1 files changed, 149 insertions, 0 deletions
diff --git a/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file3_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
new file mode 100644
index 0000000..71506a3
--- /dev/null
+++ b/FSF-2020/calculus-of-several-variables/integrals-of-multivariable-functions/fundamental-theorem-of-line-integral/file3_line_int_example.py
@@ -0,0 +1,149 @@
+from manimlib.imports import *
+
+
+class LineIntegration(GraphScene):
+    CONFIG = {
+        "x_min" : -1,
+        "x_max" : 2,
+        "y_min" : -1,
+        "y_max" : 2,
+        "graph_origin": ORIGIN+3*LEFT+1.5*DOWN,
+        "x_axis_width": 10,
+        "y_axis_height": 10 ,
+        "x_tick_frequency": 1,
+        "y_tick_frequency": 1,
+        "default_vector_field_config": {
+            "delta_x": .5,
+            "delta_y": .5,
+            "min_magnitude": 0,
+            "max_magnitude": .5,
+            "colors": [GREEN,BLUE,BLUE,TEAL],
+            "length_func": lambda norm : .4*sigmoid(norm),
+            "opacity": .75,
+            "vector_config": {
+                "stroke_width":2
+            },
+        },
+        
+        "a": .45,"b": 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)
+        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=y\hat i+x\hat j",
+            stroke_width=2
+            ).to_corner(UR,buff=.75).scale(1.2)
+            
+        vector_field_text[0][0:3].set_color(TEAL),
+        self.add(vector_field,)
+        self.play(Write(vector_field_text))
+        self.wait()
+        self.get_endpoints_of_curve()
+        self.wait(.6)
+        self.play(
+            vector_field_text.shift,5*LEFT,
+
+        )
+        vector_field.set_fill(opacity=.2)
+        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=[[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=points
+        
+    def show_line_integral(self):
+        int_text=TexMobject(
+            "\\int_\\text{\\textbf{path}}\\vec F \\cdot d\\vec r= 1",
+            color=BLUE,
+            stroke_width=1.5
+        ).scale(1.2)
+        int_text[0][0].set_color(RED_C)
+        int_text[0][5:7].set_color(TEAL)
+        int_text.to_edge(RIGHT+UP,buff=1)
+        
+        close_int=TexMobject("O").set_color(RED).scale(1.3)
+        close_int.move_to(int_text[0][0],OUT)
+        close_int_val=TexMobject("0",color=BLUE).scale(1.4)
+        close_int_val.move_to(int_text[0][-1],OUT)
+        
+        self.play(Write(int_text))
+        
+        
+        self.show_method([[0,1]])
+        self.play(Indicate(int_text))
+        self.wait()
+  
+        self.show_method([[1,0]])
+        self.play(Indicate(int_text))
+        self.wait()
+        self.remove(int_text[0][-1])
+        self.add(close_int)
+        
+        for i in range(2):
+            self.play(self.paths[i].rotate,PI)
+        self.play(Indicate(close_int))
+        self.play(Write(close_int_val))
+        self.wait()
+       
+        
+    def show_method(self,points):
+        points=points+self.end_points
+        paths=[]
+        for i in range(-1,len(points)-2):
+            path=Arrow(
+                  self.coords_to_point(*points[i]),
+                  self.coords_to_point(*points[i+1]),
+                  buff=0
+                ).set_color(BLUE)
+            paths+=VGroup(path)
+            self.play(GrowArrow(path),run_time=1.5)
+    
+        self.paths=paths       
+    
+ 
+        
+        
+        
+#uploaded by Somnath Pandit. FSF2020_Fundamental_Theorem_of_Line_Integrals
+
+
+