Undergraduate Lecture Notes in Physics

Lectures on Complex Integration

Authors: Gogolin, Alexander O.

Editors: Tsitsishvili, Elena G., Komnik, Andreas (Eds.)

  • Highly praised lecture notes, perfected for publication by colleagues after the untimely death of their author, Prof. Gogolin
  • Highlights the power and elegance of various methods of tackling complex integrals and integral equations
  • Ideal teaching material and a rich source of interesting examples with solutions
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About this Textbook

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.

About the authors

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).

Reviews

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)


Table of contents (5 chapters)

  • Basics

    Gogolin, Alexander. O. (et al.)

    Pages 1-61

  • Hypergeometric Series with Applications

    Gogolin, Alexander. O. (et al.)

    Pages 63-111

  • Integral Equations

    Gogolin, Alexander. O. (et al.)

    Pages 113-186

  • Orthogonal Polynomials

    Gogolin, Alexander. O. (et al.)

    Pages 187-220

  • Solutions to the Problems

    Gogolin, Alexander. O. (et al.)

    Pages 221-279

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-319-00212-5
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $59.99
price for USA
  • ISBN 978-3-319-00211-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $59.99
price for USA
  • ISBN 978-3-319-34398-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Lectures on Complex Integration
Authors
Editors
  • Elena G. Tsitsishvili
  • Andreas Komnik
Series Title
Undergraduate Lecture Notes in Physics
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-00212-5
DOI
10.1007/978-3-319-00212-5
Hardcover ISBN
978-3-319-00211-8
Softcover ISBN
978-3-319-34398-3
Series ISSN
2192-4791
Edition Number
1
Number of Pages
IX, 285
Number of Illustrations and Tables
64 b/w illustrations
Topics