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This book introduces seemingly complicated integrals which are effortlessly computed after reshaping them into integrals along contours, as well as apparently difficult differential and integral equations, which can be elegantly solved using similar methods.

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The theory of complex functions is a strikingly beautiful and powerful area of mathematics. Some particularly fascinating examples are seemingly complicated integrals which are effortlessly computed after reshaping them into integrals along contours, as well as apparently difficult differential and integral equations, which can be elegantly solved using similar methods. To use them is sometimes routine but in many cases it borders on an art. The goal of the book is to introduce the reader to this beautiful area of mathematics and to teach him or her how to use these methods to solve a variety of problems ranging from computation of integrals to solving difficult integral equations. This is done with a help of numerous examples and problems with detailed solutions.

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Basics.- Hypergeometric series with applications.- Integral equations.- Orthogonal polynomials.- Solutions to the problems.

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From the book reviews:

"The book is aimed at physics undergraduates, but has a good level of rigor and would also be useful for math majors interested in these subjects. There is a set of representative exercises and the end of each chapter, with complete solutions in the back of the book." (Allen Stenger, MAA Reviews, May, 2014)

"This book is a nice introduction to complex integration and its applications. It is based on lecture notes manuscripts of A. O. Gogolin and is intended for undergraduate students in physics in first place, but it can be fascinating for anyone interested in such classical topics as well." (Béla Nagy, Acta Scientiarum Mathematicarum (Szeged), Vol. 80 (1-2), 2014)

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