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This rigorous yet accessible introduction to complex analysis and differential equations covers complex numbers, holomorphic functions, analytic functions, ordinary differential equations, Fourier series and applications to partial differential equations.

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This text provides a rigorous yet accessible introduction to complex analysis and differential equations suitable for undergraduate students in mathematics, engineering, physics, economics and management. The key topics covered include complex numbers, holomorphic functions, analytic functions, ordinary differential equations, Fourier series and applications to partial differential equations. The only prerequisites are a basic knowledge of linear algebra and of differential and integral calculus.
The book is designed to accompany any course giving a first introduction to complex analysis or to differential equations and is divided into two parts essentially providing two books in one so that each part can be read independently. Moreover, a wealth of fully-worked problems and examples, and numerous exercises, of varying levels of difficulty, make this the ideal book for independent study.

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Part 1 Complex Analysis.- Basic Notions.- Holomorphic Functions.- Sequences and Series.- Analytic Functions.- Part 2 Differential Equations.- Ordinary Differential Equations.- Solving Differential Equations.- Fourier Series.- Partial Differential Equations_.

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From the reviews:
"Barreira and Valls (both, Instituto Superior Técnico, Lisbon) emphasize rigor, and have geared the book to students who are slightly more advanced than most students in first courses. ... Cumulatively, the volume includes over 160 examples, nearly 200 solved problems (about 45 percent of the text), and more than 220 exercises. Readability is enhanced by approximately 35 figures. Summing Up: Recommended. Upper-division undergraduates, graduate students, researchers/faculty, and professionals." (D. P. Turner, Choice, Vol. 50 (5), January, 2013)

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Luis Barreira is a Full Professor of Mathematics at Instituto Superior Técnico, Lisbon and a member of the Center for Mathematical Analysis, Geometry, and Dynamical Systems. He obtained his PhD from the Pennsylvania State University in 1996. In 2007 he has been awarded the Gulbenkian Science Prize.

Claudia Valls is an Invited Assistant Professor at Instituto Superior Técnico, Lisbon and a Postdoctoral Fellow at the Center for Mathematical Analysis, Geometry, and Dynamical Systems, of which she is also a member. She obtained her PhD from the Universitat de Barcelona in 1999.

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