Lectures on Complex Integration - A. O. Gogolin

Lectures on Complex Integration

Buch | Softcover
IX, 285 Seiten
2016 | 1. Softcover reprint of the original 1st ed. 2014
Springer International Publishing (Verlag)
978-3-319-34398-3 (ISBN)
58,84 inkl. MwSt
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.
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.

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).

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

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)

Erscheinungsdatum
Reihe/Serie Undergraduate Lecture Notes in Physics
Zusatzinfo IX, 285 p. 64 illus.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Naturwissenschaften Physik / Astronomie Allgemeines / Lexika
Naturwissenschaften Physik / Astronomie Theoretische Physik
Schlagworte Branch Cut Integration • Complex analysis, complex variables • Complex Integration • Contour Integrals • Examples and Solutions in Complex Integration • Functions of a Complex Variable • hypergeometric function • Mathematical Applications in the Physical Sciences • Mathematical Modelling • Mathematical Physics • Physics and Astronomy • Theoretical, Mathematical and Computational Physic • Undergraduate Course on Complex Integration • Wiener-Hopf Equation
ISBN-10 3-319-34398-X / 331934398X
ISBN-13 978-3-319-34398-3 / 9783319343983
Zustand Neuware
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