Elliptic Functions and Applications (Applied Mathematical Sciences, 80) by Derek F. Lawden (PDF)

Description

The subject matter of this book formed the substance of a mathematical se am which was worked by many of the great mathematicians of the last century. The mining metaphor is here very appropriate, for the analytical tools perfected by Cauchy permitted the mathematical argument to penetra te to unprecedented depths over a restricted region of its domain and enabled mathematicians like Abel, Jacobi, and Weierstrass to uncover a treasurehouse of results whose variety, aesthetic appeal, and capacity for arousing our astonishment have not since been equaled by research in any other area. But the circumstance that this theory can be applied to solve problems arising in many departments of science and engineering graces the topic with an additional aura and provides a powerful argument for including it in university courses for students who are expected to use mathematics as a tool for technological investigations in later life. Unfortunately, since the status of university staff is almost wholly determined by their effectiveness as research workers rather than as teachers, the content of undergraduate courses tends to reflect those academic research topics which are currently popular and bears little relationship to the future needs of students who are themselves not destined to become university teachers. Thus, having been comprehensively explored in the last century and being undoubtedly difficult .

User’s Reviews

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

⭐Congratulations dear reader for finding a diamond amongst the sea of textbooks. I think this is one of my favourite textbooks ever written! Why is that? As the author points out in the introduction, the art of elliptic functions has since passed us. Occasionally in mechanics you come across a problem that can be solved by integrals exactly but it is rare indeed. However, of those problems you come across, most are related to the elliptic functions. Check out Whittaker’s mechanics book to see what I mean (an example that comes to mind immediately is the spherical pendulum). This book has everything you could possibly want to know about elliptic functions and then some. There is something for everyone in here; those want to expand their knowledge of integrals that can be evaluated exactly, the random obscure mechanics problems that can be solved exactly (be warned they are difficult), identities (lots of them), and just random elliptic function theory.This book has everything that an applied mathematician or a physicist could want as an introduction and reference. I’ve found that with a standard undergraduate background in complex analysis, some PDE theory, and mathematical physics is all you need. I haven’t worked through the later chapters but the early chapters are very readable and a lot of brute force calculation. I highly recommend this book since it covers everything you want to know about a subject that simply isn’t taught any more because it’s difficult (as the author says). I agree. It is difficult but it’s fun!

⭐Of all the books on elliptic functions, I think in terms of price, content, and applications, so far I encounter is the best.One bad point about that is you needs a very advanced knowledge of calculus and complex analysis at GRADUATE LEVEL. I do no recommend this book for beginners,

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