Complex Analysis and Differential Equations
by Luis Barreira and Claudia Valls

Preface

This book is essentially two books in one. Namely, it is an introduction to
two large areas of mathematics—complex analysis and differential equations—
and the material is naturally divided into two parts. This includes holomorphic
functions, analytic functions, ordinary differential equations, Fourier series, and
partial differential equations. Moreover, half of the book consists of approxi-
mately 200 worked-out problems plus 200 exercises of variable level of difficulty.
The worked-out problems fill the gap between the theory and the exercises.
To a considerable extent, the parts of complex analysis and differential equa-
tions can be read independently. In the second part, some special emphasis is
given to the applications of complex analysis to differential equations. On the
other hand, the material is still developed with sufficient detail in order that the
book contains an ample introduction to differential equations, and not strictly
related to complex analysis.
The text is tailored to any course giving a first introduction to complex anal-
ysis or to differential equations, assuming as prerequisite only a basic knowledge
of linear algebra and of differential and integral calculus. But it can also be used
for independent study. In particular, the book contains a large number of ex-
amples illustrating the new concepts and results. Moreover, the worked-out
problems, carefully prepared for each part of the theory, make this the ideal
book for independent study, allowing the student to actually see how the theory
applies, before solving the exercises.
Luis Barreira and Claudia Valls