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.

About the Author

Amol Sasane received his PhD in Mathematics from the University of Groningen in the Netherlands in 2001. He also holds an undergraduate degree in Electrical Engineering from the Indian Institute of Technology, Mumbai, and a Masters degree in Theoretical Physics from Lund University, Sweden. He is currently a Professor of Mathematics at the London School of Economics, which he joined in 2004. His research interests lie in Applicable Analysis, and he is the author of two research monographs and six textbooks.

Sara Maad Sasane received her PhD in Mathematics from Uppsala University in Sweden in 2002. She is currently an Associate Professor in Mathematics at Lund University, where she joined in 2013. Her research interests lie in Partial differential equations and functional analysis, often with applications in mathematical physics or mathematical biology.

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