Introduction to Complex Analysis

Michael E. Taylor (Autor)

Buch | Softcover

480 Seiten

2019
American Mathematical Society (Verlag)
978-1-4704-6375-5 (ISBN)

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In this text, the reader will learn that all the basic functions that arise in calculus--such as powers and fractional powers, exponentials and logs, trigonometric functions and their inverses, as well as many new functions that the reader will meet--are naturally defined for complex arguments. Furthermore, this expanded setting leads to a much richer understanding of such functions than one could glean by merely considering them in the real domain. For example, understanding the exponential function in the complex domain via its differential equation provides a clean path to Euler's formula and hence to a self-contained treatment of the trigonometric functions. Complex analysis, developed in partnership with Fourier analysis, differential equations, and geometrical techniques, leads to the development of a cornucopia of functions of use in number theory, wave motion, conformal mapping, and other mathematical phenomena, which the reader can learn about from material presented here.

This book could serve for either a one-semester course or a two-semester course in complex analysis for beginning graduate students or for well-prepared undergraduates whose background includes multivariable calculus, linear algebra, and advanced calculus.

Michael E. Taylor, University of North Carolina, Chapel Hill, NC.

Basic calculus in the complex domain
Going deeper - the Cauchy integral theorem and consequences
Fourier analysis complex function theory
Residue calculus, the argument principle, and two very special functions
Conformal maps and geometrical aspects of complex function theory
Elliptic functions and elliptic integrals
Complex analysis and differential equations
Appendix A: Complementary material
Bibliography
Index

Erscheint lt. Verlag	31.1.2019
Reihe/Serie	Graduate Studies in Mathematics
Verlagsort	Providence
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4704-6375-X / 147046375X
ISBN-13	978-1-4704-6375-5 / 9781470463755
Zustand	Neuware