Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory 1999th Edition by Carl M. Bender (PDF)

Description

A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.

User’s Reviews

Editorial Reviews: Review “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)

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Rated 5 for content, 2 for quality of production. The contents are timeless – so get a used McGraw Hill edition for about the same price. This version has a glued spine and won’t last long. The contents are the same, some problems are different.

⭐This is one of those books that you can read for fun. I’d rate it as my best book along with Carrier’s ODE book. It says it’s meant for advanced undergrads and grad students. Be that as it may, I could have read it in high school (mind you, its not trivial, but the material is so accessible to anyone with a basic knowledge of calculus that you can read it in high school). Also, the usefulness of it cannot be overstated. I owe my PhD to this book. Not having taken a formal asymptotics course, I had to read up perturbation theory to set up large activation asymptotics problems in combustion. The perturbation analysis was used in making sense of (sigh) hero simulations, and the degree of accuracy of these models was just remarkable.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.

⭐A classic textbook on asymptotic and perturbative methods, honest, carefully written, and comprehensive. Although the first printing dates from 1978, the material is not outdated and still essential for applied mathematicians. The book is self-contained and has many illustrative examples. I will use to teach a one-semester class (Methods of Mathematical Physics) for advanced undergraduate mathematics students, focused on the aforementioned methods. If your class has physics students as well, you may want to include methods for the analysis of PDEs from other sources.

⭐An amazing collection of techniques and methods for attacking a wide range of linear and non-linear problems. Full of worked out examples and challenging problems. Perturbation, Pade approximation, continued fractions, continuation methods, they are all here.

⭐An understandable text on useful techniques which makes the reader feel comfortable using them. Pairs well with Carrier, Krook and Pearson’s complex variables text. I wish we had used this when I took Math Methods rather than that quirky Mathews and Walker book.

⭐I had seen this book in a bookstore over 15 years ago and regretted that I did not buy it at that time. Now that I have it, I am very disappointed. First of all, the print for the examples is very very small. The book is more of a summary of methods than any details of the methods themselves. There is no systematic development of the mathematical theory for these methods. This reinforces the worst aspects of books on aymptotic methods and perturbation theory: it’s all just a bunch of random trial and error jibbrish!The authors tried to pile in a lot of methods into the book without detailed explanations. I find it hard to believe that a scientist or engineer would get a lot out of this book. As a mathematician, I found it lacking in any significant mathematical meaning and purpose. I would recommend Nayfeh’s book on peturbation methods instead.

⭐This is the text book that follows the 16 lectures found on YouTube giver by the author carl bender.This is the answer to so many questions. pg

⭐The print quality is as if it’s been photocopied from the previously copied one.Besides that, it’s good.

⭐This is the best book I have ever received on the subject of asymptotic analysis and perturbation theory. It explains key concepts of the theory concisely and there are numerous examples in every chapter of the book to facilitate your in depth understanding. I would highly recommend this book.

⭐A fantastic text that uncovers many hidden aspects of the equations of mathematical physics. Non-standard (but very powerful) techniques are addressed. After studying this text, the reader’s vision/interpretation of ordinary differential equations will never be same again.

⭐Very pleased. Many thanks for the excellent service.

⭐An excellent book. I particularly liked the derivation of the Sterling series. Many books on the subject just show you how to get the first term (there are several ways) and leave the rest to you to figure out. The authors instead thoroughly expand on how to find each term. Much appreciated.

⭐Evito il mio bla bla. Ho deciso di prendere il libro dopo aver visto alcune delle 15 lezioni del Prof. Carl Bender. Vedi su YouTube: Mathematical Physics 01 – Carl Bender .. Mathematical Physics 15 – Carl Bender.

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