Introduction to Complex Analysis

Complex analysis is a classic and central area of mathematics, which is studies 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. 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. 1. The Complex Plane -- 2. Geometry In The Complex Plane -- 3. Topology And Analysis In The Complex Plane -- 4. Paths -- 5. Holomorphic Functions -- 6. Complex Series And Power Series -- 7. A Cornucopia Of Holomorphic Functions -- 8. Conformal Mapping -- 9. Multifunctions -- 10. Integration In The Complex Plane -- 11. Cauchy's Theorem: Basic Track -- 12. Cauchy's Theorem: Advanced Track -- 13. Cauchy's Formulae -- 14. Power Series Representation -- 15. Zeros Of Holomorphic Functions -- 16. Holomorphic Functions: Further Theory -- 17. Singularities -- 18. Cauchy's Residue Theorem -- 19. A Technical Toolkit For Contour Integration -- 20. Applications Of Contour Integration -- 21. The Laplace Transform -- 22. The Fourier Transform -- 23. Harmonic Functions And Conformal Mapping. H.a. Priestley. Previous Ed.: Oxford: Clarendon, 1990. Includes Bibliographical References (p. [319]-320) And Indexes.

Intended for use in a first course on complex analysis, this expanded second edition is arranged in short chapters and in such a way that much of the technical materials can be treated as optional (sections of chapters are designated basic track or advanced track.) In 23 chapters adopted from his lectures at the University of Oxford, Priestley discusses topics such as the complex plane, topology and analysis, zeroes of holomorphic functions, conformal mapping, multifunctions, Cauchy's theorem (basic and advanced track), singularities, the Laplace transform, the Fourier transform, and harmonic functions. An appendix briefly describes contemporary developments such as the Prime number theorem and the Bieberbach conjecture. Annotation ©2004 Book News, Inc., Portland, OR

This second edition of Priestley's well-known text is aimed at students taking an introductory core course in Complex Analysis, a classical and central area of mathematics. Graded exercises are presented throughout the text along with worked examples on the more elementary topics Complex analysis has its roots in the algebraic, geometric, and topological structure of the complex plane.