Merge pull request #13 from panditsomnath10016git/master

Added gif in Double Integrals & new file in fubini's theorem

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
new 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
new 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
new 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
new 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
index 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
new 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
new 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
+  
+