diff options
Diffstat (limited to 'FSF-2020/calculus-of-several-variables')
5 files changed, 136 insertions, 71 deletions
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/README.md b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/README.md index 221e78d..4de6c1d 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/README.md +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/README.md @@ -7,3 +7,7 @@ FSF2020--Somnath Pandit ## Fubini's Theorem
## Line Integrals
+
+## Fundamental Theorem of Line integrals
+
+## Vector Fields
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file6_doing_integration.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file6_doing_integration.gif Binary files differindex cafed44..7a9271b 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file6_doing_integration.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file6_doing_integration.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file6_doing_integration.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file6_doing_integration.py index 34d1769..5a8cec0 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file6_doing_integration.py +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file6_doing_integration.py @@ -5,13 +5,13 @@ class IntegrationProcess(SpecialThreeDScene): CONFIG = { "axes_config": { "x_min": 0, - "x_max": 8, + "x_max": 7, "y_min": 0, - "y_max": 8, + "y_max": 7, "z_min": 0, - "z_max": 6, + "z_max": 4, "a":1 ,"b": 6, "c":2 , "d":6, - "axes_shift":-3*OUT + 5*LEFT, + "axes_shift":-3*OUT, "x_axis_config": { "tick_frequency": 1, # "include_tip": False, @@ -37,7 +37,7 @@ class IntegrationProcess(SpecialThreeDScene): "stroke_color": WHITE, "stroke_opacity": 0.5, }, - "Func": lambda x,y: 2+y/4+np.cos(x) + "Func": lambda x,y: 2+y/4+np.cos(x/1.4) } @@ -45,31 +45,34 @@ class IntegrationProcess(SpecialThreeDScene): self.setup_axes() axes=self.axes + + self.camera.frame_center.shift(axes.c2p(3,4,1.7)) self.set_camera_orientation(distance=35, - phi=85 * DEGREES, - theta=-80 * DEGREES, + phi= 80 * DEGREES, + theta= -80 * DEGREES, + gamma = 0 * DEGREES ) fn_text=TextMobject("$z=f(x,y)$").set_color(PINK) self.add_fixed_in_frame_mobjects(fn_text) - fn_text.to_edge(TOP,buff=MED_SMALL_BUFF) + R=TextMobject("R").set_color(BLACK).scale(3) R.move_to(axes.input_plane,IN) self.add(R) - #get the surface + # get the surface surface= self.get_surface( axes, lambda x , y: self.Func(x,y) ) surface.set_style( - fill_opacity=0.75, + fill_opacity=.65, fill_color=PINK, stroke_width=0.8, stroke_color=WHITE, ) - + fn_text.next_to(surface,UP,buff=MED_LARGE_BUFF) slice_curve=(self.get_y_slice_graph( axes,self.Func,5,color=YELLOW)) @@ -79,10 +82,10 @@ class IntegrationProcess(SpecialThreeDScene): self.add(surface) self.get_lines() - + self.show_process(axes) - self.wait(2) + self.wait(3) @@ -90,6 +93,7 @@ class IntegrationProcess(SpecialThreeDScene): y_tracker = ValueTracker(axes.c) self.y_tracker=y_tracker y=y_tracker.get_value + graph = always_redraw( lambda: self.get_y_slice_graph( axes, self.Func, y(), @@ -107,24 +111,67 @@ class IntegrationProcess(SpecialThreeDScene): ], *[ axes.c2p(x, y(), 0) - for x in [ axes.b, axes.a,] + for x in [ axes.b, axes.a,] ], - stroke_width=0, + stroke_width=2, + fill_color=BLUE_D, + fill_opacity=.4, + )) + + plane_side1 = always_redraw(lambda: Polygon( + *[ + axes.c2p(axes.a,y,self.Func(axes.a,y)) + for y in np.arange(axes.c,y(),0.01) + ], + *[ + axes.c2p(axes.a, y, 0) + for y in [ y(),axes.c, ] + ], + stroke_width=2.5, + fill_color=BLUE_C, + fill_opacity=.2, + )) + plane_side2 = always_redraw(lambda: Polygon( + *[ + axes.c2p(axes.b,y,self.Func(axes.b,y)) + for y in np.arange(axes.c,y(),0.01) + ], + *[ + axes.c2p(axes.b, y, 0) + for y in [y(),axes.c,] + ], + stroke_width=2.5, fill_color=BLUE_E, - fill_opacity=.5, + fill_opacity=.45, )) plane.suspend_updating() + plane_side1.suspend_updating() + plane_side2.suspend_updating() + + self.play(Write(VGroup(graph,plane)),run_time=2) + self.add(plane.copy(),plane_side1,plane_side2) + + + plane_side1.resume_updating() + plane_side2.resume_updating() - self.play(Write(VGroup(graph,plane)),run_time=4) - graph.resume_updating() - plane.resume_updating() + self.move_camera( + distance=30, + phi= 85 * DEGREES, + theta= -10 * DEGREES, + run_time=1.5 + ) self.play( ApplyMethod( y_tracker.set_value, axes.d, rate_func=linear, run_time=6, - ) + ) ) + plane.suspend_updating() + plane_side1.suspend_updating() + plane_side2.suspend_updating() + def get_y_slice_graph(self, axes, func, y, **kwargs): @@ -142,35 +189,7 @@ class IntegrationProcess(SpecialThreeDScene): **config, ) return slice_curve - - '''def get_y_slice_plane(self, axes): - self.y_tracker=y_tracker - y=y_tracker.get_value() - curve_points=[ - axes.c2p(x,y,self.Func(x,y)) - for x in np.arange(axes.a,axes.b,0.01) - ] - base_points=[ - axes.c2p(x, y, 0) - for x in [ axes.b, axes.a,] - ] - plane_points= curve_points+base_points - plane = always_redraw(lambda: Polygon( - *plane_points, - stroke_width=.4, - fill_color=BLUE, - fill_opacity=0.2 - )) - plane.add_updater(lambda m: m.shift( - axes.c2p( - axes.a, - y_tracker.get_value(), - 1, - ) - plane.points[0] - )) - plane.y_tracker = y_tracker - - return plane ''' + def get_surface(self,axes, func, **kwargs): config = { @@ -195,9 +214,6 @@ class IntegrationProcess(SpecialThreeDScene): 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: @@ -207,13 +223,17 @@ class IntegrationProcess(SpecialThreeDScene): for start , end in zip(surface_corners, self.region_corners): lines.add(self.draw_lines(start,end,"RED")) - + + labels=[ + (axes.a,0,0), + (axes.b,0,0), + (0,axes.d,0), + (0,axes.c,0) + ] + self.region_corners[-1]=self.region_corners[0] 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)) + lines.add(self.draw_lines(start,end,"WHITE")) self.add(lines) @@ -223,7 +243,10 @@ class IntegrationProcess(SpecialThreeDScene): 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) @@ -260,7 +283,7 @@ class IntegrationProcess(SpecialThreeDScene): axes.input_plane = input_plane self.region_corners=[ - input_plane.get_corner(pos) for pos in (DL,DR,UR,UL)] + input_plane.get_corner(pos) for pos in (DL,DR,UL,UR)] return axes diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file7_int_process_of_example.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file7_int_process_of_example.gif Binary files differindex d48656b..9fbdde8 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file7_int_process_of_example.gif +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file7_int_process_of_example.gif diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file7_int_process_of_example.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file7_int_process_of_example.py index ab9337d..f733761 100644 --- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file7_int_process_of_example.py +++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file7_int_process_of_example.py @@ -113,7 +113,35 @@ class IntegrationProcess(SpecialThreeDScene): fill_color=BLUE_E, fill_opacity=.65, )) + plane_side1 = always_redraw(lambda: Polygon( + *[ + axes.c2p(axes.a,y,self.Func(axes.a,y)) + for y in np.arange(axes.c,y(),0.01) + ], + *[ + axes.c2p(axes.a, y, 0) + for y in [ y(),axes.c, ] + ], + stroke_width=2.5, + fill_color=BLUE_C, + fill_opacity=.2, + )) + plane_side2 = always_redraw(lambda: Polygon( + *[ + axes.c2p(axes.b,y,self.Func(axes.b,y)) + for y in np.arange(axes.c,y(),0.01) + ], + *[ + axes.c2p(axes.b, y, 0) + for y in [y(),axes.c,] + ], + stroke_width=2.5, + fill_color=BLUE_E, + fill_opacity=.45, + )) plane.suspend_updating() + plane_side1.suspend_updating() + plane_side2.suspend_updating() first_x_text=TextMobject("First the $x$ integration..",color=YELLOW) first_x_text.to_corner(UR,buff=1.1) @@ -138,8 +166,11 @@ class IntegrationProcess(SpecialThreeDScene): self.remove(first_x_text) self.add_fixed_in_frame_mobjects(then_y_text) self.play(Write(then_y_text)) + self.add(plane.copy(),plane_side1,plane_side2) graph.resume_updating() plane.resume_updating() + plane_side1.resume_updating() + plane_side2.resume_updating() self.play( ApplyMethod( y_tracker.set_value, axes.d, @@ -148,6 +179,11 @@ class IntegrationProcess(SpecialThreeDScene): ) ) + graph.suspend_updating() + plane.suspend_updating() + plane_side1.suspend_updating() + plane_side2.suspend_updating() + def get_y_slice_graph(self, axes, func, y, **kwargs): config = dict() @@ -189,9 +225,6 @@ class IntegrationProcess(SpecialThreeDScene): 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: @@ -201,13 +234,17 @@ class IntegrationProcess(SpecialThreeDScene): for start , end in zip(surface_corners, self.region_corners): lines.add(self.draw_lines(start,end,"RED")) - + + labels=[ + (axes.a,0,0), + (axes.b,0,0), + (0,axes.d,0), + (0,axes.c,0) + ] + self.region_corners[-1]=self.region_corners[0] 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)) + lines.add(self.draw_lines(start,end,"WHITE")) self.add(lines) @@ -217,9 +254,10 @@ class IntegrationProcess(SpecialThreeDScene): line=DashedLine(start,end,color=color) return line - - - #customize 3D axes + + +#------------------------------------------------------------ + #customize 3d axes def get_three_d_axes(self, include_labels=True, include_numbers=True, **kwargs): config = dict(self.axes_config) config.update(kwargs) @@ -256,7 +294,7 @@ class IntegrationProcess(SpecialThreeDScene): axes.input_plane = input_plane self.region_corners=[ - input_plane.get_corner(pos) for pos in (DL,DR,UR,UL)] + input_plane.get_corner(pos) for pos in (DL,DR,UL,UR)] return axes |
