Line Integrals and Potentials
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Potentials
Equations are omitted for technical reasons - download the original pdf
Let F be a vector field in a domain D. Then the line integral [Equation goes here - download the original pdf to see it.] is independent of path, if, and only if [Equation goes here - download the original pdf to see it.] for some scalar field f. [Example goes here - download the original pdf to see it.]
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Contents of
Line Integrals and Potentials
1 Line integrals that are independent of path
2 Curve of integration
3 Line integrals
4 Potentials
5 Proof of the theorem
6 The line integral depends on path
7 Potentials and integration around a closed curve
8 The line integral does not depend on the parameter
9 Conservative scalar fields
10 Work integral
11 Work done is equal to gain in kinetic energy
12 Exact differential forms
13 Simply connected domains
14 Exactness and independence of path
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