Introductory Complex and Analysis Applications
Published on 10. May 2014
232 pages
978-1-4832-6048-8 (ISBN)
Description
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.
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William R. Derrick
Introductory Complex Analysis and Applications
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04/1972
Academic Press
€19.75
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Content
¿PrefaceTable of Symbols1. 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 1.6. Continuation Notes2. 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 Notes3. Infinite Series 3.1. Taylor Series 3.2. Uniform Convergence of Series 3.3. Laurent Series 3.4. Isolated Singularities 3.5. Analytic Continuation 3.6. Riemann Surfaces Notes4. Contour Integration 4.1. The Residue Theorem 4.2. Evaluation of Improper Real Integrals 4.3. Continuation 4.4. Integration of Multivalued Functions 4.5. Other Integration Techniques 4.6. The Argument Principle Notes5. Conformal Mappings 5.1. General Properties 5.2. Linear Fractional Transformations 5.3. Continuation 5.4. The Schwarz-Christoffel Formula 5.5. Physical Applications Notes6. Boundary-Value Problems 6.1. Harmonic Functions 6.2. Poisson's Integral Formula 6.3. Applications Notes7. Fourier and Laplace Transformations 7.1. Fourier Series 7.2. Fourier Transforms 7.3. Laplace Transforms 7.4. Properties of Laplace Transforms Notes8. Asymptotic Expansions 8.1. Definitions and Properties 8.2. Method of Steepest Descent 8.3. Continuation NotesAppendix A.1. Table of Conformal MappingsReferencesIndex
