This text is intended for undergraduate, students in mathematics, physics, and engineering. It is intended to balance between the pure and applied aspects of complex analysis and to present concepts in a clear writing style that is understandable to students at the junior or senior undergraduate level. A wealth of exercises that vary in both difficulty and substance gives the text flexibility. Sufficient applications are included to illustrate how complex analysis is used in science and engineering. Cover Page......Page 1 Title Page......Page 2 ISBN 0763702706......Page 3 3 Analytic and Harmonic Functions......Page 4 4 Sequences, Series, and Julia and Mandelbrot Sets......Page 5 7 Taylor and Laurent Series......Page 6 9 Conformal Mapping......Page 7 11 Fourier Series and the Laplace Transform......Page 8 Index......Page 9 Preface......Page 10 1 Complex Numbers......Page 13 2 Complex Functions......Page 50 3 Analytic and Harmonic Functions......Page 83 4 Sequences, Series, and Julia and Mandelbrot Sets......Page 107 5 Elementary Functions......Page 137 6 Complex Integration......Page 169 7 Taylor and Laurent Series......Page 220 8 Residue Theory......Page 256 9 Conformal Mapping......Page 293 10 Applications of Harmonic Functions......Page 322 11 Fourier Series and the Laplace Transform......Page 409 Appendix: Undergraduate Student Research Projects......Page 468 Bibliography......Page 470 Answers to Selected Problems......Page 478 Color Plates......Page 489 A......Page 493 B......Page 494 C......Page 495 D......Page 500 E......Page 502 F......Page 504 G......Page 506 H......Page 507 I......Page 508 L......Page 511 M......Page 514 O......Page 516 P......Page 517 R......Page 520 S......Page 521 T......Page 524 U......Page 526 V......Page 527 Z......Page 528 The new Fifth Edition of Complex Analysis for Mathematics and Engineering presents a comprehensive, student-friendly introduction to Complex Analysis concepts. Its clear, concise writing style and numerous applications make the foundations of the subject matter easily accessible to students. Believing that mathematicians, engineers, and scientists should be exposed to a careful presentation of mathematics, the authors devote attention to important topics, such as ensuring that required assumptions are met before using a theorem, confirming that algebraic operations are valid, and checking that formulas are not blindly applied. A new chapter on z-transforms and applications provides students with a current look at Digital Filter Design and Signal Processing. -- Provided by publisher. Annotation The new Fifth Edition of Complex Analysis for Mathematics and Engineering presents a comprehensive, student-friendly introduction to Complex Analysis concepts. Its clear, concise writing style and numerous applications make the foundations of the subject matter easily accessible to students. Believing that mathematicians, engineers, and scientists should be exposed to a careful presentation of mathematics, the authors devote attention to important topics, such as ensuring that required assumptions are met before using a theorem, confirming that algebraic operations are valid, and checking that formulas are not blindly applied. A new chapter on z-transforms and applications provides students with a current look at Digital Filter Design and Signal Processing
