Home > books, Mathematics > Advanced Mathematical Methods for Scientists and Engineers: Asymptotic Methods and Perturbation Theory

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

This is, perhaps, one of the best textbooks I have ever read. I have a habit of reading books that are far above my education and skills. There are multiple motivations to this approach: obtaining insight into areas of interest, learning from the introductory aspects and inspiration to learn more when the book and my understanding start to rapidly diverge.

This book is no exception with respect to this habit. However, the authors  clarity and coherence exceeds many others I have read. In particular, the examples used are simple enough to be easily understood but powerful enough to illustrate the authors point, particularly when used as counterexamples or to show a limitation of a particular technique.  The emphasis is on understanding and ‘seeing for yourself’  what happens with various techniques and where they fall down. The authors also openly expose common misconceptions or pitfalls in thinking, particularly with respect to what is convergence, the importance of divergent series, the  rendering meaningful  of summation of divergent series.

Every chapter starts with motivating examples and builds to increasingly complex cases. Connections between areas in the book and limitations of analogies  (e.g differential and difference equations) are clearly discussed. It was particularly interesting to see the connection between Pade approximants and continued fractions.

Finally, the quotations from Sherlock Holmes were delightful  entres (and well chosen for chapter content).

I am left wishing I had the time to do this textbook justice and encouraged to start to fill the enormous gaps in my knowledge the book made clear to me.

 

 

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Categories: books, Mathematics

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