Book description
Complex Analysis presents a comprehensive and studentfriendly introduction to the important concepts of the subject. Its clear, concise writing style and numerous applications make the basics easily accessible to students, and serves as an excellent resource for selfstudy. Its comprehensive coverage includes CauchyGoursat theorem, along with the description of connected domains and its extensions and a separate chapter on analytic functions explaining the concepts of limits, continuity and differentiability.
Table of contents
 Cover
 Title page
 Contents
 Preface

Chapter 1. Complex Numbers
 1.1 Introduction
 1.2 Complex Numbers
 1.3 Graphical Representation of a Complex Number
 1.4 Vector Form of Complex Numbers
 1.5 Absolute Value and Conjugate
 1.6 Triangle Inequality
 1.7 Polar Form of a Complex Number
 1.8 Exponential Form of a Complex Number
 1.9 De Moivre’s Theorem
 1.10 Roots of Complex Numbers
 1.11 Stereographic Projection
 1.12 Regions in the Complex Plane
 Summary
 Chapter 2. Analytic Functions

Chapter 3. Elementary Functions
 3.1 Introduction
 3.2 Elementary Functions
 3.3 Periodic Functions
 3.4 Exponential Function
 3.5 Trigonometric Functions
 3.6 Hyperbolic Functions
 3.7 Branches, Branch Point and Branch Line
 3.8 Logarithmic Function
 3.9 Complex Exponents
 3.10 Inverse Trigonometric Functions
 Inverse Hyperbolic Functions
 Summary

Chapter 4. Complex Integration
 4.1 Introduction
 4.2 Derivative of Function w(t)
 4.3 Definite Integrals of Functions
 4.4 Contours
 4.5 Contour Integrals
 4.6 Moduli of Contour Integrals
 4.7 Indefinite Integral
 4.8 Cauchy’s Theorem
 4.9 CauchyGoursat Theorem
 4.10 Winding Number
 4.11 Cauchy’s Integral Formula
 4.12 Consequences of Cauchy’s Integral Formula
 4.13 Maximum Moduli of Functions
 Summary
 Chapter 5. Sequence and Series
 Chapter 6. Singularities and Residues
 Chapter 7. Applications of Residues

Chapter 8. Bilinear and Conformal Transformations
 8.1 Introduction
 8.2 Linear Transformations
 8.3 Transformation w = 1/z
 8.4 Bilinear Transformation
 8.5 Cross Ratio
 8.6 Special Bilinear Transformations
 8.7 Transformation W = z2
 8.8 Transformation W = eZ
 8.9 Trigonometric Transformations
 8.10 Angle of Rotation
 8.11 Conformal Transformation
 8.12 Transformation
 8.13 Transformation of Multivalued Functions
 8.14 Riemann Surfaces
 8.15 Mapping of Real Axis onto a Polygon
 8.16 Schwarz–Christoffel Transformation
 Summary
 Chapter 9. Special Topics
 Appendix
 Glossary
 Acknowledgement
 Copyright
Product information
 Title: Complex Analysis
 Author(s):
 Release date: April 2012
 Publisher(s): Pearson India
 ISBN: 9788131772492
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