Introduction to Complex Analysis (2nd edition)

ISBN : 9780198525622

H. A. Priestley
344 Pages
156 x 233 mm
Pub date
Aug 2003
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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
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
Cauchy's residue theorem
Contour integration: a technical toolkit
Applications of contour integration
The Laplace transform
The Fourier transform
Harmonic functions and holomorphic functions
Notation index

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