Line Integrals and Potentials
DOWNLOAD
FREE
|
Conservative scalar fields
Equations are omitted for technical reasons - download the original pdf
Since, for any line integral that is independent of path in a domain D, the value of the integral is zero, this means that the work done (energy expended) in such a field in moving from a point A back to A is zero. Thus, all potential fields are conservative, meaning mechanical energy is conserved and no work is expended in moving around a closed loop. Obvious examples are the gravitational and electrical potentials. Friction tends to dissipate the energy of particles moving. If friction can be ignored the field is conservative; otherwise it is called nonconservative or dissipative.
|
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
|
