## Tutoring on Surface Integrals

Learning Objectives:

#### Understand and Apply Surface Integrals.

Math Tutoring on Surface Integrals

To parameterize a surface in math tutoring, we will need two parameters and three dependent variables.

Where u and v define a region R in the uv – plane.  will sweep out the surface.

Surface Integral with Surface Defined Parametrically:

If a smooth surface given by  and f is a continuous function then the Surface Integral will be –

Surface Integral with Surface Defined Explicitly:

For a surface S given by , that is continuous and differentiable over a region R in the xy – plane, then the Surface Integral will be –

Divergence Theorem:

This theorem states the total Divergence of a Vector Field in a solid region V equals the total flow across the Boundary Surface S. So the Flux of a Vector Field across a Surface in Space will be –

This shows the relationship between a Triple Integral over a solid region and Surface Integral over a surface.

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Hook Questions:

1.     How to parameterize a Surface?

2.     Define Surface Integral with Surface defined Parametrically and Explicitly?

3.     State Divergence Theorem.

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