Merge branch 'panditsomnath10016git-master'

7 files changed, 721 insertions, 0 deletions

diff --git a/FSF-2020/integrals-of-multivariable-functions/README.md b/FSF-2020/integrals-of-multivariable-functions/README.md
index e69de29..a321caf 100644
--- a/FSF-2020/integrals-of-multivariable-functions/README.md
+++ b/FSF-2020/integrals-of-multivariable-functions/README.md
@@ -0,0 +1 @@
+FSF2020--Somnath Pandit

diff --git a/FSF-2020/integrals-of-multivariable-functions/YlimitXdependent.gif b/FSF-2020/integrals-of-multivariable-functions/YlimitXdependent.gif
new file mode 100644
index 0000000..a2bfd9d
--- /dev/null
+++ b/FSF-2020/integrals-of-multivariable-functions/YlimitXdependent.gif
diff --git a/FSF-2020/integrals-of-multivariable-functions/area_under_func.py b/FSF-2020/integrals-of-multivariable-functions/area_under_func.py
new file mode 100644
index 0000000..773840c
--- /dev/null
+++ b/FSF-2020/integrals-of-multivariable-functions/area_under_func.py
@@ -0,0 +1,73 @@
+from manimlib.imports import *
+
+
+class AreaUnderIntegral(GraphScene):
+    CONFIG = {
+        "x_min" : 0,
+        "x_max" : 5,
+        "y_min" : 0,
+        "y_max" : 6,
+        "Func":lambda x : 1+x**2*np.exp(-.15*x**2)
+    }  
+
+    def construct(self):
+        X = RIGHT*self.x_axis_width/(self.x_max- self.x_min)
+        Y = UP*self.y_axis_height/(self.y_max- self.y_min)
+        
+        int_area_sym=TextMobject("$$\int_{a}^b f(x)dx$$").shift(2*UP)
+        area_mean_text = TextMobject(r"means area under the curve of $f(x)$ \\ in the region $a\leq x\leq b$").next_to(int_area_sym,DOWN)
+        
+        opening_text=VGroup(*[int_area_sym,area_mean_text])
+        self.play(Write(opening_text),run_time=4)
+        self.wait(2)
+        self.play(FadeOut(opening_text))
+
+        self.setup_axes(animate=True)
+        func= self.get_graph(self.Func, x_min=0,x_max=5)
+        self.curve=func 
+        
+        func_text = TextMobject(r"$y = f(x)$").next_to(func,UP)
+        min_lim = self.get_vertical_line_to_graph(1,func,DashedLine,color=YELLOW)
+        tick_a=TextMobject(r"$a$").next_to(min_lim,DOWN)
+        max_lim = self.get_vertical_line_to_graph(4,func,DashedLine,color=YELLOW)
+        tick_b=TextMobject(r"$b$").next_to(max_lim,DOWN)
+        
+ #       area = self.get_area(func,1,4)
+
+        self.play(ShowCreation(func), ShowCreation(func_text))
+	
+        self.wait(2)
+        self.play(ShowCreation(min_lim),Write(tick_a), ShowCreation(max_lim),Write(tick_b),run_time=0.5)
+        
+  
+        approx_text=TextMobject(r"The area can be approximated as \\ sum of small rectangles").next_to(func,4*Y) 
+        self.play(Write(approx_text))
+        
+        rect_list = self.get_riemann_rectangles_list(
+            self.curve, 5, 
+            max_dx = 0.25,
+            x_min = 1,
+            x_max = 4,
+        )
+        flat_graph = self.get_graph(lambda t : 0)
+        rects = self.get_riemann_rectangles( flat_graph, x_min = 1, x_max = 4, dx = 0.5)
+        for new_rects in rect_list:
+            new_rects.set_fill(opacity = 0.8)
+            rects.align_submobjects(new_rects)
+            for alt_rect in rects[::2]:
+                alt_rect.set_fill(opacity = 0)
+            self.play(Transform(
+                rects, new_rects,
+                run_time = 1.5,
+                lag_ratio = 0.5
+            ))
+        conclude_text=TextMobject(r"Making the rectangles infinitesimally thin \\ we get the real area under the curve.").next_to(func,4*Y) 
+        self.play(Transform(approx_text,conclude_text))
+        self.wait(3)
+        int_area_sym.next_to(self.curve,IN)
+        self.play(Transform(conclude_text,int_area_sym))
+        
+ #       self.play(ShowCreation(area))
+        self.wait(3)
+        
+#uploaded by Somnath Pandit.FSF2020_Double_Integral
diff --git a/FSF-2020/integrals-of-multivariable-functions/elementary_area.py b/FSF-2020/integrals-of-multivariable-functions/elementary_area.py
new file mode 100644
index 0000000..362b6f8
--- /dev/null
+++ b/FSF-2020/integrals-of-multivariable-functions/elementary_area.py
@@ -0,0 +1,144 @@
+from manimlib.imports import *
+
+class ElementaryArea(GraphScene):
+    CONFIG = {
+        "x_min" : 0,
+        "x_max" : 2,
+        "y_min" : 0,
+        "y_max" : 2, 
+        "x_tick_frequency" : 1,
+        "y_tick_frequency" : 1,
+     #   "x_labeled_nums": list(np.arange(0,3)),
+      #  "y_labeled_nums": list(np.arange(0 ,3)),
+        "x_axis_width": 6,
+        "y_axis_height": 6,
+        "graph_origin": ORIGIN+3.5*LEFT+3.5*DOWN,    
+    }
+
+    def construct(self):
+        X = self.x_axis_width/(self.x_max- self.x_min)
+        Y = self.y_axis_height/(self.y_max- self.y_min)
+        self.X=X ;self.Y=Y 
+        self.setup_axes(animate=False)
+        
+        caption=TextMobject("The elementary area in ").to_edge(UP)
+        rect_text=TextMobject("Cartesian Coordinates").next_to(caption,DOWN,)
+        polar_text=TextMobject("Polar Coordinates").next_to(caption,DOWN,) 
+        
+        self.add(caption)
+        self.play(Write(rect_text))
+        self.get_rect_element()
+    #    self.play(Write(polar_text))
+        self.play(ReplacementTransform(rect_text,polar_text),
+          FadeOut(VGroup(self.dydx,self.rect_brace_gr)))
+        self.get_polar_element()
+        
+        
+        
+    def get_rect_element(self):
+        rect=Rectangle(
+            height=2, width=3,fill_color=BLUE_D,
+            fill_opacity=1, color=BLUE_D
+            ).scale(.75).move_to(
+            self.graph_origin+(RIGHT*self.X+UP*self.Y)
+            )
+        dx_brace=Brace(rect, DOWN, buff = SMALL_BUFF)
+        dx_label=dx_brace.get_text("$dx$", buff = SMALL_BUFF)
+        dx_brace_gr=VGroup(dx_brace,dx_label)
+        
+        dy_brace=Brace(rect,RIGHT, buff = SMALL_BUFF)
+        dy_label=dy_brace.get_text("$dy$", buff = SMALL_BUFF)
+        dy_brace_gr=VGroup(dy_brace,dy_label)
+        
+        brace_gr=VGroup(dx_brace_gr,dy_brace_gr)
+        
+        dydx=TextMobject("$dxdy$",color=BLACK).next_to(rect,IN)
+
+        self.play(FadeIn(rect))
+        self.play(GrowFromCenter(brace_gr))
+        self.play(GrowFromCenter(dydx))
+                 
+        self.rect=rect
+        self.rect_brace_gr=brace_gr
+        self.dydx=dydx
+        self.wait(2)
+  
+        
+    def  get_polar_element(self):
+        X=self.X ;Y=self.Y 
+        theta1=25*DEGREES
+        dtheta=TAU/12
+        r_in=1.3*X ; r_out=1.9*X
+        
+        arc=AnnularSector(
+        arc_center=self.graph_origin,
+        inner_radius=r_in,
+        outer_radius=r_out ,
+        angle= dtheta,
+        start_angle= theta1,
+        fill_opacity= 1,
+        stroke_width= 0,
+        color= BLUE_D, 
+        )
+        
+        
+    # # #getting braces
+        r_in_theta1=self.graph_origin+r_in*(np.cos(theta1)*RIGHT+np.sin(theta1)*UP)
+        dr_line=Line(r_in_theta1,r_in_theta1+RIGHT*(r_out-r_in))
+        dr_brace=Brace(dr_line, DOWN, buff = SMALL_BUFF
+            ).rotate(theta1, about_point=r_in_theta1
+            )
+        dr_label=dr_brace.get_text("$dr$", buff = SMALL_BUFF)
+        dr_brace_gr=VGroup(dr_brace,dr_label)
+        
+        theta2=theta1+dtheta
+        r_out_theta2=self.graph_origin+r_out*(
+            np.cos(theta2)*RIGHT+np.sin(theta2)*UP
+            )
+        rdt_line=Line(r_out_theta2,r_out_theta2
+            +DOWN*(r_out*dtheta)
+            )
+        rdt_brace=Brace(rdt_line, RIGHT, 
+            buff = MED_SMALL_BUFF).rotate(
+            theta2-(dtheta/2), about_point=r_out_theta2
+            )
+        rdt_label=rdt_brace.get_text("$rd\\theta$",buff = SMALL_BUFF)
+        rdt_brace_gr=VGroup(rdt_brace,rdt_label)
+   
+   #getting label r and dtheta 
+        r1=DashedLine(self.graph_origin,r_in_theta1).set_color(RED)
+        r2=DashedLine(self.graph_origin,r_out_theta2).set_color(RED)   
+        r_brace=Brace(r1, DOWN, buff = SMALL_BUFF).rotate(theta1, about_point=self.graph_origin)
+        r_label=r_brace.get_text("$r$", buff = SMALL_BUFF)
+        r_brace_gr=VGroup(r_brace,r_label)
+        
+        dtheta_arc=Arc(
+        arc_center=self.graph_origin,
+        radius=.5*X,
+        angle= dtheta,
+        start_angle=  theta1,
+        )
+        dtheta_arc_label=TextMobject("$d\\theta$").move_to(.99*dtheta_arc.get_corner(UR))
+        dtheta_label=VGroup(dtheta_arc,dtheta_arc_label)
+        
+        
+        rdrdt=TextMobject("$rdrd\\theta$",color=BLACK).next_to(arc,IN)
+        self.play(ReplacementTransform(self.rect,arc))
+        self.wait()
+        self.play(ShowCreation(r1),
+                ShowCreation(r2)
+                )
+        self.play(ShowCreation(r_brace_gr),
+                Write(dtheta_label)
+                )
+        self.wait()
+        self.play(GrowFromCenter(rdt_brace_gr))
+        self.wait(.5)
+        self.play(GrowFromCenter(dr_brace_gr))
+        self.wait(.5)
+        self.play(GrowFromCenter(rdrdt))
+        
+        self.wait(2)
+        
+        
+  #uploaded by Somnath Pandit.FSF2020_Double_Integral
diff --git a/FSF-2020/integrals-of-multivariable-functions/non_rect_region.py b/FSF-2020/integrals-of-multivariable-functions/non_rect_region.py
new file mode 100644
index 0000000..793a000
--- /dev/null
+++ b/FSF-2020/integrals-of-multivariable-functions/non_rect_region.py
@@ -0,0 +1,154 @@
+from manimlib.imports import *
+
+class AreaUnderCurve(GraphScene):
+    CONFIG = {
+        "x_min" : -1,
+        "x_max" : 8,
+        "y_min" : -1,
+        "y_max" : 5, 
+        "y_axis_label": "$y$",
+        "x_tick_frequency" : 1,
+        "y_tick_frequency" : 1,
+        "x_labeled_nums": list(np.arange(-1, 9)),
+	    "y_labeled_nums": list(np.arange(-1, 6)),
+	    "y_axis_height":5.5,
+        "graph_origin": ORIGIN+4*LEFT+2.5*DOWN,    
+    }
+
+    def construct(self):
+        X = RIGHT*self.x_axis_width/(self.x_max- self.x_min)
+        Y = UP*self.y_axis_height/(self.y_max- self.y_min)
+        
+        sofar_text=TextMobject(r"So far we have integrated  over \\ rectangular regions")
+        self.play(Write(sofar_text))
+        self.play(sofar_text.to_edge,UP)
+        
+        self.setup_axes(animate=False)
+        
+        rect= self.get_graph(
+            lambda x : 3,
+            x_min = 0,
+            x_max = 5,
+            color = GREEN)
+            
+        rect_region = self.get_riemann_rectangles(
+            rect, 
+            x_min = 0,
+            x_max = 5,
+            dx =.01,
+            start_color = GREEN,
+            end_color = GREEN,
+            fill_opacity = 0.75,
+            stroke_width = 0,
+        )
+        
+        self.play(ShowCreation(rect_region))
+        self.wait(.5)
+        
+        rect_int=TextMobject(r"Here the integration limits are set as").to_edge(UP)
+        rect_lim=TextMobject(r"$$\int_{x=0}^{5}\int_{y=0}^{3}$$").next_to(rect_int,DOWN) 
+        const_text=TextMobject(r"$\longleftarrow $ \textsf the limits are\\ constant values").next_to(rect_lim,RIGHT)
+        
+        self.play(ReplacementTransform(sofar_text,rect_int))
+        self.wait(1.5)
+        self.play(FadeIn(rect_lim))
+        self.wait(2)
+        self.play(Write(const_text))
+        self.wait(2)
+        self.play(FadeOut(rect_int), FadeOut(rect_lim),FadeOut(const_text))
+        
+        
+        non_rect_text=TextMobject(r"Now we see how to integrate over \\ non-rectangular regions")
+        non_rect_text.to_edge(UP)
+        self.play(Write(non_rect_text))
+        self.wait(1.5)
+        self.play(FadeOut(rect_region))
+        
+        c1= self.get_graph(
+            lambda x : x**2/4,
+            x_min = 0,
+            x_max = 4,
+            color = RED)
+            
+        c1_region = self.get_riemann_rectangles(
+            c1, 
+            x_min = 0,
+            x_max = 4,
+            dx =.01,
+            start_color = BLUE,
+            end_color = BLUE,
+            fill_opacity = 0.75,
+            stroke_width = 0,
+        )
+        self.add(c1,c1_region)
+ #       self.wait(2)
+        
+        c2= self.get_graph(
+            lambda x :12-2*x,
+            x_min = 4,
+            x_max = 6,
+            color = RED)
+            
+        c2_region = self.get_riemann_rectangles(
+            c2, 
+            x_min = 4,
+            x_max = 6,
+            dx =.01,
+            start_color = BLUE,
+            end_color = BLUE,
+            fill_opacity = .75,
+            stroke_width = 0,
+        )
+        self.add(c2_region,c2)
+        self.wait(1.5)
+        c=VGroup(*[c1,c2])
+        
+        no_func_text=TextMobject(r"The whole region can't be expressed as\\ bounded by a single $f(x)$").next_to(c2,UP,buff=LARGE_BUFF)
+        
+        self.play(ReplacementTransform(non_rect_text,no_func_text))
+        self.wait(1)
+        self.play(Indicate(c))
+        self.wait(2)
+        
+        div_region_text=TextMobject(r"So the region is divided into two").next_to(c2,UP,buff=MED_LARGE_BUFF)
+        self.play(ReplacementTransform(no_func_text,div_region_text))
+        
+        c2.set_color(YELLOW)
+        self.play(c2_region.set_color,YELLOW)
+        c1_text=TextMobject("$\dfrac{x^2}{4}$").next_to(c1,IN)
+        c2_text=TextMobject("$12-2x$").next_to(c2,IN+2*X)
+        c_text=VGroup(*[c1_text,c2_text])
+        
+        self.play(FadeIn(c_text))
+        self.wait(.4)
+        self.play(Indicate(c1),Indicate(c1_text))
+        self.play(Indicate(c2),Indicate(c2_text))
+        
+        easy_text=TextMobject(r"Now the limis can be set easily").next_to(c2,UP,buff=.5)
+        self.play(ReplacementTransform(div_region_text,easy_text))
+        
+        c1_int=TextMobject(r"$$\int_{x=0}^{4}\int_{y=0}^{\dfrac{x^2}{4}}$$").next_to(c1,IN).shift(.5*(-X+1.3*Y))
+        c2_int=TextMobject(r"$$\int_{x=4}^{6}\int_{y=0}^{12-2x}$$").next_to(c2,IN+X)
+        
+        self.play(ReplacementTransform(c1_text,c1_int),ReplacementTransform(c2_text,c2_int))
+        self.wait(2)
+        
+        total_int=TextMobject(r"The total integraton= ").to_edge(UP)
+        plus=TextMobject("$$+$$").move_to(self.graph_origin+4*X+4.8*Y)
+        self.play(ReplacementTransform(easy_text,total_int))
+        self.play(c2_region.set_color,BLUE)
+        self.play(c1_int.next_to,c1,.1*UP, c2_int.next_to,plus,RIGHT, FadeIn(plus))
+        
+        region=VGroup(*[c1_region,c2_region])
+        region.set_color(GREEN)
+        self.play(ShowCreation(region))
+        self.wait(3)
+
+        
+	
+#uploaded by Somnath Pandit.FSF2020_Double_Integral
+        
+        
+        
+        
+        
diff --git a/FSF-2020/integrals-of-multivariable-functions/surface.py b/FSF-2020/integrals-of-multivariable-functions/surface.py
new file mode 100644
index 0000000..a794f46
--- /dev/null
+++ b/FSF-2020/integrals-of-multivariable-functions/surface.py
@@ -0,0 +1,236 @@
+from manimlib.imports import *
+
+class SurfacesAnimation(ThreeDScene):
+
+    CONFIG = {
+        "axes_config": {
+            "x_min": 0,
+            "x_max": 8,
+            "y_min": 0,
+            "y_max": 8,
+            "z_min": 0,
+            "z_max": 6,
+            "a":1 ,"b": 6, "c":2 , "d":6,
+            "axes_shift":-3*OUT + 5*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: 2+y/4+np.sin(x)
+    }
+
+
+    def construct(self):
+
+        self.setup_axes()
+        self.set_camera_orientation(distance=35,
+            phi=80 * DEGREES,
+            theta=-80 * 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(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=0.8,
+            fill_color=PINK,
+            stroke_width=0.8,
+            stroke_color=WHITE,
+        )
+        
+        
+        self.begin_ambient_camera_rotation(rate=0.07)
+        self.play(Write(surface))
+      #  self.play(LaggedStart(ShowCreation(surface)))
+        
+        self.get_lines()
+   #     self.play(FadeIn(self.axes.input_plane))
+        self.wait(3)
+      
+    def get_surface(self,axes, func, **kwargs):
+        config = {
+            "u_min": axes.a,
+            "u_max": axes.b,
+            "v_min": axes.c,
+            "v_max": axes.d,
+            "resolution": (
+                (axes.y_max - axes.y_min) // axes.y_axis.tick_frequency,
+                (axes.x_max - axes.x_min) // axes.x_axis.tick_frequency,
+            ),
+        }
+        
+        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,"RED"))
+            
+        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, RIGHT,
+            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=0.5,
+            fill_color=TEAL,
+            stroke_width=0,
+            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),
+            ("b", axes.b),
+        ]
+        tex_vals_y=[
+            ("c", axes.c),
+            ("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)
+            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(1.5)
+            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, RIGHT)
+        z_label.next_to(axes.z_axis.get_zenith(), RIGHT)
+        axes.z_axis.label = z_label
+        for axis in axes:
+            axis.add(axis.label)
+        return axes    
+        
+    
+
+#uploaded by Somnath Pandit.FSF2020_Double_Integral
diff --git a/FSF-2020/integrals-of-multivariable-functions/y_limit_dependent_on_x.py b/FSF-2020/integrals-of-multivariable-functions/y_limit_dependent_on_x.py
new file mode 100644
index 0000000..4894ebf
--- /dev/null
+++ b/FSF-2020/integrals-of-multivariable-functions/y_limit_dependent_on_x.py
@@ -0,0 +1,113 @@
+from manimlib.imports import *
+
+class YlimitXdependent(GraphScene):
+    CONFIG = {
+        "x_min" : 0,
+        "x_max" : 1,
+        "y_min" : 0,
+        "y_max" : 2, 
+        "x_tick_frequency" : 1,
+        "y_tick_frequency" : 1,
+        "x_labeled_nums": list(np.arange(0,2)),
+        "y_labeled_nums": list(np.arange(0 ,3)),
+        "x_axis_width": 3.5,
+        "y_axis_height": 6,
+        "graph_origin": ORIGIN+2.5*LEFT+3*DOWN,    
+    }
+
+    def construct(self):
+        X = RIGHT*self.x_axis_width/(self.x_max- self.x_min)
+        Y = UP*self.y_axis_height/(self.y_max- self.y_min)
+        
+        self.setup_axes(animate=False)
+        
+        line= self.get_graph(
+            lambda x : 2-2*x ,
+            x_min = 0,
+            x_max = 1,
+            color = RED)
+        line_eqn=TextMobject("2x+y=2").move_to(self.graph_origin+.8*X+Y).rotate(np.arctan(-2))
+        self.line=line
+        
+        caption=TextMobject(r"See the value of $y$ \\ is changing with $x$").move_to(self.graph_origin+1.2*X+1.8*Y)
+        self.play(ShowCreation(line),Write(line_eqn))
+   #     self.show_area()
+        self.show_rects()
+        self.play(Write(caption))
+        self.show_y_values_at_different_x()
+
+        self.wait(.5)
+        
+  ###################         
+    def show_area(self):
+        area = self.get_riemann_rectangles(
+            self.line, 
+            x_min = 0,
+            x_max = 1,
+            dx =.0001,
+            start_color = BLUE,
+            end_color = BLUE,
+            fill_opacity = 1,
+            stroke_width = 0,
+        )
+        self.play(ShowCreation(area))
+  #      self.transform_between_riemann_rects(self.rects,area)
+        self.area = area
+                
+    def show_rects(self):
+        rects = self.get_riemann_rectangles(
+            self.line, 
+            x_min = 0,
+            x_max = 1,
+            dx =.01,
+            start_color = BLUE,
+            end_color = BLUE,
+            fill_opacity =1,
+            stroke_width = 0,
+        )
+     #   self.play(ShowCreation(rects))
+     #   self.transform_between_riemann_rects(self.area,rects)
+        self.rects=rects 
+        
+    def show_y_values_at_different_x(self):
+        rects=self.rects
+        rect = rects[len(rects)*1//10]
+        dx_brace = Brace(rect, DOWN, buff = 0)
+        dx_label = dx_brace.get_text("$dx$", buff = SMALL_BUFF)
+        dx_brace_group = VGroup(dx_brace,dx_label)
+        rp=int(len(rects)/10)
+        rects_subset = self.rects[3*rp:5*rp]
+
+        last_rect = None
+        for rect in rects_subset:
+            brace = Brace(rect, LEFT, buff = 0)
+            y = TexMobject("y=2-2x")#.rotate(PI/2)
+            y.next_to(brace, LEFT, SMALL_BUFF)
+            anims = [
+                rect.set_fill, BLUE_E, 1,
+                dx_brace_group.next_to, rect, DOWN, SMALL_BUFF
+            ]
+            if last_rect is not None:
+                anims += [
+                    last_rect.set_fill, None, 0,
+       #             last_rect.set_fill, BLUE, .75,
+                    ReplacementTransform(last_brace, brace),
+                    ReplacementTransform(last_y, y),
+                ]
+            else:
+                anims += [
+                    GrowFromCenter(brace),
+                    Write(y)
+                ]
+            self.play(*anims)
+           # self.wait(.2)
+
+            last_rect = rect
+            last_brace = brace
+            last_y = y
+
+        y = last_y
+        y_brace = last_brace
+        
+          
+#uploaded by Somnath Pandit.FSF2020_Double_Integral