Introduction to Complex Analysis

OUP Oxford, 28.08.2003 - 344 Seiten
Complex analysis is a classic and central area of mathematics, which is studied and exploited in a range of important fields, from number theory to engineering. Introduction to Complex Analysis was first published in 1985, and for this much awaited second edition the text has been considerably expanded, while retaining the style of the original. More detailed presentation is given of elementary topics, to reflect the knowledge base of current students. Exercise setshave been substantially revised and enlarged, with carefully graded exercises at the end of each chapter.This is the latest addition to the growing list of Oxford undergraduate textbooks in mathematics, which includes: Biggs: Discrete Mathematics 2nd Edition, Cameron: Introduction to Algebra, Needham: Visual Complex Analysis, Kaye and Wilson: Linear Algebra, Acheson: Elementary Fluid Dynamics, Jordan and Smith: Nonlinear Ordinary Differential Equations, Smith: Numerical Solution of Partial Differential Equations, Wilson: Graphs, Colourings and the Four-Colour Theorem, Bishop: Neural Networks forPattern Recognition, Gelman and Nolan: Teaching Statistics.

Inhalt

 1 The complex plane 1 2 Geometry in the complex plane 12 3 Topology and analysis in the complex plane 30 4 Paths 47 5 Holomorphic functions 56 6 Complex series and power series 67 7 A cornucopia of holomorphic functions 78 8 Conformal mapping 91
 15 Zeros of holomorphic functions 176 further theory 188 17 Singularities 194 18 Cauchys residue theorem 211 19 A technical toolkit for contour integration 221 20 Applications of contour integration 234 21 The Laplace transform 256 22 The Fourier transform 278

 9 Multifunctions 107 10 Integration in the complex plane 119 basic track 128 advanced track 142 13 Cauchys formulae 151 14 Power series representation 161
 23 Harmonic functions and conformal mapping 289 new perspectives 309 Bibliography 319 Notation index 321 Index 323 Urheberrecht

Beliebte Passagen

Seite vii - The power and significance of Cauchy's theorem — the centrepiece of complex analysis — is, I believe, best revealed initially through its applications.
Seite viii - Albert for their help with proof-reading, and to the staff of the Oxford University Press for encouraging me to write the book and for their assistance during its production.

Verweise auf dieses Buch

 Elementary Fluid DynamicsD. J. AchesonKeine Leseprobe verfügbar - 1990
 Basic Theory of Surface StatesEingeschränkte Leseprobe - 1996
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