diff options
Diffstat (limited to 'FSF-2020')
9 files changed, 518 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/area_Under_func.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/area_Under_func.gif Binary files differnew file mode 100644 index 0000000..223218b --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/area_Under_func.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/elementary_area.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/elementary_area.gif Binary files differnew file mode 100644 index 0000000..5c9ac03 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/elementary_area.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/non_rect_region.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/non_rect_region.gif Binary files differnew file mode 100644 index 0000000..c8e7c8c --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/non_rect_region.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/surface.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/surface.gif Binary files differnew file mode 100644 index 0000000..ae23a7b --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/surface.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/YlimitXdependent.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/y_limit_dependent_on_x.gif Binary files differindex a2bfd9d..a2bfd9d 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/YlimitXdependent.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/y_limit_dependent_on_x.gif 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 differnew file mode 100644 index 0000000..8c9fa0a --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface1.gif 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 new file mode 100644 index 0000000..a590a53 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface1.py @@ -0,0 +1,232 @@ +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 differnew file mode 100644 index 0000000..ac13f21 --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.gif 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 new file mode 100644 index 0000000..c998f3b --- /dev/null +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fubini's_theorem/surface2.py @@ -0,0 +1,286 @@ +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 + + |
