Friendly Approach To Complex Analysis, A second Edition

Details about Friendly Approach To Complex Analysis, A second Edition:

The book constitutes a basic, concise, yet rigorous first course in complex analysis, for undergraduate students who have studied multivariable calculus and linear algebra. The textbook should be particularly useful for students of joint programmes with mathematics, as well as engineering students seeking rigour. The aim of the book is to cover the bare bones of the subject with minimal prerequisites. The core content of the book is the three main pillars of complex analysis: the Cauchy-Riemann equations, the Cauchy Integral Theorem, and Taylor and Laurent series. Each section contains several problems, which are not drill exercises, but are meant to reinforce the fundamental concepts. Detailed solutions to all the 243 exercises appear at the end of the book, making the book ideal for self-study. There are many figures illustrating the text.

The second edition corrects errors from the first edition, and includes 89 new exercises, some of which cover auxiliary topics that were omitted in the first edition. Two new appendices have been added, one containing a detailed rigorous proof of the Cauchy Integral Theorem, and another providing background in real analysis needed to make the book self-contained.

Contents:

• Complex Numbers and Their Geometry
• Complex Differentiability
• Cauchy Integral Theorem
• Taylor and Laurent Series
• Harmonic Functions
• Solutions to All Exercises

Readership: Undergraduate students in complex analysis.

Reviews of the First Edition:This book is ‘friendly’ because the treatment is rigorous and makes no concessions to lazy-mindedness. Another reason is that the narrative always conveys a sense of direction, and it makes many valuable comparisons with real and complex analysis. Overall, this is a very nice addition to the existing literature on complex analysis. It is rich in ideas and there is a very effective use of diagrams at key points in the text. - Mathematical Association of America

'This textbook is a really friendly approach to Complex Analysis in one variable. This friendly introduction to complex analysis can be really helpful for readers starting to learn in that field and may act as a stimulant for more.' - Zentralblatt MATH

Key Features:

• Concise, yet rigorous
• Minimal prerequisites
• 243 exercises
• Includes solutions to all the exercises, making the book ideal for self-study
• Many figures
• Includes an appendix with real analysis background, making the book self-contained