This text provides an accessible, self-contained and rigorous introduction to complex analysis and differential equations. Topics covered include holomorphic functions, Fourier series, ordinary and partial differential equations.

The text is divided into two parts: part one focuses on complex analysis and part two on differential equations. Each part can be read independently, so in essence this text offers two books in one. In the second part of the book, some emphasis is given to the application of complex analysis to differential equations. Half of the book consists of approximately 200 worked out problems, carefully prepared for each part of theory, plus 200 exercises of variable levels of difficulty.

Tailored to any course giving the first introduction to complex analysis or differential equations, this text assumes only a basic knowledge of linear algebra and differential and integral calculus. Moreover, the large number of examples, worked out problems and exercises makes this the ideal book for independent study.

Table of Contents

Part I: Complex Analysis

1: Basic Notions

2: Holomorphic Functions

3: Sequences and Series

4: Analytic Functions

Part II: Differential Equations

5: Ordinary Differential Equations

6: Solving Differential Equations

7: Fourier Series

8: Partial Differential Equations

Review

“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)