Complex Analysis by Dennis G Zill is a widely recognized textbook that provides a comprehensive introduction to the subject of complex analysis. This book is designed for undergraduate and graduate students studying mathematics and aims to provide a solid foundation in the concepts and techniques of complex analysis.
The book starts by introducing the reader to the basic concepts of complex numbers and the complex plane. From there, the book explores complex functions, including derivatives, complex integration, and the Cauchy integral theorem. The book also covers topics such as power series, conformal mapping, and Mobius transformations.
Table of Contents
Chapter 1. Complex Numbers and the Complex Plane
- Complex Numbers and Their Properties
- Complex Plane
- Polar Form of Complex Numbers
- Powers and Roots
- Sets of Points in the Complex Plane
- Applications
Chapter 2. Complex Functions and Mappings
- Complex Functions
- Complex Functions as Mappings
- Linear Mappings
- Special Power Functions
- The Power Function zn
- The Power Function z1/n
- Reciprocal Function
- Limits and Continuity
- Limits
- Continuity
- Applications
Chapter3. Analytic Functions
- Differentiability and Analyticity
- Cauchy-Riemann Equations
- Harmonic Functions
- Applications
.
Chapter4. Elementary Functions
- Exponential and Logarithmic Functions
- Complex Exponential Function
- Complex Logarithmic Function
- Complex Powers
- Trigonometric and Hyperbolic Functions
- Complex Trigonometric Functions
- Complex Hyperbolic Functions
- Inverse Trigonometric and Hyperbolic Functions
- Applications
Chapter 5. Integration in the Complex Plane
- Real Integrals
- Complex Integrals
- Cauchy-Goursat Theorem
- Independence of Path
- Cauchy’s Integral Formulas and Their Consequences
- Cauchy’s Two Integral Formulas
- Some Consequences of the Integral
- Formulas
- Applications
Chapter 6 Series and Residues
- Sequences and Series
- Taylor Series
- Laurent Series
- Zeros and Poles
- Residues and Residue Theorem
- Some Consequences of the Residue Theorem
- Evaluation of Real Trigonometric Integrals
- Evaluation of Real Improper Integrals
- Integration along a Branch Cut
- The Argument Principle and Rouch´e’s Theorem
- Summing Infinite Series
- Application
Chapter7 Conformal Mappings
- Conformal Mapping
- Linear Fractional Transformations
- Schwarz-Christoffel Transformations
- Poisson Integral Formulas
- Applications
- Boundary-Value Problems
One of the strengths of Complex Analysis by Dennis G Zill is its clear and accessible writing style, which makes the material easy to understand for students with varying levels of mathematical background. The book also includes numerous examples and exercises, which help to reinforce the concepts covered in each chapter and provide opportunities for further exploration of the subject.
In addition, the book is known for its comprehensive coverage of complex analysis, making it a valuable resource for students who want to deepen their understanding of this important area of mathematics. Whether you are a student looking to build a solid foundation in complex analysis or a professional seeking to refresh your knowledge of the subject, Complex Analysis by Dennis G Zill is an excellent resource that is sure to meet your needs.
Download Now Book in PDF
One of the strengths of Complex Analysis by Dennis G Zill is its clear and accessible writing style, which makes the material easy to understand for students with varying levels of mathematical background. The book also includes numerous examples and exercises, which help to reinforce the concepts covered in each chapter and provide opportunities for further exploration of the subject.
In addition, the book is known for its comprehensive coverage of complex analysis, making it a valuable resource for students who want to deepen their understanding of this important area of mathematics. Whether you are a student looking to build a solid foundation in complex analysis or a professional seeking to refresh your knowledge of the subject, Complex Analysis by Dennis G Zill is an excellent resource that is sure to meet your needs.
