new file and rename

5 files changed, 185 insertions, 17 deletions

diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/README.md b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/README.md
index edd176f..aa8c7f8 100644
--- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/README.md
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/README.md
@@ -1,5 +1,9 @@
 **file1_grad_of_scalar_function**
 ![file1_grad_of_scalar_function](https://github.com/panditsomnath10016git/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file1_grad_of_scalar_function.gif)
 
-**file2_line_int_example**
-![file2_line_int_example](https://github.com/panditsomnath10016git/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_example.gif)
+**file2_line_int_independent_of_path**
+![file2_line_int_independent_of_path](https://github.com/panditsomnath10016git/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_independent_of_path.gif)
+
+**file3_line_int_example**
+![file3_line_int_example](https://github.com/panditsomnath10016git/FSF-mathematics-python-code-archive/blob/master/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file3_line_int_example.gif)
+
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_independent_of_path.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_independent_of_path.gif
new file mode 100644
index 0000000..29c6d02
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_independent_of_path.gif
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_independent_of_path.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_independent_of_path.py
new file mode 100644
index 0000000..b9597b6
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_independent_of_path.py
@@ -0,0 +1,174 @@
+from manimlib.imports import *
+
+
+class LineIntegration(GraphScene):
+    CONFIG = {
+        "x_min" : -5,
+        "x_max" : 5,
+        "y_min" : -5,
+        "y_max" : 5,
+        "axes_color":BLACK,
+        "graph_origin": ORIGIN+1.2*DOWN,
+        "x_axis_width": 10,
+        "y_axis_height": 10 ,
+        "x_axis_label": "",
+        "y_axis_label": "",
+        "x_tick_frequency": 1,
+        "y_tick_frequency": 1,
+        "default_vector_field_config": {
+            "delta_x": .6,
+            "delta_y": .6,
+            "min_magnitude": 0,
+            "max_magnitude": .5,
+            "colors": [GREEN,BLUE,BLUE,TEAL],
+            "length_func": lambda norm : .45*sigmoid(norm),
+            "opacity": .75,
+            "vector_config": {
+                "stroke_width":1.5
+            },
+        },
+        
+        "a": .45,"b": 2, 
+        "path_color": PURPLE
+    }  
+
+    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.X=X ;self.Y=Y
+        
+        self.setup_axes(animate=False)
+        
+        
+        
+        
+        vector_field=self.get_vector_field(
+            lambda v: np.array([
+            v[1]-self.graph_origin[1],  
+            v[0]-self.graph_origin[0],  
+            0,
+            ])
+        ) 
+        vector_field_text=TexMobject(
+            "\\vec F(x,y)","=y\hat i+x\hat j",
+            stroke_width=1.5
+            ).to_edge(TOP,buff=.2)
+            
+        vector_field_text[0][0:2].set_color(TEAL)
+        
+        grad_f=TexMobject(
+            "\\vec\\nabla f(x,y)",
+            stroke_width=1.5
+        )
+        grad_f[0][2].set_color(LIGHT_BROWN)
+        grad_f.move_to(vector_field_text[0])
+        
+        self.add(vector_field,)
+        self.play(Write(vector_field_text))
+        self.wait()
+        self.play(
+            ReplacementTransform(
+                vector_field_text[0],grad_f
+            )
+        )
+        self.get_endpoints_of_curve()
+        self.wait(.6)
+        vector_field.set_fill(opacity=.4)
+        self.show_line_integral()
+        self.wait(2)
+    
+    
+    
+    
+        
+    def get_vector_field(self,func,**kwargs):
+        config = dict()
+        config.update(self.default_vector_field_config)
+        config.update(kwargs)
+        vector_field= VectorField(func,**config)
+        
+        self.vector_field= vector_field
+        
+        return vector_field   
+
+ 
+    
+    def get_endpoints_of_curve(self):
+        points=[[-3,0],[2,2]]
+        point_labels= ["P_i","P_f"]
+        for point,label in zip(points,point_labels):
+            dot=Dot(self.coords_to_point(*point)).set_color(RED)
+            dot_label=TexMobject(label)
+            dot_label.next_to(dot,DR,buff=.2)
+            self.play(FadeIn(VGroup(dot,dot_label)))
+            self.wait(.2)
+            
+        self.end_points=points
+        
+    def show_line_integral(self):
+        int_text=TexMobject(
+            r"\int_{P_i}^{P_f}\vec F \cdot d\vec r",
+            stroke_width=1.5,
+        ).scale(1.2)
+        int_text[0][0].set_color(self.path_color)
+        int_text[0][5:7].set_color(TEAL)
+        int_text.to_edge(RIGHT+UP,buff=1)
+        
+        int_value= TexMobject(r"=f(P_i)-f(P_f)",
+            stroke_width=1.5
+        ).next_to(int_text,DOWN)
+        VGroup(int_value[0][1],
+            int_value[0][7]
+        ).set_color(LIGHT_BROWN)
+        
+        path_indepent_text=TextMobject(
+            r"Value of the Line Integral is\\ independent of Path",color=GOLD,stroke_width=2,).to_corner(DR,buff=1)
+        
+        path_indepent_text[0][-4:].set_color(self.path_color)
+        
+        
+        self.play(Write(VGroup(
+            int_text,int_value
+            )),
+            run_time=2
+        )
+        self.wait(1.5)
+       
+        
+        self.show_path([[0,1],[-1,2],[1,3]])
+        self.play(Indicate(int_value))
+        self.play(Uncreate(self.path))
+        
+        self.show_path([[0,1]])
+        self.play(Indicate(int_value))
+        self.play(Uncreate(self.path))
+        
+        self.show_path([[-1,1],[-1,-2],[-5,0],[-2,3.5],[1,1]])
+        self.play(Indicate(int_value),run_time=2)
+        self.wait(.6)
+        
+        self.play(Write(path_indepent_text))
+  
+       
+        
+    def show_path(self,points):
+        points=[self.end_points[0]]+points+[self.end_points[1]]
+        
+        path= VMobject()
+        path.set_points_smoothly([
+            self.coords_to_point(*point)
+                for point in points
+        ])
+        path.set_color(self.path_color)
+        self.play(ShowCreation(path),run_time=1.5)
+    
+        self.path=path     
+    
+ 
+        
+        
+        
+#uploaded by Somnath Pandit. FSF2020_Fundamental_Theorem_of_Line_Integrals
+
+
+       
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_example.gif b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file3_line_int_example.gif
index 20ed081..20ed081 100644
--- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_example.gif
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file3_line_int_example.gif
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_example.py b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file3_line_int_example.py
index 6dabe49..71506a3 100644
--- a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file2_line_int_example.py
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file3_line_int_example.py
@@ -79,26 +79,16 @@ class LineIntegration(GraphScene):
         return vector_field   
 
         
-        
-    def get_points(self):
-        dn=.1
-        x_vals=np.arange(self.a,self.b,dn)
-        y_vals=np.arange(self.a,self.b,dn)
-        points=[]
-        for x_val in x_vals:
-          for y_val in y_vals:
-            points+=[self.coords_to_point(x_val,y_val)]
-        return points 
     
     def get_endpoints_of_curve(self):
-        dots=[[1,1],[0,0]]
-        dot_labels= ["(1,1)","(0,0)"]
-        for dot,label in zip(dots,dot_labels):
-            dot=Dot(self.coords_to_point(*dot)).set_color(RED)
+        points=[[1,1],[0,0]]
+        point_labels= ["(1,1)","(0,0)"]
+        for point,label in zip(points,point_labels):
+            dot=Dot(self.coords_to_point(*point)).set_color(RED)
             dot_label=TexMobject(label)
             dot_label.next_to(dot,DR)
             self.add(dot,dot_label)
-        self.end_points=dots
+        self.end_points=points
         
     def show_line_integral(self):
         int_text=TexMobject(