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 sets
have 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 for
Pattern Recognition, Gelman and Nolan: Teaching Statistics.
Complex numbers ; Geometry in the complex plane ; Topology and analysis in the complex plane ; Holomorphic functions ; Complex series and power series ; A menagerie of holomorphic functions ; Paths ; Multifunctions: basic track ; Conformal mapping ; Cauchy's theorem: basic track ; Cauchy's theorem: advanced track ; Cauchy's formulae ; Power series representation ; Zeros of holomorphic functions ; Further theory of holomorphic functions ; Singularities ; Cauchy's residue theorem ; Contour integration: a technical toolkit ; Applications of contour integration ; The Laplace transform ; The Fourier transform ; Harmonic functions and holomorphic functions ; Bibliography ; Notation index ; Index