Book description
Complex Analysis presents a comprehensive and student-friendly 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 self-study. Its comprehensive coverage includes Cauchy-Goursat 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 Cauchy-Goursat 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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