Vector Calculus Part2 (Line Integrals & Surface Integrals 1)

VECTOR CALCULUS in Mathematics is a sub-division of Calculus that deals with the differentiation and integration of Vector Functions. Vector Calculus, also known as Vector Analysis, deals with the differentiation and integration of vector field, especially in the three-dimensional Euclidean space.

This Course on Vector Calculus is covering the LINE INTEGRALS & SURFACE INTEGRALS that is beautifully covered with the contents that are listed below_

LINE INTEGRALS

1) Introduction to Line integrals and Detailed concept of Tangential Line Integrals

2) Circulation of a vector along the Curves.

3)Evaluating the Line integrals along the parabolic curve, curve joining the two points.

4) Evaluating the Line Integrals along the Triangles, Rectangles along the path with parametric equations, along  the Straight Line joining the points and along the Closed Path.

SURFACE INTEGRALS

1) Introduction to Surface Integrals and Normal Surface Integrals

2) Detailed concepts about the Direction Cosines and Unit Vector Normal

3) Evaluating the Surface Integrals & Volume Integrals with detailed concepts.

4) Evaluating the Surface Integrals for a Sphere with origin at center, Sphere in the first Octant, part of the sphere in the first octant.

5)Evaluating the Surface Integrals for a Plane in the first Octant, for a Cylinder in the first Octant.

6) Finding the Total Work Done in moving a particle in a force Field.

7) Investigating a Vector Point Function to be the Gradient Vector.

GAUSS DIVERGENCE THEOREM

1) Statement and Proof of Gauss Divergence Theorem and its Corollary with Important Results covering Gradient, Divergence and Curl of a Vector Function.

2) Evaluating the Surface Integrals using Gauss Divergence Theorem including Solved Assignments.

And, all the Expected Theorems, Results and assignments covering all the above Contents.

Thanks and Regards!