Complex Analysis: A Modern First Course in Function Theory

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9781118705223: Complex Analysis: A Modern First Course in Function Theory

A thorough introduction to the theory of complex functions emphasizing the beauty, power, and counterintuitive nature of the subject

Written with a reader-friendly approach, Complex Analysis: A Modern First Course in Function Theory 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.

Thoroughly classroom tested at multiple universities, Complex Analysis: A Modern First Course in Function Theory features:

  • Plentiful exercises, both computational and theoretical, of varying levels of difficulty, including several that could be used for student projects
  • Numerous figures to illustrate geometric concepts and constructions used in proofs
  • 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
  • Appendices on the basics of sets and functions and a handful of useful results from advanced calculus
Appropriate for students majoring in pure or applied mathematics as well as physics or engineering, Complex Analysis: A Modern First Course in Function Theory 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.

 

 

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About the Author:

Jerry R. Muir, Jr. PhD, is Professor of Mathematics at The University of Scranton. He has authored over one dozen research articles in complex-flavored analysis, primarily on geometric function theory in several complex variables.

Review:

"The textbook is appropriate for students and can serve as a key reference for anyone interested in learning or reviewing the theory of complex functions of a complex variable." (Zentralblatt MATH 2016) The textbook is appropriate for students and can serve as a key reference for anyone interested in learning or reviewing the theory of complex functions of a complex variable.

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