Section 8.1 The Residue Theorem - Maple Application Center
Application Center Applications Section 8.1 The Residue Theorem

Section 8.1 The Residue Theorem

Authors
: Dr. John Mathews
Engineering software solutions from Maplesoft
This Application runs in Maple. Don't have Maple? No problem!
 Try Maple free for 15 days!
The Cauchy-integral formulas in Section 6.5 are useful in evaluating contour integrals over a simple closed contour C; where the integrand has the form f(z)/((z-z[0])^k); and f; is an analytic function. In this case, the singularity of the integrand is at worst a pole of order k at z[0]. In this section we extend this result to integrals that have a finite number of isolated singularities and lie inside the contour C. This new method can be used in cases where the integrand has an essential singularity at z[0] and is an important extension of the previous method.

Application Details

Publish Date: October 01, 2003
Created In: Maple V
Language: English

Tags

relativity

More Like This

Section 1.5 The Algebra of Complex Numbers, Revisited
Section 1.1 The Origin of Complex Numbers
2
Section 1.3 The Geometry of Complex Numbers
Section 2.3 The Mappings w = z^n and w = z^`1/n`
Section 2.1 Functions of a Complex Variable
Section 2.4 Limits and Continuity
Section 1.4 The Geometry of Complex Numbers, Continued
Section 1.2 The Algebra of Complex Numbers
Section 2.2 Transformations and Linear Mappings
Section 1.6 The Topology of Complex Numbers
Section 2.6 The Reciprocal Transformation w = 1/z
Section 2.5 Branches of Functions