Section 6.6 The Theorems of Morera and Liouville and Some Applications - Maple Application Center
Application Center Applications Section 6.6 The Theorems of Morera and Liouville and Some Applications

Section 6.6 The Theorems of Morera and Liouville and Some Applications

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!
In this section we investigate some of the qualitative properties of analytic and harmonic functions. Our first result shows that the existence of an antiderivative for a continuous function is equivalent to the statement that the integral of f; is independent of the path of integration. This result is stated in a form that will serve as a converse to the Cauchy-Goursat theorem.

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 2.2 Transformations and Linear Mappings
Section 1.2 The Algebra of Complex Numbers
Section 1.6 The Topology of Complex Numbers
Section 2.6 The Reciprocal Transformation w = 1/z
Section 2.5 Branches of Functions