ISBN 9789380108193,A First Course in Complex Analysis with Applications

A First Course in Complex Analysis with Applications



Jones & Bartlett Learning

Publication Year 2010

ISBN 9789380108193

ISBN-10 9380108192


Edition 2nd edition
Number of Pages 458 Pages
Language (English)

Educational: Mathematics & numeracy

The new Second Edition of A First Course in Complex Analysis with Applications is a truly accessible introduction to the fundamental principles and applications of complex analysis. Designed for the undergraduate student with a calculus background but no prior experience with complex variables, this text discusses theory of the most relevant mathematical topics in a student-friendly manner. With Zill’s clear and straightforward writing style, concepts are introduced through numerous examples and clear illustrations. Students are guided and supported through numerous proofs providing them with a higher level of mathematical insight and maturity. Each chapter contains a separate section on the applications of complex variables, providing students with the opportunity to develop a practical and clear understanding of complex analysis.

Key features

Portions of the text and examples have been revised or rewritten to clarify or expand upon the topics at hand.
Each chapter opens with an overview of the material to be covered in the chapter. End-of-chapter materials include Computer Lab Assignments and a Chapter Review Quiz. Numerous Exercises are included at the end of each section.
Remarks conclude most sections and discuss the relationships and differences between important concepts.
Proof Problems offer an additional learning experience for students, who are supported through each step of the process by hints and guides.

Table of Contents
Chapter 1: Complex Numbers and the Complex Plane


Complex numbers and their properties
Complex plane
Polar form of complex numbers
Power and roots
Sets of points in the complex plane
Chapter 1 Review quiz

Chapter 2: Complex Functions and Mappings


Complex functions
Complex functions as mappings
Linear mappings
Special power functions
Reciprocal function
Limits and continuity
Chapter 2: Review quiz

Chapter 3: Analytic Functions


Differentiability and analyticity
Cauchy- Reimann equations
Harmonic functions
Chapter 3 Review quiz

Chapter 4: Elementary Functions


Exponential and logarithmic functions
Complex powers
Trigonometric and hyperbolic functions
Inverse trigonometric and hyperbolic functions
Chapter 4 Review Quiz

Chapter 5: Integration in the Complex Plane


Real integrals
Complex integrals
Cauchy-Goursat Theorem
Independence of Path
Cauchy’s Integral formulas and their consequences
Chapter 5 Review quiz

Chapter 6: Series and Residues


Sequences and series
Taylor series
Laurent series
Zeros and poles
Residue and residue theorem
Some consequences of the residue theorem
Chapter 6 Review quiz

Chapter 7: Conformal Mappings


Conformal mapping
Linear fractional transformations
Schwartz- Christoffel Transformations
Poisson integral formulas
Applications 1 Chapter 7 Review quiz



Proof of Theorem 2.6.1 APP-1
Proof of the Cauchy- Goursat Theorem
Table of conformal mappings