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Other titles in the Springer Undergraduate Mathematics series:
Complex Analysisby John M. Howie
Synopses & ReviewsPublisher Comments:Complex analysis is one of the most attractive of all the core topics in an undergraduate mathematics course. Its importance to applications means that it can be studied both from a very pure perspective and a very applied perspective. This book takes account of these varying needs and backgrounds and provides a selfstudy text for students in mathematics, science and engineering. Beginning with a summary of what the student needs to know at the outset, it covers all the topics likely to feature in a first course in the subject, including: complex numbers, differentiation, integration, Cauchy's theorem, and its consequences, Laurent series and the residue theorem, applications of contour integration, conformal mappings, and harmonic functions. A brief final chapter explains the Riemann hypothesis, the most celebrated of all the unsolved problems in mathematics, and ends with a short descriptive account of iteration, Julia sets and the Mandelbrot set. Clear and careful explanations are backed up with worked examples and more than 100 exercises, for which full solutions are provided.
Synopsis:Complex analysis can be a difficult subject and many introductory texts are just too ambitious for today's students. This book takes a lower starting point than is traditional and concentrates on explaining the key ideas through worked examples and informal explanations, rather than through "dry" theory.
Table of ContentsWhat Do I Need to Know? Complex Numbers. Prelude to Complex Analysis. Differentiation. Complex Integration. Cauchy's Theorem. Some Consequences of Cauchy's Theorem. Laurent Series and the Residue Theorem. Applications of Contour Integration. Further Topics. Conformal Mappings. Final Remarks. Solutions to Exercises. Bibliography. Index.
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Other books you might likeRelated SubjectsReference » Science Reference » General Science and Mathematics » Mathematics » Analysis General Science and Mathematics » Mathematics » Calculus » General Science and Mathematics » Mathematics » Complex Analysis Science and Mathematics » Mathematics » Functional Analysis Science and Mathematics » Mathematics » General Science and Mathematics » Nature Studies » General 

