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Complex Variables
About this book
Complex Variables deals with complex variables and covers topics ranging from Cauchy's theorem to entire functions, families of analytic functions, and the prime number theorem. Major applications of the basic principles, such as residue theory, the Poisson integral, and analytic continuation are given. Comprised of seven chapters, this book begins with an introduction to the basic definitions and concepts in complex variables such as the extended plane, analytic and elementary functions, and Cauchy-Riemann equations. The first chapter defines the integral of a complex function on a path in the complex plane and develops the machinery to prove an elementary version of Cauchy's theorem. Some applications, including the basic properties of power series, are then presented. Subsequent chapters focus on the general Cauchy theorem and its applications; entire functions; families of analytic functions; and the prime number theorem. The geometric intuition underlying the concept of winding number is emphasized. The linear space viewpoint is also discussed, along with analytic number theory, residue theory, and the Poisson integral. This book is intended primarily for students who are just beginning their professional training in mathematics.
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Yes, you can access Complex Variables by Robert B. Ash in PDF and/or ePUB format, as well as other popular books in Mathematics & Calculus. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- Front Cover
- Complex Variables
- Copyright Page
- Table of Contents
- Preface
- Chapter 0. PREREQUISITES
- Chapter 1. THE ELEMENTARY THEORY
- Chapter 2. THE GENERAL CAUCHY THEOREM
- Chapter 3. APPLICATIONS OF THE CAUCHY THEORY
- Chapter 4. ENTIRE FUNCTIONS
- Chapter 5. FAMILIES OF ANALYTIC FUNCTIONS
- Chapter 6. THE PRIME NUMBER THEOREM
- Solutions To Problems
- Subject Index