From the Preface: "The material in this book is based on notes for a course which I gave several times at Brown University. The target of the course was juniors and seniors majoring in applied mathematics, engineering and other sciences. My basic goal in the course was to teach standard methods, or what I regard as a basic "bag of tricks". In my opinion the material contained here, for the most part, does not depart widely from traditional subject matter. One such departure is the discussion of discrete linear systems. Besides being interesting in its own right, this topic is included because the treatment of such systems leads naturally to the use of discrete Fourier series, discrete Fourier transforms, and their extension, the Z-transform. On making the transition to continuous systems we derive their continuous analogues, viz., Fourier series, Fourier transforms, Fourier integrals and Laplace transforms. A main advantage to the approach taken is that a wide variety of techniques are seen to result from one or two very simple but central ideas. Above all, this course is intended as being one which gives the student a "can-do" frame of mind about mathematics. Students should be given confidence in using mathematics and not be made fearful of it. I have, therefore, forgone the theorem-proof format for a more informal style. Finally, a concerted effort was made to present an assortment of examples from diverse applications with the hope of attracting the interest of the student, and an equally dedicated effort was made to be kind to the reader."
First in a new Springer-Verlag series. Text derived from a course taught at Brown University, in which the author's modestly realistic objective is to acquaint advanced undergraduate and beginning graduate students with fairly standard contents of the applied mathematician's basic bag of tricks. Strength of the text (in a crowded field) derives from the author's determination to treat clearly and insightfully/concretely the topics he does treat, and to resist every urge to produce yet another encyclopedia of mathematical methods; computationally self-confident students were his primary objective. Nine chapters, frequent problem sets, useful examples, basic references, acceptable typography, reasonable price. (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)