Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory

I must say that this book is very complete and brings stuff other traditional books about mathematical methods of Physicists do not bring, Having said that I have only used it for studying asymptotic expansions of integrals and series, which is the subject of chapter 6. Here it presents Laplace Method's with full detail, The method of stationary phase and the method of Steepest Descent, all crucial methods for a Physicists to know!! One thing more to add, this is the only book that I know that brings a chapter of Difference equations and that makes it very wordy although myself have never used them but I do know that this equations are used sometimes specially when programming.

This book is absolutely amazing. I’m not sharing anything new by saying these authors are fantastic. I’m not embarrassed to be a part of a fan club in this case. I watch Carl Bender on YouTube and am more familiar with him. Anyway the book is fun.

Contains a lot of useful calculations and information. Definitely fun to read. However the subjects are not very well organized you have to find them here and there using the index and follow up on the references in the text.

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.

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.

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.

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.

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.

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.

Un très bon livre pour commencer à apprendre les méthodes d'asymptotique, il vieillit très bien! Je l'utilise en thèse de Mathématiques appliquées pour compléter quelques notions peu vues en France.

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.