Back to School Savings: Save up to 30% on print books and eBooks. No promo code needed.
Back to School Savings: Save up to 30%
Introductory Complex and Analysis Applications
1st Edition - January 1, 1972
Author: William R. Derrick
9 7 8 - 1 - 4 8 3 2 - 6 0 4 8 - 8
Introductory Complex and Analysis Applications provides an introduction to the functions of a complex variable, emphasizing applications. This book covers a variety of topics,… Read more
Save 50% on book bundles
Immediately download your ebook while waiting for your print delivery. No promo code is needed.
Introductory Complex and Analysis Applications provides an introduction to the functions of a complex variable, emphasizing applications. This book covers a variety of topics, including integral transforms, asymptotic expansions, harmonic functions, Fourier transformation, and infinite series. Organized into eight chapters, this book begins with an overview of the theory of functions of a complex variable. This text then examines the properties of analytical functions, which are all consequences of the differentiability of the function. Other chapters consider the converse of Taylor's Theorem, namely that convergent power series are analytical functions in their domain of convergence. This book discusses as well the Residue Theorem, which is of fundamental significance in complex analysis and is the core concept in the development of the techniques. The final chapter deals with the method of steepest descent, which is useful in determining the asymptotic behavior of integral representations of analytic functions. This book is a valuable resource for undergraduate students in engineering and mathematics.
Table of Symbols
1. Analytic Functions
1.1. Complex Numbers
1.2. Properties of the Complex Plane
1.3. Functions of a Complex Variable
1.4. Sufficient Conditions for Analyticity
1.5. Some Elementary Functions
2. Complex Integration
2.1. Line Integrals
2.2. The Cauchy-Goursat Theorem
2.3. The Fundamental Theorem of Integration
2.4. The Cauchy Integral Formula
2.5. Liouville's Theorem and the Maximum Principle