- Hardcover: 593 pages
- Publisher: Springer; 1999 edition (October 29, 1999)
- Language: English
- ISBN-10: 0387989315
- ISBN-13: 978-0387989310
- Product Dimensions: 6.1 x 1.4 x 9.2 inches
- Shipping Weight: 2.2 pounds (View shipping rates and policies)
- Average Customer Review: 29 customer reviews
- Amazon Best Sellers Rank: #314,236 in Books (See Top 100 in Books)
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Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory 1999th Edition
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"This book is a reprint of the original published by McGraw-Hill \ref [MR0538168 (80d:00030)]. The only changes are the addition of the Roman numeral I to the title and the provision of a subtitle, "Asymptotic methods and perturbation theory". This latter improvement is much needed, as the original title suggested that this was a teaching book for undergraduate scientists and engineers. It is not, but is an excellent introduction to asymptotic and perturbation methods for master's degree students or beginning research students. Certain parts of it could be used for a course in asymptotics for final year undergraduates in applied mathematics or mathematical physics.
This is a book that has stood the test of time and I cannot but endorse the remarks of the original reviewer. It is written in a fresh and lively style and the many graphs and tables, comparing the results of exact and approximate methods, were in advance of its time. I have owned a copy of the original for over twenty years, using it on a regular basis, and, after the original had gone out of print, lending it to my research students. Springer-Verlag has done a great service to users of, and researchers in, asymptotics and perturbation theory by reprinting this classic." (A.D. Wood, Mathematical Reviews)
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Apart from the general high level of quality of examples and problems, the book almost literally talks to you. Beautiful phrases, such as 'executing several sleazy manoeuvres' and Holmes references are among those things that are perpetually endearing. Although I don't do any math anymore I still read this book a lot - on the BART train, or on a lazy Sunday afternoon. Very fun problems too. But best of all is that this book is genuinely useful to an idiot engineer. It exposes the power and beauty of perturbation theory in a way that you can look at a real problem and say 'Ah, it is simple'. I've spent many hours dreaming about things such as the interface between light and shadows, boundary layers (yes! the 'abrupt' transition from U_infty to 0 at the wall), why we need implicit formulations near the wall, and general considerations about stiff equations. This book is basically the vehicle that transports you there, and with minimum fuss.
This is the answer to so many questions. pg