Complex Variables for Engineers with Mathematica

Complex variable theory is attractive for engineers as it offers elegant approaches for certain types of differential equations in engineering including heat transfer, solid mechanics, and fluid mechanics. However, a gap exists between books written by mathematicians and books written by engineers in their specific fields. Naturally, mathematicians tend to emphasize rigorousness and consistency while less emphasizing applications. On the other hand, books written by engineers often jump directly to the specific topics assuming that the readers already have sufficient background of complex variables and the pathway from theory to the application is not clearly elucidated. This book closes the gap in the literature. providing a smooth transition from basic theory to the application is accomplished. Although it is not possible to cover all the topics in engineering exhaustively, the readers can at least find the logic of how and why complex variables are effective for some of the engineering problems. Another motivation for writing this book is to demonstrate that the readers can take advantage of a computer algebra system, Mathematica, to facilitate tedious algebra and visualize complex functions so that they can focus on principles instead of spending endless hours on algebra by hand. Unlike numerical tools such as MATLAB and FORTRAN, Mathematica can expand, differentiate, and integrate complex-valued functions symbolically. Mathematica can be used as a stand-alone symbolic calculator or a programming tool using the Wolfram Language. If Mathematica is not available locally, Wolfram Cloud Basic can be used online as a free service to execute Mathematica statements.

Seiichi Nomura is a Professor in the Department of Mechanical and Aerospace Engineering at the University of Texas at Arlington. He is the author of Micromechanics with Mathematica, co-author of Heat Conduction in Composite Materials with  A. Haj--Sheikh, and author of C Programming and Numerical Analysis. His research interests include miromechanics, analysis of composite materials and applications of computer algebra systems. He holds a Dr. of Eng. degree from the University of Tokyo and a Ph.D. from the University of Deleware.

1. Functions of Complex Variables

   • Seiichi Nomura

   Pages 1-21

2. Calculus of Functions of Complex Variables

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   Pages 23-33

3. Integrations of Functions of Complex Variables

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   Pages 35-52

4. Series of Complex Variable Functions

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   Pages 53-74

5. Residues

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   Pages 75-103

6. Applications to Engineering Problems

   • Seiichi Nomura

   Pages 105-152

7. Back Matter

   Pages 153-172