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 sometimesroutine 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...

Die Funktionentheorie ist ein wunderschones und ausserordentlich machtiges Gebiet der Mathematik. Einige der sehr eindrucksvollen Beispiele dafur sind vermeintlich schwierige Integrale, die sich nach einer Umformung zu Integralen entlang der Wege in der komplexen Ebene muhelos berechnen lassen - sowie extrem komplizierte Differential- und Integralgleichungen, die mit Hilfe ahnlicher Methoden sehr elegant gelost werden konnen. Manchmal ist die Anwendung dieser Techniken reine Routine, in vielen Fallen jedoch grenzt sie an Kunst. Das Ziel dieses Buchs ist es, den Leser in dieses wunderbare...

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.