The illustrated wavelet transform handbook. Introductory theory and applications in science, engineering, medicine and finance (Q2719327)

The book has the aim to show the ways how one can apply the wavelet analysis in different problems of mechanics, engineering, medicine, economics etc. It perfectly meets this aim. From the very beginning the discussion concerns mainly with two questions: what are the reason to make one or another construction and how it is possible to apply these constructions for specific models? Answering theses questions the author has deeply described the most modern concepts of wavelet analysis. The book is a good combination of a well-organized textbook, an advanced research exposition, a collection of extremely useful recipes for solving applied problems, and a handy book containing a lot of prominent examples and attractive illustrations of the theory and recent results from wavelet-based works. The book consists of 7 chapters, Appendix and enlarged Bibliography on the theme containing more than 700 items. The material is organized as suitable for the reader as possible. NEWLINENEWLINEThe first chapter ``Getting started'' describes the main ideas put into the book. They are given in general setting. It is also presented a detailed description of the structure of the material which is involved in the book. It is chosen the following way to maintain these ideas: starting from integral transform the author tries to show advantages of this approach in comparison with Fourier-type approaches (Chapter 2). ``Mexican hat'' is chosen as example of the wavelet base on which one can develop the main technique. Chapter 3 deals with algebraic, functional and other aspects of the discrete transform. The rest of the book is devoted to applications. Three directions are described in detail, namely, fluid mechanics (Chapter 4), engineering problems (Chapter 5), medicine (Chapter 6) as the most close to scientific interest of the author. Other directions are touched only briefly. These are possible applications and bibliographical review on fractal geometry, finance, geophysics, astronomy, chemistry etc. (Chapter 7). An information useful for readers is given in the Appendix. NEWLINENEWLINEThe author has reviewed the most interesting books on the subject and described the material contained on certain web-sites. The book can be extremely interesting for a wide auditorium: for students and beginners, for researchers and experts, for those who try to apply methods developed to different subjects.