Applications of Complex Variables: Asymptotics and Integral Transforms (De Gruyter Textbook)

✍ Scribed by Foluso Ladeinde

• Publisher: De Gruyter
• Year: 2024
• Tongue: English
• Leaves: 606
• Edition: 1
• Category: Library

✦ Synopsis

The subject of applied complex variables is so fundamental that most of the other topics in advanced engineering mathematics (AEM) depend on it. The present book contains complete coverage of the subject, summarizing the more elementary aspects that you find in most AEM textbooks and delving into the more specialized topics that are less commonplace. The book represents a one-stop reference for complex variables in engineering. The applications of conformal mapping in this book are significantly more extensive than in other AEM textbooks. The treatments of complex integral transforms enable a much larger class of functions that can be transformed, resulting in an expanded use of complex-transform techniques in engineering analysis. The inclusion of the asymptotics of complex integrals enables the analysis of models with irregular singular points. The book, which has more than 300 illustrations, is generous with realistic example problems.

✦ Table of Contents

About the author
Preface
Acknowledgments
Contents
Abbreviations
Nomenclature
Part I: Introduction to complex variables
Introduction to Part I
1 Introductory concepts
2 Laurent series, residue theorem, and contour integration
3 Conformal mapping and its applications
4 Application of complex variable theory and conformal mapping to perfect fluid flow
Part II: Complex integral transforms
Introduction to Part II
5 The techniques of complex Laplace transform
6 Asymptotic behavior of complex integrals
7 The techniques of complex Fourier transform
8 Modern applications of complex variables
Appendix A Table of Laplace transforms pairs in diffusion analysis
Appendix B Table of general properties of Laplace transforms
Appendix C Table of common Laplace transform pairs
Appendix D Table of special functions
Appendix E Bessel Functions
Appendix F Special functions
Appendix G Miscellaneous functions
Appendix H Table of transformations of regions
List of figures
Index