Linear and complex analysis for applications (Q2832006)

``Linear and Complex Analysis for Applications'' provides the reader with a deep appreciation of linear analysis and complex analysis and how these subjects fit into mathematics. The main goals of this volume are the following: (i) to develop enough linear analysis and complex variable theory to prepare students in engineering or applied mathematics for advanced work; (ii) to unify many distinct and seemingly isolated topics; (iii) to show mathematics as both interesting and useful, especially via the juxtaposition of examples and theorems.NEWLINENEWLINEIn the first part of this volume, the author provides some basic results of linear algebra, complex numbers, as well as topics from calculus III. The material on linear algebra includes infinite-dimensional examples arising from elementary calculus and differential equations. Line and surface integrals are computed both in the language of classical vector analysis and by using differential forms. Interesting connections between various topics and applications appear throughout the book.NEWLINENEWLINEThe content of this book is divided into the following seven chapters: 1. Linear algebra; 2. Complex numbers; 3. Vector analysis; 4. Complex analysis; 5. Transform methods; 6. Hilbert spaces; 7. Examples and applications. There is also an appendix devoted to the language of mathematics. All the topics are motivated very nicely, and there are many exercises, which make the book ideal for a course on the subject. The style is concise, always very neat, and proofs are given with full details. Hence, I certainly suggest this nice textbook to anyone interested in the subject, even for self-study.