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.

Autorentext

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).

Inhalt

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