vect[0] ** 2 + vect[1] ** 2 + vect[2] ** 2) - v = Vector( - (1.5/mag) * vect, - color=RED_B, - stroke_width=4).shift(2*x * RIGHT + 2*y * UP + 2*z * OUT) - return v diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file2_mobius_strip.gif b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file2_mobius_strip.gif Binary files differdeleted file mode 100644 index 9623046..0000000 --- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file2_mobius_strip.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file2_mobius_strip.py b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file2_mobius_strip.py deleted file mode 100644 index 31b1990..0000000 --- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file2_mobius_strip.py +++ /dev/null @@ -1,81 +0,0 @@ -from manimlib.imports import * - -class Mobius(ThreeDScene): - def construct(self): - axes=ThreeDAxes() - - - - R=2.5 - - - mobius = ParametricSurface( - lambda u, v: np.array([ - (R+u*np.cos(v/2))*np.cos(v), - (R+u*np.cos(v/2))*np.sin( v), - u*np.sin(v/2) - ]), - u_min = -0.5, u_max = 0.5, v_min = 0, v_max = 2*PI, - - resolution=(6, 32)).fade(0.5) #Resolution of the surfaces - circle=Circle(radius=2.5, color=BLUE) - - - - mobius.rotate(PI/2, axis=RIGHT) - mobius.rotate(PI/2, axis=OUT) - # # mobius.shift(RIGHT+OUT+DOWN) - - - - - - along = ParametricSurface( - lambda u, v: np.array([ - (R+u*np.cos(v/2))*np.cos(v), - (R+u*np.cos(v/2))*np.sin(v), - 0 - ]), - u_min = -0.5, u_max = 0.5, v_min = 0, v_max = 2*PI, - - resolution=(6, 32)).fade(0.5) #Resolution of the surfaces - circle=Circle(radius=2.5, color=BLUE) - - - - - - - - - - - - - - - - - - - - - - - - self.set_camera_orientation(phi=75 * DEGREES,theta=-75*DEGREES) - - self.play(Write(mobius)) - - self.wait(1) - self.begin_ambient_camera_rotation(rate=0.65) - - self.wait(10) - self.stop_ambient_camera_rotation() - self.wait(1) - - - - - - diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.gif b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.gif Binary files differindex c6101cf..001edb8 100644 --- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.gif +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.gif diff --git a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.py b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.py index 9301a00..146d955 100644 --- a/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.py +++ b/FSF-2020/calculus-of-several-variables/triple-and-surface-integrals/flux/file4_cube_surface.py @@ -1,7 +1,4 @@ from manimlib.imports import* - - - class cuber(ThreeDScene): def construct(self): @@ -41,6 +38,7 @@ class cuber(ThreeDScene): n1=TextMobject(r"$\vec{n}$",color=YELLOW) n1.scale(0.8) n1.rotate(PI/2,axis=RIGHT) + n1.rotate(PI,axis=OUT) n1.shift(3*RIGHT+1.3*OUT+DOWN) spaceloc = [[0,0,2],[1,0,2],[-1,0,2],[2,0,2],[-2,0,2],[3,0,2],[-3,0,2], @@ -59,158 +57,128 @@ class cuber(ThreeDScene): [0,3,2],[1,3,2],[-1,3,2],[2,3,2],[-2,3,2],[3,3,2],[-3,3,2]] - veclist1=[Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E)] + veclist1=[Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY)] - [veclist1[i].rotate(PI/4,axis=RIGHT) for i in range(10,30,1)] - [veclist1[i].rotate(PI/4,axis=RIGHT) for i in range(40,80,2)] - [veclist1[i].rotate(PI/6,axis=OUT) for i in range(98)] - [veclist1[i].rotate(PI/8,axis=DOWN) for i in range(98)] + [veclist1[i].rotate(PI/4,axis=RIGHT) for i in range(42)] + [veclist1[i].rotate(PI/6,axis=OUT) for i in range(42)] + [veclist1[i].rotate(PI/8,axis=DOWN) for i in range(42)] vectorfield1=VGroup(*veclist1) - [veclist1[i].shift(spaceloc[i]) for i in range(98)] + [veclist1[i].shift(spaceloc[i]) for i in range(42)] - veclist2=[Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E), - Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E),Vector(color=GOLD_E)] + veclist2=[Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY)] - [veclist2[i].rotate(PI/4,axis=RIGHT) for i in range(10,30,1)] - [veclist2[i].rotate(PI/4,axis=RIGHT) for i in range(40,80,2)] - [veclist2[i].rotate(PI/6,axis=OUT) for i in range(98)] - [veclist2[i].rotate(PI/8,axis=DOWN) for i in range(98)] + [veclist2[i].rotate(PI/4,axis=RIGHT) for i in range(42)] + [veclist2[i].rotate(PI/4,axis=RIGHT) for i in range(42)] + [veclist2[i].rotate(PI/6,axis=OUT) for i in range(42)] + [veclist2[i].rotate(PI/8,axis=DOWN) for i in range(42)] vectorfield2=VGroup(*veclist2) - [veclist2[i].shift(spaceloc[i]) for i in range(98)] + [veclist2[i].shift(spaceloc[i]) for i in range(42)] - veclist3=[Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector()] + veclist3=[Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY)] - [veclist3[i].rotate(PI/4,axis=RIGHT) for i in range(10,30,1)] - [veclist3[i].rotate(PI/4,axis=RIGHT) for i in range(40,80,2)] - [veclist3[i].rotate(PI/6,axis=OUT) for i in range(98)] - [veclist3[i].rotate(PI/8,axis=DOWN) for i in range(98)] + [veclist3[i].rotate(PI/4,axis=RIGHT) for i in range(42)] + [veclist3[i].rotate(PI/4,axis=RIGHT) for i in range(42)] + [veclist3[i].rotate(PI/6,axis=OUT) for i in range(42)] + [veclist3[i].rotate(PI/8,axis=DOWN) for i in range(42)] vectorfield3=VGroup(*veclist3) - [veclist3[i].shift(spaceloc[i]) for i in range(98)] + [veclist3[i].shift(spaceloc[i]) for i in range(42)] - veclist4=[Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector(), - Vector(color=RED),Vector(color=GREEN),Vector(color=BLUE),Vector(color=PINK),Vector(color=MAROON),Vector(color=GREEN),Vector()] + veclist4=[Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY)] - [veclist4[i].rotate(PI/4,axis=RIGHT) for i in range(10,30,1)] - [veclist4[i].rotate(PI/4,axis=RIGHT) for i in range(40,80,2)] - [veclist4[i].rotate(PI/6,axis=OUT) for i in range(98)] - [veclist4[i].rotate(PI/8,axis=DOWN) for i in range(98)] + [veclist4[i].rotate(PI/4,axis=RIGHT) for i in range(42)] + [veclist4[i].rotate(PI/4,axis=RIGHT) for i in range(42)] + [veclist4[i].rotate(PI/6,axis=OUT) for i in range(42)] + [veclist4[i].rotate(PI/8,axis=DOWN) for i in range(42)] vectorfield4=VGroup(*veclist4) - [veclist4[i].shift(spaceloc[i]) for i in range(98)] + [veclist4[i].shift(spaceloc[i]) for i in range(42)] vectorfield1.shift(1.5*DOWN) vectorfield2.shift(IN+1.5*DOWN) vectorfield3.shift(2*IN+1.5*DOWN) - vectorfield4.shift(3*IN+1.5*DOWN) + vectorfield4.shift(3*IN+1.5*DOWN) + vectors=[vectorfield1,vectorfield2,vectorfield3,vectorfield4] vectorfield=VGroup(*vectors) - vectorfield.scale(1.25) + vectorfield.scale(1.3) + - fv=[Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE), - Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE), - Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE), - Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE),Vector(color=ORANGE), + fv=[Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY),Vector(color=GREY),Vector(color=GREY),Vector(color=GREY), + Vector(color=GREY) ] - spaceloc2 = [[1.5,0.5,0.5],[1.5,1,0.5],[1.5,1.5,0.5],[1.5,2,0.5], - [1.5,0.5,1],[1.5,1,1],[1.5,1.5,1],[1.5,2,1], - [1.5,0.5,1.5],[1.5,1,1.5],[1.5,1.5,1.5],[1.5,2,1.5], - [1.5,0.5,2],[1.5,1,2],[1.5,1.5,2],[1.5,2,2]] - - [fv[i].rotate(PI/4,axis=RIGHT) for i in range(1)] - [fv[i].rotate(PI/6,axis=OUT) for i in range(16)] - [fv[i].rotate(PI/8,axis=DOWN) for i in range(16)] - [fv[i].shift(spaceloc2[i]) for i in range(16)] + spaceloc2 = [[1.5,0.5,0.5],[1.5,1,0.5],[1.5,1.5,0.5], + [1.5,0.5,1],[1.5,1,1],[1.5,1.5,1], + [1.5,0.5,1.5],[1.5,1,1.5],[1.5,1.5,1.5] + ] + [fv[i].rotate(PI/4,axis=RIGHT) for i in range(9)] + [fv[i].rotate(PI/6,axis=OUT) for i in range(9)] + [fv[i].rotate(PI/8,axis=DOWN) for i in range(9)] + [fv[i].shift(spaceloc2[i]) for i in range(9)] fvfield=VGroup(*fv) - fvfield.shift(0.5*IN+2*DOWN) + fvfield.shift(2*DOWN) + fvfield.scale(1.3) - flux=TextMobject("Flux through one side of the cube").set_color(ORANGE) - flux.shift(3*UP+1.5*LEFT) + flux=TextMobject("Flux through one side of the cube").set_color(GOLD) + flux.shift(3.5*UP+0.5*LEFT) + alll=[vectorfield1,vectorfield2,vectorfield3,vectorfield4,fvfield] + alllvectors=VGroup(*alll) self.set_camera_orientation(phi=70 * DEGREES,theta=-75*DEGREES) self.play(ShowCreation(axes),ShowCreation(axis_label)) - self.play(ShowCreation(vectorfield)) - self.add(fvfield) - self.begin_ambient_camera_rotation(rate=0.01) + self.begin_ambient_camera_rotation(rate=0.2) + self.play(ShowCreation(alllvectors)) + # self.add(fvfield) self.play(ShowCreation(cube, run_time=1)) @@ -223,6 +191,6 @@ class cuber(ThreeDScene): # self.play(ShowCreation(flux)) self.wait(1) self.play(ShowCreation(v1),ShowCreation(n1)) - self.wait(6) - # self.stop_ambient_camera_rotation() - + self.wait(5) + self.stop_ambient_camera_rotation() + self.wait(1) diff --git a/FSF-2020/calculus/intro-to-calculus/limit/limit3.py b/FSF-2020/calculus/intro-to-calculus/limit/limit3.py new file mode 100644 index 0000000..a4f07d7 --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/limit/limit3.py @@ -0,0 +1,95 @@ +from manimlib.imports import * +class limit3(GraphScene, MovingCameraScene): + def setup(self): + GraphScene.setup(self) + MovingCameraScene.setup(self) + CONFIG = { + "y_max" : 10, + "y_min" : 0, + "x_max" : 100, + "x_min" : 0, + "y_tick_frequency" : 1, + "x_tick_frequency" : 10, + "axes_color" : WHITE, + "num_graph_anchor_points": 3000, #this is the number of points that graph manim + "graph_origin" : ORIGIN+3*DOWN+4*LEFT, + "x_labeled_nums": list(range(0,101))[::10], + "y_labeled_nums": list(range(0,11)), + "x_axis_label":"$x$", + "y_axis_label":"$f(x)$", + "x_axis_width": 10, + "y_axis_height": 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) + sqr1 = Square(side_length = 15).move_to(np.array([1,0.5,0])) + sqr2 = Square(side_length = 15).move_to(np.array([-4,-3,0])) + + textdef = TextMobject("") + text20 = TextMobject("f(x) is not defined at x=50").move_to(np.array([1,0.3,0])).scale(0.2) + text21 = TexMobject(r"\text {f(x) is not defined in interval }",r" (-\infty ,\quad 1]").move_to(np.array([-4,-3.2,0])).scale(0.18) + text22 = TextMobject("1").move_to(np.array([-3.9,-3.05,0])).scale(0.2) + text1 = TexMobject(r"\text {Let }" ,r"f\left( x \right) =\begin{cases} \sqrt { x-1 } ,x\in \quad (1,\infty )-50 \end{cases}") + text2 = TextMobject("Graph of f(x) is ") + text3 = TextMobject("Right hand neighbour of 50 will approximately be 50.000001").move_to(np.array([1,0.3,0])).scale(0.15) + text4 = TextMobject("Left hand neighbour of 50 will approximately be 49.999999").move_to(np.array([1,0.3,0])).scale(0.15) + text5 = TexMobject(r"\text {Hence R.H.L }", r"=\lim _{ x\rightarrow { 50 }^{ + } }{ \sqrt { 50.000001 - 1 } } \approx 7.000000071").move_to(np.array([1,0.3,0])).scale(0.13) + text6 = TexMobject(r"\text{Hence L.H.L }", r" = \lim _{ x\rightarrow { 50 }^{ - } }{ \sqrt { 49.999999-1 } }\approx 6.999999929").move_to(np.array([1,0.3,0])).scale(0.13) + text7 = TextMobject("7.000000071").move_to(np.array([1.9,0.25,0])).scale(0.1) + text8 = TextMobject("6.999999929").move_to(np.array([0.1,0.25,0])).scale(0.1) + text9 = TexMobject(r"6.999999929\quad \approx \quad 7.000000071 \quad \approx 7").move_to(np.array([1,0.25,0])).scale(0.2) + text10 = TexMobject(r"\text{Because LHL }" ,r"\approx" ,r"\text{ RHL, Limit exists at x=50 and equals 7").move_to(np.array([1,0.25,0])).scale(0.13) + text11 = TextMobject("There is no Left hand neighbour of x=1").move_to(np.array([-4,-3.2,0])).scale(0.22) + text12 = TexMobject(r"\therefore\quad \lim _{ x\rightarrow 0 }{ f(x) } \quad =\quad \lim _{ x\rightarrow { 0 }^{ + } }{ f(x) } ").move_to(np.array([-4,-3.2,0])).scale(0.25) + text13 = TexMobject(r"\text {R.H.L =}",r" \lim _{ x\rightarrow { 0 }^{ + } }{ \sqrt { 1.000000000001-1 } } \quad \approx 0").move_to(np.array([-4,-3.2,0])).scale(0.13) + text14 = TexMobject(r"\therefore \quad \lim _{ x\rightarrow 0 }{ f(x)\quad =\quad 0 }").move_to(np.array([-4,-3.2,0])).scale(0.13) + self.camera_frame.save_state() + self.play(ShowCreation(text1)) + self.wait(3) + self.play(ReplacementTransform(text1, text2)) + self.wait() + self.play(ReplacementTransform(text2, textdef)) + self.setup_axes() + self.setup() + graph_1 = self.get_graph(lambda x : (x-1)**(1/2),color = PINK, x_min = 1, x_max = 49.9) + graph_2 = self.get_graph(lambda x : (x-1)**(1/2),color = PINK, x_min = 50.1, x_max = 100) + graph_3 = self.get_graph(lambda x : (x-1)**(1/2),color = PINK, x_min = 1.05, x_max = 1.001) + dot1 = SmallDot(color = PURPLE_A) + cir = Circle(radius = 0.01, color = GREEN_SCREEN).move_to(np.array([1,0.5,0])) + grp1 = VGroup(graph_1, graph_2, cir) + grp2 = VGroup(text7, text8) + self.play(ShowCreation(grp1)) + self.wait(2) + self.play(self.camera_frame.set_width,2.25,self.camera_frame.move_to,sqr1,run_time = 2) + self.wait(1) + self.play(ShowCreation(text20)) + self.wait(2) + self.play(ReplacementTransform(text20, text3)) + self.wait(3) + self.play(ReplacementTransform(text3, text5)) + self.wait(3) + self.play(ReplacementTransform(text5, text7), ShowCreation(text4)) + self.wait(4) + self.play(ReplacementTransform(text4, text6)) + self.wait(3) + self.play(ReplacementTransform(text6, text8)) + self.wait(1.5) + self.play(ReplacementTransform(grp2, text9)) + self.wait(1.5) + self.play(ReplacementTransform(text9, text10)) + self.wait(3) + self.play(self.camera_frame.set_width,2.25,self.camera_frame.move_to,sqr2,run_time = 2) + self.play(ShowCreation(text21), ShowCreation(text22)) + self.play(MoveAlongPath(dot1, graph_3), run_time = 3) + self.wait(3) + self.play(ReplacementTransform(text21, text11)) + self.wait(3) + self.play(ReplacementTransform(text11, text12)) + self.wait(3) + self.play(ReplacementTransform(text12, text13)) + self.wait(2) + self.play(ReplacementTransform(text13, text14)) + self.wait(3) + self.play(ReplacementTransform(text14, textdef)) + self.wait(2) diff --git a/FSF-2020/calculus/intro-to-calculus/riemannintegrals/README.md b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/README.md new file mode 100644 index 0000000..a9ad0bb --- /dev/null +++ b/FSF-2020/calculus/intro-to-calculus/riemannintegrals/README.md @@ -0,0 +1,18 @@ +rierect1.gif + + + +rierect2.gif + + + +rierect3.gif + + + +RiemannRectanglesAnimation. + + + +mimi.gif + |
