Synopses & Reviews
Methods of Applied Mathematics with a MATLAB Overview is devoted to the applications of Fourier analysis; topics encompass the classical applications in partial differential equations and boundary value problems as well as the concepts and methods associated to the Laplace, Fourier, and discrete transforms. Transform inversion problems are covered, along with the necessary background in complex variables and Sturm-Liouville theory. The final chapter provides an examination of wavelets, short-time Fourier analysis, and geometrically-based transforms. The use of the computer program MATLAB has been integrated throughout the text, with particular emphasis on the program's numerical and graphing capabilities. Key topics and features: • Clear, consistent exposition with a strong focus on mathematical fundamentals and useful techniques • Extensive examples, illustrations, and modern applications • A variety of problems of wide-ranging difficulty, many with solutions • Numerous MATLAB exercises and routines, with an introduction to MATLAB provided in an appendix • Comprehensive references and index Requiring only familiarity with calculus and linear algebra and some introductory acquaintance with differential equations and vector calculus, this work can be used flexibly, either for a one-semester survey or an in-depth, year-long course. With its broad scope and careful pedagogy, this treatment will serve students in pure and applied mathematics, physical sciences, and engineering. Solutions manual available upon adoption of text.
Review
"Overall, this textbook has an attractive format with lots of figures, programs, and formulas, and it presents, in a very traditional way, a body of material that is fundamental in applied mathematics, science, and engineering. It would make an excellent textbook for courses focused around Fourier analysis and applications to differential equations." --SIAM Review "The aim of this book is to provide an introduction to a number of methods of applied mathematics, especially those arising from Fourier analysis. Classical problems of [a] mathematical physics nature are discussed throughout the book. Those problems represent the pretext or the basis for the elaboration of mathematical models. The book presents numerical schemes and analytical results as well.... This book is excellent material for students of applied mathematics and engineers, covering the theory of Fourier analysis with interesting applications and numerical examples in MATLAB." --Zentralblatt MATH "This book is devoted to the application of Fourier analysis. The author mixed in a remarkable way theoretical results and applications illustrating the results. Flexibility of presentation (increasing and decreasing level of rigor, accessibility) is a key feature. ...The book contains extensive examples, presented in an intuitive way with high quality figures (some of them quite spectacular), useful MATLAB codes. MATLAB exercises and routines are well integrated within the text, and a concise introduction into MATLAB is given in an appendix. The emphasis is on the program's numerical and graphical capabilities and its applications, not on its syntax.... Applications are modern and up to date.... Comprehensive references are attached to each chapter. Intended audience: especially students in pure and applied mathematics, physics and computer science, but also useful to applied mathematicians, engineers and computer scientists interested in applications of Fourier analysis." --Mathematica "The topics covered are useful both in traditional continuum mechanics and mathematical physics areas, as well as in applied mathematics domains such as control and communications. The book provides in a clear and distinct manner the fundamental concepts and techniques of this area and a wide variety of problems in which these methods are useful. Both the theoretical and the computational aspects are emphasized. ...Davis's book has many novel features being quite different from most other textbooks on applied mathematics. Besides a nice treatment of all these topics...it also contains a very deep treatment of MATLAB implementations of methods and algorithms. Mainly it has a clear and consistent exposition with a strong focus on mathematical fundamentals and useful techniques. It has numerous extensive examples, illustrations, comments, and a very modern graphical presentation of results. A variety of problems of wide-ranging difficulty together with their solutions are presented. Plenty of MATLAB routines and exercises are also provided. ...The book has style. Every theorem and mathematical result has a wonderful appealing comment. While the author does not purposely go out of his way to be rigorous and very technical, he illustrates all these results by numerical examples implemented and solved in the MATLAB environment. ...All in all, I greatly enjoyed reviewing this book, and I recommend it without any hesitation as a textbook for advanced graduate or master's level courses in engineering." --Studies in Informatics and Control
Synopsis
Broadly organized around the applications of Fourier analysis, "Methods of Applied Mathematics with a MATLAB Overview" covers both classical applications in partial differential equations and boundary value problems, as well as the concepts and methods associated to the Laplace, Fourier, and discrete transforms. Transform inversion problems are also examined, along with the necessary background in complex variables. A final chapter treats wavelets, short-time Fourier analysis, and geometrically-based transforms. The computer program MATLAB is emphasized throughout, and an introduction to MATLAB is provided in an appendix. Rich in examples, illustrations, and exercises of varying difficulty, this text can be used for a one- or two-semester course and is ideal for students in pure and applied mathematics, physics, and engineering.
Table of Contents
Preface.- Introduction.- Fourier Series.- Elementary Boundary Value Problems.- Sturm-Liouville Theory and Boundary Value Problems.- Functions of a Complex Variable.- Laplace Transforms.- Fourier Transforms.- Discrete Variable Transforms.- Additional Topics.- Linear Algebra Overview.- Software Resources.- Transform Tables.- Index.