Applied Complex Variables for Scientists and Engineers

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Cambridge University Press, Jun 24, 2010 - Mathematics - 438 pages
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This introduction to complex variable methods begins by carefully defining complex numbers and analytic functions, and proceeds to give accounts of complex integration, Taylor series, singularities, residues and mappings. Both algebraic and geometric tools are employed to provide the greatest understanding, with many diagrams illustrating the concepts introduced. The emphasis is laid on understanding the use of methods, rather than on rigorous proofs. Throughout the text, many of the important theoretical results in complex function theory are followed by relevant and vivid examples in physical sciences. This second edition now contains 350 stimulating exercises of high quality, with solutions given to many of them. Material has been updated and additional proofs on some of the important theorems in complex function theory are now included, e.g. the Weierstrass–Casorati theorem. The book is highly suitable for students wishing to learn the elements of complex analysis in an applied context.
 

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Contents

1 Complex Numbers
1
2 Analytic Functions
46
3 Exponential Logarithmic and Trigonometric Functions
93
4 Complex Integration
133
5 Taylor and Laurent Series
194
6 Singularities and Calculus of Residues
248
7 Boundary Value Problems and InitialBoundary Value Problems
311
8 Conformal Mappings and Applications
358
Answers to Problems
419
Index
434
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About the author (2010)

Yue Kuen Kwok is a Professor in the Department of Mathematics at the Hong Kong University of Science and Technology.

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