From dd85fa70fa196fac02b88b84bdac4587a76139b8 Mon Sep 17 00:00:00 2001
From: Somnath Pandit
Date: Wed, 10 Jun 2020 22:21:44 +0530
Subject: update with upgrade
---
.../integrals-of-multivariable-functions/README.md | 4 +
.../double-integrals/file6_doing_integration.gif | Bin 6661372 -> 3349455 bytes
.../double-integrals/file6_doing_integration.py | 141 ++++++++++++---------
.../file7_int_process_of_example.gif | Bin 6100824 -> 3031924 bytes
.../file7_int_process_of_example.py | 62 +++++++--
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
index cafed44..7a9271b 100644
Binary files a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file6_doing_integration.gif and b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file6_doing_integration.gif differ
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
index d48656b..9fbdde8 100644
Binary files a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file7_int_process_of_example.gif and b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file7_int_process_of_example.gif differ
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
--
cgit