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Delete file4_partial_deriv_example.py
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py')
| -rw-r--r-- | FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py | 246 |
1 files changed, 0 insertions, 246 deletions
diff --git a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py b/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py deleted file mode 100644 index 5712a62..0000000 --- a/FSF-2020/calculus-of-several-variables/multivariable-functions-and-paritial-derivatives/partial-derivatives/file4_partial_deriv_example.py +++ /dev/null @@ -1,246 +0,0 @@ -from manimlib.imports import *
-
-class PartialDerivX(ThreeDScene):
- def construct(self):
- axes = ThreeDAxes()
-
- paraboloid = ParametricSurface(
- lambda u, v: np.array([
- 2*np.sin(u)*np.cos(v),
- 2*np.sin(u)*np.sin(v),
- -2*2*np.sin(u)*np.sin(u)+2
- ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[PINK, PURPLE],
- resolution=(15, 32)).scale(1)
-
- paraboloid_copy = paraboloid.copy()
-
-
- paraboloid_x = ParametricSurface(
- lambda u, v: np.array([
- 2*np.sin(u)*np.cos(v),
- 2*np.sin(u)*np.sin(v),
- -2*2*np.sin(u)*np.sin(u)+2
- ]),u_min=0,u_max=PI/2,v_min=PI,v_max=2*PI,checkerboard_colors=[PINK, PURPLE],
- resolution=(15, 32)).scale(1)
-
-
- parabola =ParametricFunction(
- lambda u : np.array([
- u,
- 0,
- -(u*u) + 2
- ]),color="#006400",t_min=-2,t_max=2,
- )
-
- plane = Polygon(np.array([-2.2,0,-2.5]),np.array([2.2,0,-2.5]),np.array([2.2,0,2.5]),np.array([-2.2,0,2.5]),np.array([-2.2,0,-2.5]), color = GREEN, fill_color = GREEN, fill_opacity = 0.2)
- plane_text = TextMobject(r"$y = 0$", color = GREEN_C).move_to(2*UP + 3*RIGHT)
-
- surface_eqn = TextMobject("Surface", r"$z = 2- x^2 -y^2$", color = PINK).scale(0.6).move_to(np.array([3*LEFT +3*UP]))
- surface_eqn[0].set_color(BLUE_C)
-
- line = Line(np.array([-2,0,0]), np.array([2,0,0]), color = RED_C)
-
-
- self.add(axes)
-
- axis = TextMobject(r"X",r"Y",r"Z")
- axis[0].move_to(6*RIGHT)
- axis[1].move_to(6*UP)
- axis[2].move_to(3.7*UP)
-
- self.add_fixed_in_frame_mobjects(axis[2])
- self.add_fixed_orientation_mobjects(axis[0])
- self.add_fixed_orientation_mobjects(axis[1])
-
-
- self.set_camera_orientation(phi=80 * DEGREES, theta = 0*DEGREES)
-
- self.play(Write(paraboloid))
-
- self.add_fixed_in_frame_mobjects(surface_eqn)
- #self.move_camera(phi=80* DEGREES,theta=95*DEGREES)
- self.move_camera(phi=80* DEGREES,theta=45*DEGREES)
- self.play(ShowCreation(plane))
- self.add_fixed_in_frame_mobjects(plane_text)
- self.wait()
- self.play(ReplacementTransform(paraboloid, paraboloid_x))
- self.play(FadeOut(plane), FadeOut(plane_text))
- self.play(ShowCreation(parabola), ShowCreation(line))
-
- text1 = TextMobject("Moving small", r"$dx$", r"steps").scale(0.6).move_to(3*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, BLUE, PURPLE)
-
- text2 = TextMobject("Observing change in function, keeping", r"$y$", r"constant").scale(0.6).move_to(2.6*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
-
- slope_text = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "x}").scale(0.6).move_to(2*UP + 3.5*RIGHT)
- slope_text[0].set_color(BLUE_E)
- slope_text.set_color_by_tex("\\partial",PINK)
- slope_text.set_color_by_tex("f","#006400")
- slope_text[5].set_color(RED_C)
-
- self.add_fixed_in_frame_mobjects(text1, text2)
- self.wait()
- self.add_fixed_in_frame_mobjects(slope_text)
- #add_fixed_orientation_mobjects
-
-
- dot = Dot().rotate(PI/2).set_color(RED_C)
- alpha = ValueTracker(0)
- vector = self.get_tangent_vector(alpha.get_value(),parabola,scale=1.5)
- dot.add_updater(lambda m: m.move_to(vector.get_center()))
- self.play(
- ShowCreation(parabola),
- GrowFromCenter(dot),
- GrowArrow(vector)
- )
- vector.add_updater(
- lambda m: m.become(
- self.get_tangent_vector(alpha.get_value()%1,parabola,scale=1.5)
- )
- )
- self.add(vector,dot)
- self.play(alpha.increment_value, 1, run_time=10, rate_func=linear)
- self.wait()
-
-
- '''
- for i in np.arange(-2,2,0.2):
- self.play(ReplacementTransform(Line(np.array([i,0,0]), np.array([i,0,-i*i + 2]), color = GREEN_C), Line(np.array([i+0.2,0,0]), np.array([i+0.2,0,-(i+0.2)**2 + 2]), color = GREEN_C)))
- #self.wait()
- '''
-
- self.wait()
- self.play(FadeOut(parabola), FadeOut(line), FadeOut(vector), FadeOut(dot), FadeOut(text1), FadeOut(text2), FadeOut(slope_text),FadeOut(surface_eqn))
-
- #self.move_camera(phi=80* DEGREES,theta= 0*DEGREES)
- self.play(ReplacementTransform(paraboloid_x, paraboloid_copy))
- self.wait()
-
-
- def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1):
- coord_i = curve.point_from_proportion(proportion)
- coord_f = curve.point_from_proportion(proportion + dx)
- reference_line = Line(coord_i,coord_f)
- unit_vector = reference_line.get_unit_vector() * scale
- vector = Line(coord_i - unit_vector, coord_i + unit_vector, color = BLUE_E, buff=0)
- return vector
-
-
-class PartialDerivY(ThreeDScene):
- def construct(self):
- axes = ThreeDAxes()
-
- paraboloid = ParametricSurface(
- lambda u, v: np.array([
- 2*np.sin(u)*np.cos(v),
- 2*np.sin(u)*np.sin(v),
- -2*2*np.sin(u)*np.sin(u)+2
- ]),u_min=0,u_max=PI/2,v_min=0,v_max=2*PI,checkerboard_colors=[PINK, PURPLE],
- resolution=(15, 32)).scale(1)
-
- paraboloid_copy = paraboloid.copy()
-
-
- paraboloid_y = ParametricSurface(
- lambda u, v: np.array([
- 2*np.sin(u)*np.cos(v),
- 2*np.sin(u)*np.sin(v),
- -2*2*np.sin(u)*np.sin(u)+2
- ]),u_min=0,u_max=PI/2,v_min=PI/2,v_max=3*PI/2,checkerboard_colors=[PINK, PURPLE],
- resolution=(15, 32)).scale(1)
-
-
- parabola =ParametricFunction(
- lambda u : np.array([
- 0,
- u,
- -(u*u) + 2
- ]),color=YELLOW_C,t_min=-2,t_max=2,
- )
-
- plane = Polygon(np.array([0,-2.2,-2.5]),np.array([0,2.2,-2.5]),np.array([0,2.2,2.5]),np.array([0,-2.2,2.5]),np.array([0,-2.2,-2.5]), color = BLUE, fill_color = BLUE, fill_opacity = 0.2)
- plane_text = TextMobject(r"$x = 0$", color = BLUE_C).move_to(2*UP + 3*RIGHT)
-
- surface_eqn = TextMobject("Surface", r"$z = 2- x^2 -y^2$", color = PINK).scale(0.6).move_to(np.array([3*LEFT +3*UP]))
- surface_eqn[0].set_color(BLUE_C)
-
- line = Line(np.array([0,-2,0]), np.array([0,2,0]), color = RED_C)
-
- self.add(axes)
-
- axis = TextMobject(r"X",r"Y",r"Z")
- axis[0].move_to(6*RIGHT)
- axis[1].move_to(6*UP)
- axis[2].move_to(3.7*UP)
-
- self.add_fixed_in_frame_mobjects(axis[2])
- self.add_fixed_orientation_mobjects(axis[0])
- self.add_fixed_orientation_mobjects(axis[1])
-
- self.set_camera_orientation(phi=80 * DEGREES, theta = 45*DEGREES)
-
- self.play(Write(paraboloid))
-
- self.add_fixed_in_frame_mobjects(surface_eqn)
- #self.move_camera(phi=80* DEGREES,theta=5*DEGREES)
- self.play(ShowCreation(plane))
- self.add_fixed_in_frame_mobjects(plane_text)
- self.wait()
- self.play(ReplacementTransform(paraboloid, paraboloid_y))
- self.play(FadeOut(plane), FadeOut(plane_text))
- self.play(ShowCreation(parabola), ShowCreation(line))
-
- text1 = TextMobject("Moving small", r"$dy$", r"steps").scale(0.6).move_to(3*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, BLUE, PURPLE)
-
- text2 = TextMobject("Observing change in function, keeping", r"$x$", r"constant").scale(0.6).move_to(2.6*UP + 3.5*RIGHT).set_color_by_gradient(RED, ORANGE, YELLOW, GREEN, BLUE, PURPLE)
-
- slope_text = TexMobject("Slope =", "{\\partial", "f", "\\over", "\\partial", "y}").scale(0.6).move_to(2*UP + 3.5*RIGHT)
- slope_text[0].set_color("#006400")
- slope_text.set_color_by_tex("\\partial",PINK)
- slope_text.set_color_by_tex("f",YELLOW_C)
- slope_text[5].set_color(RED_C)
-
- self.add_fixed_in_frame_mobjects(text1, text2)
- self.wait()
- self.add_fixed_in_frame_mobjects(slope_text)
-
- dot = Dot().rotate(PI/2).set_color(RED_C)
- alpha = ValueTracker(0)
- vector = self.get_tangent_vector(alpha.get_value(),parabola,scale=1.5)
- dot.add_updater(lambda m: m.move_to(vector.get_center()))
- self.play(
- ShowCreation(parabola),
- GrowFromCenter(dot),
- GrowArrow(vector)
- )
- vector.add_updater(
- lambda m: m.become(
- self.get_tangent_vector(alpha.get_value()%1,parabola,scale=1.5)
- )
- )
- self.add(vector,dot)
- self.play(alpha.increment_value, 1, run_time=10, rate_func=linear)
- self.wait()
-
- '''
- for i in np.arange(-2,2,0.2):
- self.play(ReplacementTransform(Line(np.array([0,i,0]), np.array([0,i,-i*i + 2]), color = BLUE_C), Line(np.array([0,i+0.2,0]), np.array([0,i+0.2,-(i+0.2)**2 + 2]), color = BLUE_C)))
- #self.wait()
- '''
-
-
- self.wait()
- self.play(FadeOut(parabola), FadeOut(line), FadeOut(vector), FadeOut(dot), FadeOut(text1), FadeOut(text2), FadeOut(slope_text),FadeOut(surface_eqn))
-
- #self.move_camera(phi=80* DEGREES,theta= 90*DEGREES)
- self.play(ReplacementTransform(paraboloid_y, paraboloid_copy))
- self.wait()
-
- def get_tangent_vector(self, proportion, curve, dx=0.001, scale=1):
- coord_i = curve.point_from_proportion(proportion)
- coord_f = curve.point_from_proportion(proportion + dx)
- reference_line = Line(coord_i,coord_f)
- unit_vector = reference_line.get_unit_vector() * scale
- vector = Line(coord_i - unit_vector, coord_i + unit_vector, color = "#006400", buff=0)
- return vector
-
-
\ No newline at end of file |