Complex Variables with Applications – A. David Wunsch – 2nd Edition

Description

The second edition of this unique text remains accessible to of and with varying mathematical backgrounds. Designed for a one-semester course in analysis, there is optional review for students who have studied only calculus and .

The subject of ‘Complex Analysis’ usually forms part of the core for maths degrees and often turns up in mathematical physics courses as well so if you are studying either of these, then the chances are that you will come across it sooner or later. I am working towards a Phd in physics and have found that this subject is of incredible use in what I will be doing in the future. So what is complex analysis you may ask?

Well to start off with it doesn’t mean hard or difficult analysis, instead what it deals with are functions of (variables that can be complex numbers) that have a derivative (or are analytic in the language of the field). When you start the subject it seems as if everything is similar to the standard real analysis or basic calculus courses that you may have done in the first year – but in fact things are totally different. For example – if a function of a complex has a first derivative then it has all the higher derivatives as well – something that is not the case in standard calculus.

Table of Content

1. Complex Numbers.
2. The Complex Function and Its Derivative.
3. The Basic Transcendental Functions.
4. Integration in the Complex Plane.
5. Infinite Series Involving a Complex Variable.
6. Residues and Their Use in Integrations.
7. Laplace Transforms and Stability of Systems.
8. Conformal Mapping and Some of Its Applications.

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