A Friendly Approach to Complex Analysis

The book constitutes a basic, concise, yet rigorous course in complex analysis, for students who have studied calculus in one and several variables, but have not previously been exposed to complex analysis. The textbook should be particularly useful and relevant for undergraduate students in joint programmes with mathematics, as well as engineering students. 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 expansions.

Each section contains several problems, which are not purely drill exercises, but are rather meant to reinforce the fundamental concepts. Detailed solutions to all the exercises appear at the end of the book, making the book ideal also for self-study.

There are many figures illustrating the text.

Errata(s)
Errata (72 KB)

Sample Chapter(s)
Chapter 1: Complex numbers and their geometry (464 KB)

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• Complex Numbers and Their Geometry
• Complex Differentiability
• Cauchy Integral Theorem and Consequences
• Taylor and Laurent Series
• Harmonic Functions

“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.”

"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."

Errata(s)
Errata (61 KB)

Sample Chapter(s)
Chapter 1: Complex numbers and their geometry (464 KB)