Summary of Jan. 31, 2007


	Differential elements and line integral	Jan. 31, 2007

+ For a system with [equation] ,

, ,
dV = .

+ Line integration (Examples 3.2 & 3.9): [equation] which measures circulation when the path is closed, i.e. . Steps:
1) find
2) find equations of the path (line). May be in pieces.
3) substitute the equations of the lines into and set the limits of integration.

+ General method for evaluating line integral, [equation] :
Parametric equation for a line, e.g. in (x,y,z)
x=f(t), y=g(t), z=h(t)
Calculate

Example 1.11: Line integration

Example 1.12: Ampere's Law
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HW #4	due 2/6/07

1. Find (i) [equation]

and (ii) P.2-12 (c) (in my notation [equation]

) and (e) (in my notation [equation]

) only (p. 68).
2. Identify the number of surfaces, equation for each surface, normal and scalar differential surface element of each surface for the volume described by [equation]