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Line Integrals and Potentials


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Simply connected domains


A domain D is called simply connected if every closed path in D can be continuously shrunck to any point in D without leaving D.
Contents of
Line Integrals and Potentials

1 Line integrals that are independent of path
2 Curve of integration
3 Potentials
4 Line integrals
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 Exact differential forms
12 Work done is equal to gain in kinetic energy
13 Simply connected domains
14 Exactness and independence of path

Related articles: (1) The Curl of a Vector Field, (2) Green's Theorem in the Plane