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 –
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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1. How to parameterize a Surface?
2. Define Surface Integral with Surface defined Parametrically and Explicitly?
3. State Divergence Theorem.
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