Line Integrals and Potentials
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Exactness and independence of path
Equations are omitted for technical reasons - download the original pdf
Let [Equation goes here - download the original pdf to see it.] be such that [Equation goes here - download the original pdf to see it.]have continuous first partial derivatives in the domain D. Then [Equation goes here - download the original pdf to see it.] [Equation goes here - download the original pdf to see it.] Proof [Equation goes here - download the original pdf to see it.] (This is by the theorem: If f is a scalar function, then [Equation goes here - download the original pdf to see it.] , which is demonstrated when the definition of curl F is introduced.) [Equation 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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