Modern advanced mathematics for engineers (Q2715822)

According to the authors' statement in the Preface, ``this book is written with the aim of providing students with strong foundation in modern applied mathematics. It is intended for use as a text for an introductory one-semester graduate course for engineering students.''NEWLINENEWLINENEWLINEAs a matter of fact, the book starts from ``level zero'' (elementary facts on sets and functions) and takes the reader on 300 pages to some notions of functional analysis, operator theory, and partial differential equations. It consists of 11 chapters with the following headings: 1. The Basics of Set Theory; 2. Relations and Mappings; 3. Mathematical Logic; 4. Algebraic Structures: Group through Linear Spaces; 5. Linear mappings and Matrices; 6. Metrics and Topological Properties; 7. Banach and Hilbert Spaces; 8. Orthonormal Bases and Fourier Series; 9. Operator Equations; 10. Fourier and Laplace Transforms; 11. Partial Differential Equations.NEWLINENEWLINENEWLINEWhy yet another textbook for engineers? In view of the vast market of books of this type this is of course a legitimate question. The answer could be: because of the original choice of topics and the careful presentation of results. The reviewer particularly appreciated the fact that the authors close every chapter with a brief summary, a very short collection of exercises, and a list of suggested references for further reading. Of course, in view of the wealth of problem books in applied mathematics and engineering, there is no need to present a large amount of exercises. However, a list of symbols at the end of the book would be helpful and should be added in subsequent editions.NEWLINENEWLINENEWLINEAt the end of the Preface, the authors note that ``this book (or any book) is not meant as a substitute for the knowledgeable and enthusiastic person teaching the course. The aim is to guide both teachers and students through the study of modern applied mathematics.'' One should be grateful to the authors for this critical remark, and also for having done a good job.