diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem')
4 files changed, 0 insertions, 518 deletions
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface1.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface1.gif Binary files differdeleted file mode 100644 index 8c9fa0a..0000000 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface1.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface1.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface1.py deleted file mode 100644 index a590a53..0000000 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface1.py +++ /dev/null @@ -1,232 +0,0 @@ -from manimlib.imports import * - -class SurfacesAnimation(ThreeDScene): - - CONFIG = { - "axes_config": { - "x_min": 0, - "x_max": 4, - "y_min": 0, - "y_max": 4, - "z_min": -4, - "z_max": 4, - "a":0 ,"b": 4, "c":0 , "d":4, - "axes_shift":IN+LEFT, - "x_axis_config": { - "tick_frequency": 1, - "include_tip": False, - }, - "y_axis_config": { - "tick_frequency": 1, - "include_tip": False, - }, - "z_axis_config": { - "tick_frequency": 1, - # "include_tip": False, - }, - "num_axis_pieces": 1, - }, - "default_graph_style": { - "stroke_width": 2, - "stroke_color": WHITE, - }, - "default_surface_config": { - "fill_opacity": 0.5, - "checkerboard_colors": [LIGHT_GREY], - "stroke_width": 0.5, - "stroke_color": WHITE, - "stroke_opacity": 0.5, - }, - "Func": lambda x,y: 5*(x**2-y**2)/((1e-4+x**2+y**2)**2) - } - - - def construct(self): - - self.setup_axes() - self.set_camera_orientation(#distance=10, - phi=80 * DEGREES, - theta=35 * DEGREES, - ) - - fn_text=TextMobject("$z=\dfrac{x^2-y^2}{(x^2+y^2)^2}$").set_color(BLUE) - fn_text.to_corner(UR,buff=1) - self.add_fixed_in_frame_mobjects(fn_text) - - R=TextMobject("R").set_color(BLACK).scale(2).rotate(180*DEGREES , OUT) - R.move_to(self.axes.input_plane,IN) - self.add(R) - - #get the surface - surface= self.get_surface( - self.axes, lambda x , y: - self.Func(x,y) - ) - surface.set_style( - fill_opacity=0.6, - fill_color=BLUE_E, - stroke_width=0.8, - stroke_color=WHITE, - ) - - - self.begin_ambient_camera_rotation(rate=0.2) - self.play(Write(surface)) - - self.get_lines() - self.wait(4) - - def get_surface(self,axes, func, **kwargs): - config = { - "u_min": axes.x_max, - "u_max": axes.x_min, - "v_min": axes.y_max, - "v_max": axes.y_min, - "resolution": (10,10), - } - - config.update(self.default_surface_config) - config.update(kwargs) - return ParametricSurface( - lambda x,y : axes.c2p( - x, y, func(x, y) - ), - **config - ) - - def get_lines(self): - axes = self.axes - labels=[axes.x_axis.n2p(axes.a), axes.x_axis.n2p(axes.b), axes.y_axis.n2p(axes.c), - axes.y_axis.n2p(axes.d)] - - - surface_corners=[] - for x,y,z in self.region_corners: - surface_corners.append([x,y,self.Func(x,y)]) - - lines=VGroup() - for start , end in zip(surface_corners, - self.region_corners): - lines.add(self.draw_lines(start,end,"YELLOW")) - - for start , end in zip(labels, - self.region_corners): - # lines.add(self.draw_lines(start,end,"BLUE")) - # print (start,end) - pass - self.play(ShowCreation(lines)) - - - def draw_lines(self,start,end,color): - start=self.axes.c2p(*start) - end=self.axes.c2p(*end) - line=DashedLine(start,end,color=color) - - return line - - def get_three_d_axes(self, include_labels=True, include_numbers=True, **kwargs): - config = dict(self.axes_config) - config.update(kwargs) - axes = ThreeDAxes(**config) - axes.set_stroke(width=2) - - if include_numbers: - self.add_axes_numbers(axes) - - if include_labels: - self.add_axes_labels(axes) - - # Adjust axis orientation - axes.x_axis.rotate( - 90 * DEGREES, LEFT, - about_point=axes.c2p(0, 0, 0), - ) - axes.y_axis.rotate( - 90 * DEGREES, UP, - about_point=axes.c2p(0, 0, 0), - ) - - # Add xy-plane - input_plane = self.get_surface( - axes, lambda x, t: 0 - ) - input_plane.set_style( - fill_opacity=0.3, - fill_color=PINK, - stroke_width=.2, - stroke_color=WHITE, - ) - - axes.input_plane = input_plane - - self.region_corners=[ - input_plane.get_corner(pos) for pos in (DL,DR,UR,UL)] - - return axes - - - def setup_axes(self): - axes = self.get_three_d_axes(include_labels=True) - axes.add(axes.input_plane) - axes.scale(1) - # axes.center() - axes.shift(axes.axes_shift) - - self.add(axes) - self.axes = axes - - def add_axes_numbers(self, axes): - x_axis = axes.x_axis - y_axis = axes.y_axis - tex_vals_x = [ - ("a", axes.a+.4), - ("b", axes.b), - ] - tex_vals_y=[ - ("c", axes.c+.4), - ("d", axes.d) - ] - x_labels = VGroup() - y_labels = VGroup() - for tex, val in tex_vals_x: - label = TexMobject(tex) - label.scale(1) - label.next_to(x_axis.n2p(val), DOWN) - label.rotate(180 * DEGREES) - x_labels.add(label) - x_axis.add(x_labels) - x_axis.numbers = x_labels - - for tex, val in tex_vals_y: - label = TexMobject(tex) - label.scale(1) - label.next_to(y_axis.n2p(val), LEFT) - label.rotate(90 * DEGREES) - y_labels.add(label) - - y_axis.add(y_labels) - y_axis.numbers = y_labels - - return axes - - def add_axes_labels(self, axes): - x_label = TexMobject("x") - x_label.next_to(axes.x_axis.get_end(), RIGHT) - axes.x_axis.label = x_label - - y_label = TextMobject("y") - y_label.rotate(90 * DEGREES, OUT) - y_label.next_to(axes.y_axis.get_end(), UP) - axes.y_axis.label = y_label - - z_label = TextMobject("z") - z_label.rotate(90 * DEGREES, LEFT) - z_label.next_to(axes.z_axis.get_zenith(), LEFT) - axes.z_axis.label = z_label - for axis in axes: - axis.add(axis.label) - return axes - -#uploaded by Somnath Pandit.FSF2020_Fubini's_Theorem - - diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.gif Binary files differdeleted file mode 100644 index ac13f21..0000000 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.gif +++ /dev/null diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.py deleted file mode 100644 index c998f3b..0000000 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.py +++ /dev/null @@ -1,286 +0,0 @@ -from manimlib.imports import * - -class SurfacesAnimation(ThreeDScene): - - CONFIG = { - "axes_config": { - "x_min": 0, - "x_max": 4, - "y_min": 0, - "y_max": 4, - "z_min": -2, - "z_max": 4, - "a":0 ,"b": 4, "c":0 , "d":4, - "axes_shift":IN+2*LEFT+2*DOWN, - "x_axis_config": { - "tick_frequency": 1, - "include_tip": False, - }, - "y_axis_config": { - "tick_frequency": 1, - "include_tip": False, - }, - "z_axis_config": { - "tick_frequency": 1, - # "include_tip": False, - }, - "num_axis_pieces": 1, - }, - "default_graph_style": { - "stroke_width": 2, - "stroke_color": WHITE, - }, - "default_surface_config": { - "fill_opacity": 0.5, - "checkerboard_colors": [LIGHT_GREY], - "stroke_width": 0.5, - "stroke_color": WHITE, - "stroke_opacity": 0.5, - }, - "Func": lambda x,y: x*y/4 - } - - - def construct(self): - - self.setup_axes() - self.set_camera_orientation( - distance=30, - phi=75 * DEGREES, - theta=20 * DEGREES, - ) - - fn_text=TextMobject("$z=xy$").set_color(BLUE).scale(1.5) - fn_text.to_corner(UR,buff=2) - self.add_fixed_in_frame_mobjects(fn_text) - - - #get the surface - surface= self.get_surface( - self.axes, lambda x , y: - self.Func(x,y) - ) - surface.set_style( - fill_opacity=.5, - fill_color=BLUE_E, - stroke_width=0.2, - stroke_color=WHITE, - ) - #get boundary curves - c1=self.get_curve( - self.axes, lambda x: x**2/4 - ) - c1_label=TextMobject("$y=x^2$").next_to(c1,IN+OUT).shift(DOWN+RIGHT) - c1_label.rotate(PI) - c1_group=VGroup(c1,c1_label).set_color(ORANGE) - - c2=self.get_curve( - self.axes, lambda x: x - ).set_color(PINK) - c2_label=TextMobject("$y=x$").next_to(c2,IN+OUT) - c2_label.rotate(PI/2,about_point=(c2_label.get_corner(UL))) - c2_group=VGroup(c2,c2_label).set_color(YELLOW_E) - - - - self.add(c1,c2,c1_label,c2_label) - - self.begin_ambient_camera_rotation(rate=0.4) - self.get_region(self.axes,c1,c2) - self.play(Write(surface)) - self.get_lines() - self.wait(1) - self.stop_ambient_camera_rotation() - self.move_camera( - distance=20, - phi=10 * DEGREES, - theta=80 * DEGREES, - run_time=2.5 - ) - self.wait(2) - - - - def get_curve(self,axes, func, **kwargs): - config = { - "t_min": axes.x_min, - "t_max": axes.x_max, - } - config.update(kwargs) - return ParametricFunction( - lambda x : axes.c2p( - x, func(x),0 - ), - **config - ) - - def get_region(self,axes,curve1,curve2,**kwargs): - x_vals=np.arange(axes.x_min,axes.x_max,.1) - c1_points=[curve1.get_point_from_function(x) for x in x_vals] - c2_points=[curve2.get_point_from_function(x) for x in x_vals] - c2_points.reverse() - points=c1_points+c2_points - region=Polygon(*points, - stroke_width=0, - fill_color=PINK, - fill_opacity=.5 - ) - R=TextMobject("R").set_color(PINK).scale(2).rotate(180*DEGREES , OUT) - R.move_to(region,IN+RIGHT) - - self.play(Write(region)) - self.add(R) - - def get_surface(self,axes, func, **kwargs): - config = { - "u_min": axes.x_max, - "u_max": axes.x_min, - "v_min": axes.y_max, - "v_max": axes.y_min, - "resolution": (10,10), - } - - config.update(self.default_surface_config) - config.update(kwargs) - return ParametricSurface( - lambda x,y : axes.c2p( - x, y, func(x, y) - ), - **config - ) - - def get_lines(self): - axes = self.axes - labels=[axes.x_axis.n2p(axes.a), axes.x_axis.n2p(axes.b), axes.y_axis.n2p(axes.c), - axes.y_axis.n2p(axes.d)] - - - surface_corners=[] - for x,y,z in self.region_corners: - surface_corners.append([x,y,self.Func(x,y)]) - - lines=VGroup() - for start , end in zip(surface_corners, - self.region_corners): - lines.add(self.draw_lines(start,end,"YELLOW")) - - for start , end in zip(labels, - self.region_corners): - # lines.add(self.draw_lines(start,end,"BLUE")) - # print (start,end) - pass - self.play(ShowCreation(lines)) - - - def draw_lines(self,start,end,color): - start=self.axes.c2p(*start) - end=self.axes.c2p(*end) - line=DashedLine(start,end,color=color) - - return line - - #customize 3D axes - def get_three_d_axes(self, include_labels=True, include_numbers=True, **kwargs): - config = dict(self.axes_config) - config.update(kwargs) - axes = ThreeDAxes(**config) - axes.set_stroke(width=2) - - if include_numbers: - self.add_axes_numbers(axes) - - if include_labels: - self.add_axes_labels(axes) - - # Adjust axis orientation - axes.x_axis.rotate( - 90 * DEGREES, LEFT, - about_point=axes.c2p(0, 0, 0), - ) - axes.y_axis.rotate( - 90 * DEGREES, UP, - about_point=axes.c2p(0, 0, 0), - ) - - # Add xy-plane - input_plane = self.get_surface( - axes, lambda x, t: 0 - ) - input_plane.set_style( - fill_opacity=0.3, - fill_color=PINK, - stroke_width=.2, - stroke_color=WHITE, - ) - - axes.input_plane = input_plane - - self.region_corners=[ - input_plane.get_corner(pos) for pos in (DL,DR,UR,UL)] - - return axes - - - def setup_axes(self): - axes = self.get_three_d_axes(include_labels=True) - # axes.add(axes.input_plane) - axes.scale(1) - # axes.center() - axes.shift(axes.axes_shift) - - self.add(axes) - self.axes = axes - - def add_axes_numbers(self, axes): - x_axis = axes.x_axis - y_axis = axes.y_axis - tex_vals_x = [ - ("1", axes.b), - ] - tex_vals_y=[ - ("1", axes.d) - ] - x_labels = VGroup() - y_labels = VGroup() - for tex, val in tex_vals_x: - label = TexMobject(tex) - label.scale(1) - label.next_to(x_axis.n2p(val), DOWN) - label.rotate(180 * DEGREES) - x_labels.add(label) - x_axis.add(x_labels) - x_axis.numbers = x_labels - - for tex, val in tex_vals_y: - label = TexMobject(tex) - label.scale(1) - label.next_to(y_axis.n2p(val), LEFT) - label.rotate(90 * DEGREES) - y_labels.add(label) - - y_axis.add(y_labels) - y_axis.numbers = y_labels - - return axes - - def add_axes_labels(self, axes): - x_label = TexMobject("x") - x_label.next_to(axes.x_axis.get_end(), RIGHT) - axes.x_axis.label = x_label - - y_label = TextMobject("y") - y_label.rotate(90 * DEGREES, OUT) - y_label.next_to(axes.y_axis.get_end(), UP) - axes.y_axis.label = y_label - - z_label = TextMobject("z") - z_label.rotate(90 * DEGREES, LEFT) - z_label.next_to(axes.z_axis.get_zenith(), LEFT) - axes.z_axis.label = z_label - for axis in axes: - axis.add(axis.label) - return axes - - #uploaded by Somnath Pandit.FSF2020_Fubini's_Theorem - 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