This book appears in the series Systems & Control: Foundations & Applications and is intended as a textbook for classes in variational calculus and applied functional analysis for graduate students in engineering and applied mathematics.
The book is the result of the courses taught by the authors through the years and tries to address the different backgrounds the different types of students come in with when taking these courses. The topics covered provide both a treatment of the theoretical aspects of functional analysis, as well as their applications to variational calculus, mechanics and control theory.
The chapters included in the book address the advertised goals very well, as they include: Classical Abstract Spaces in Functional Analysis, Linear Functionals and Linear Operators, Common Function Spaces and Applications, Differential Calculus in Normed Vector Spaces, Minimization of Functionals, Convex Functionals, Lower Semicontinouos Functionals.
The book includes a list of References that can be used for further studies. Some readers might want to use those references, because some of the proofs are omitted in the present text and there are very few exercises. However, the goals of the book are met and there are many examples that make the book even more readable.
I am sure that many instructors seeking a textbook for a course on the applications of functional analysis for engineering or applied mathematics students will find this text very useful.
Mihaela Poplicher is an assistant professor of mathematics at the University of Cincinnati. Her research interests include functional analysis, harmonic analysis, and complex analysis. She is also interested in the teaching of mathematics. Her email address is Mihaela.Poplicher@uc.edu.