Surface Integrals, Gauss Divergence Theorem, Divergence Theorem, Vector calculus, Multiple Integrals,
SURFACE INTEGRALS
What you’ll learn
- Students will learn about how to evaluate Surface Integrals.
- To evaluate Surface Integrals using Gauss Divergence Theorem.
- Use of Gauss Divergence Theorem in solving many examples and in proving many Results.
- Expected Assignments and many Important Concept on Surface Integrals.
Course Content
- Surface Integral for the Cube –> 2 lectures • 26min.
- To Verify the Gauss’s Divergence Theorem –> 2 lectures • 29min.
- Expected Examples of Gauss Divergence Theorem –> 5 lectures • 31min.
- Evaluating the Surface Integral –> 21 lectures • 1hr 53min.
Requirements
SURFACE INTEGRALS
A surface integral is a mathematical concept that involves integrating over a surface in multivariable calculus. It’s a generalization of Multiple Integrals and is similar to a line integral, but instead of integrating over a curve, it’s done over a surface in 3-space.
This 2 hour 55 minutes Super Course ‘ VECTOR CALCULUS PART 3‘ is based on Evaluating the Surface Integrals using GAUSS DIVERGENCE THEOREM.
The contents for this course are listed below:
1) Evaluating the surface integral for the coterminous edges of a cube.
2) Direct Evaluation of the Surface Integral without using Gauss divergence theorem.
3) Evaluating the Surface integral of the cube bounded by the planes x = 0, x = a; y = 0, y = a; z = 0, z = a .
4) Verifying the Gauss Divergence Theorem for a vector function taken over the rectangular parallelopiped .
5) To verify the Gauss Divergence theorem for the vector function for the region occupied by the cube.
6) Evaluating the Surface integral for the surface of the sphere x²+y²+z²= 1.
7)Evaluating the Surface integral for the closed surface bounded by the planes z= 0, z = b and the cylinder x²+y²= a² by transforming to a Triple Integral.
8) Evaluating the Surface Integral over the surface of the cube bounded by the planes and the coordinate planes using the Divergence theorem in Cartesian form.
9) To show that given Surface Integral is the volume of the space enclosed by the surface S.
10) Proof of many important results using Gauss divergence Theorem and many more Expected Assignments.
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