Lectures on Complex Integration

1. Front Matter

   Pages i-ix

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2. Basics

   • Alexander. O. Gogolin, Elena G. Tsitsishvili, Andreas Komnik

   Pages 1-61

3. Hypergeometric Series with Applications

   • Alexander. O. Gogolin, Elena G. Tsitsishvili, Andreas Komnik

   Pages 63-111

4. Integral Equations

   • Alexander. O. Gogolin, Elena G. Tsitsishvili, Andreas Komnik

   Pages 113-186

5. Orthogonal Polynomials

   • Alexander. O. Gogolin, Elena G. Tsitsishvili, Andreas Komnik

   Pages 187-220

6. Solutions to the Problems

   • Alexander. O. Gogolin, Elena G. Tsitsishvili, Andreas Komnik

   Pages 221-279

7. Back Matter

   Pages 281-285

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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.

• Branch Cut Integration
• Complex Integration
• Contour Integrals
• Examples and Solutions in Complex Integration
• Hypergeometric Function
• Undergraduate Course on Complex Integration
• Wiener-Hopf Equation

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)

• Institute for Cybernetics, Tbilisi Technical University, Tbilisi, Georgia

  Elena G. Tsitsishvili

• Institut für Theoretische Physik, Universität Heidelberg, Heidelberg, Germany

  Andreas Komnik

• Illford Essex, United Kingdom

  A. O. Gogolin

Alexander Gogolin was born in Tbilisi (Georgia) in 1965. After graduation from Lomonosov State University (Moscow, Russia) he defended his PhD thesis at the Lebedev Physical Institute (Moscow, Russia) in 1991. Soon after that he became a permanent member of staff of Landau Institute for theoretical physics (Moscow, Russia). In 1995 he moved to UK where he soon became a Professor of mathematical physics at the Department of Mathematics of the Imperial College London (UK). He died in London in April 2011. 

Ellen Tsitsishvili was born in Tbilisi (Georgia) in 1941 and received her PhD degree from Lomonosov State University (Moscow, Russia) in 1970. Since 1964 she is a permanent member of staff and professor at the Institute for Cybernetics (Tbilisi, Georgia). She is working on problems in condensed matter theory in many international collaborations with researchers of Scuola Normale (Pisa, Italy), University of Strasbourg (France), Weizmann Institute of Science (Israel), Center of Functional Nanostructures (Karlsruhe, Germany) and  University of Kaiserslautern (Germany).

Andreas Komnik was born in Karaganda (Kazakhstan) in 1972. He studied physics at Moscow Institute of Physics and Technology (Russia) and University of Freiburg (Germany), where in 1999 he acquired his PhD degree. After that he was research associate at the Department of Mathematics of the Imperial College London (UK) and at CEA Saclay (France). Between 2008 and 2012 he was a professor of physics at the University of Heidelberg (Germany).

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