Complex Analysis

<p><b>A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject</b></p> <p>Written with a reader-friendly approach, <i>Complex Analysis: A Modern First Course in Function Theory </i>features a self-contained, concise development of the fundamental principles of complex analysis. After laying groundwork on complex numbers and the calculus and geometric mapping properties of functions of a complex variable, the author uses power series as a unifying theme to define and study the many rich and occasionally surprising properties of analytic functions, including the Cauchy theory and residue theorem. The book concludes with a treatment of harmonic functions and an epilogue on the Riemann mapping theorem.</p> <p>Thoroughly classroom tested at multiple universities, <i>Complex Analysis: A Modern First Course in Function Theory </i>features:</p> <ul> <li>Plentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projects</li> <li>Numerous figures to illustrate geometric concepts and constructions used in proofs</li> <li>Remarks at the conclusion of each section that place the main concepts in context, compare and contrast results with the calculus of real functions, and provide historical notes</li> <li>Appendices on the basics of sets and functions and a handful of useful results from advanced calculus</li> </ul> Appropriate for students majoring in pure or applied mathematics as well as physics or engineering, <i>Complex Analysis: A Modern First Course in Function Theory </i>is an ideal textbook for a one-semester course in complex analysis for those with a strong foundation in multivariable calculus. The logically complete book also serves as a key reference for mathematicians, physicists, and engineers and is an excellent source for anyone interested in independently learning or reviewing the beautiful subject of complex analysis.<br /> <p> </p> <p> </p>