   Chapter 16, Problem 13RCC

Chapter
Section
Textbook Problem

(a) What is an oriented surface? Give an example of a non-orientable surface.(b) Define the surface integral (or flux) of a vector field F over an oriented surface S with unit normal vector n.(c) How do you evaluate such an integral if S is a parametric surface given by a vector function r(u, v)?(d) What if S is given by an equation z = g(x, y)?

(a)

To determine

To explain: The oriented surface and example of a non-oriented surface.

Explanation

The oriented surface S is a surface which has a possibility choose a unit normal vector (n) at every point on surface S and the unit normal vector varies point to point continuously over the surface. The orientation of surface either positive or negative is decided by the orientation of choice of unit normal vectors over surface

(b)

To determine

To define: The surface integral of a vector field F over oriented surface S with unit normal vector n .

(c)

To determine

To evaluate: The surface integral of a vector field F over oriented surface S given by vector function r(u,v) with unit normal vector n .

(d)

To determine

To find: The surface integral of vector field F with surface of equation z=g(x,y) .

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