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

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

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 of complex variables (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 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 as well – something that is not the case in standard calculus.

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  • 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.
  • Citation

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