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 self-study 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.
Topics
Functions of a Complex Variable
Analysis
Author(s): John M. Howie
Series: Springer Undergraduate Mathematics Series
Publisher: Springer
Year: 2003
Language: English
Pages: 260
Tags: Математика;Комплексное исчисление;
Front Matter Pages i-xi
Chapter 1 What Do I Need to Know? Pages 1-18
Chapter 2 Complex Numbers Pages 19-34
Chapter 3 Prelude to Complex Analysis Pages 35-49
Chapter 4 Differentiation Pages 51-78
Chapter 5 Complex Integration Pages 79-106
Chapter 6 Cauchy’s Theorem Pages 107-117
Chapter 7 Some Consequences of Cauchy’s Theorem Pages 119-136
Chapter 8 Laurent Series and the Residue Theorem Pages 137-152
Chapter 9 Applications of Contour Integration Pages 153-181
Chapter 10 Further Topics Pages 183-194
Chapter 11 Conformal Mappings Pages 195-215
Chapter 12 Final Remarks Pages 217-224
Chapter 13 Solutions to Exercises Pages 225-253
Back Matter Pages 255-260
