Path Integral
Let 👁 gamma
be a path
given parametrically by 👁 sigma(t)
.
Let 👁 s
denote arc
length from the initial point. Then
| 👁 int_gammaf(s)ds | 👁 = | 👁 int_a^bf(sigma(t))|sigma^'(t)|dt |
(1)
|
| 👁 Image | 👁 = | 👁 int_a^bf(x(t),y(t),z(t))|sigma^'(t)|dt, |
(2)
|
where 👁 gamma:{sigma(t):a<=t<=b}
.
See also
Contour Integral, Integral, Line Integral, PathExplore with Wolfram|Alpha
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References
Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. "Evaluation of Functions by Path Integration." §5.14 in Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 201-204, 1992.Referenced on Wolfram|Alpha
Path IntegralCite this as:
Weisstein, Eric W. "Path Integral." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PathIntegral.html