1 files changed, 144 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file5_elementary_area.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file5_elementary_area.py
new file mode 100644
index 0000000..362b6f8
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/double-integrals/file5_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