Introduction to complex analysis

Author(s)

• Taylor, Michael Eugene

Bibliographic Information

Introduction to complex analysis

Michael E. Taylor

（Graduate studies in mathematics, v. 202）

American Mathematical Society, c2019

Note

Includes bibliographical references (p. 473-475) and index

Description and Table of Contents

Description

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.

Table of Contents

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.

by "Nielsen BookData"

Details

• NCID: BB29094925
• ISBN:
  • 9781470452865
• LCCN: 2019019267
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Providence, R.I.
• Pages/Volumes: xiv, 480 p.
• Size: 27 cm
• Classification:
  • LCC : QA331.7
  • DC23 : 515/.9
• Subject Headings:
  • LCSH : Functions of complex variables
  • LCSH : Numbers, Complex
  • LCSH : Mathematical analysis
• Parent Bibliography ID:
  • BA20542214