Amold concentrates on the simplest equations of a given type and shows how the key ideas play out. For example, he attacks the general theory of one first-order equation, first via wave-particle duality, then via Hamiltonian dynamics. The author's stature and the book's lucidity make this an essential acquisition for all College libraries. Professor Arnold's Lectures on Partial Differential Equations is an ambitious, intensely personal effort to reconnect the subject with some of its roots in modeling physical processes.
He does so in a lively lecture-style format, resulting in a book that would complement almost any course in PDEs. As can be gleaned from the previous paragraph, we bouth found the book by V.
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Arnold most stimulating and thought provoking, leading to statements such as, "It has been years since I enjoyed a book so much" by RBG and "I cannot point to any other book in mathematics written with the same intensity" by EAT. Arnold's book It can be used together with any book on PDEs and students will welcome its directness and freshness.
We know of no other book like it on the market and highly recommend it for individual reading and as an accompaniment to any course in PDEs.
The presentation gives a vivid sense of what was actually said and discussed in the lecture course, and in this fashion the book differs markedly from many text books with similar titles. Professor Arnold stresses the importance of physical intuitions and offers in his lecture a deep geometric insight into these equations.
The book is highly recommended to anybody interested in partial differential equations as well as those involved in lecturing on these topics. I encourage readers of this book to take note of the Preface which contains very interesting comments on the role of Bourbaki's group in mathematics, a theme which resurfaces many times in these lectures.
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As a result the author has aimed to impart to students with pre-knowledge of only a basic kind linear algebra, basic analysis, ordinary differential equations, Of course the subject is fundamental in mathematics and in physics and the author is an evangelist for keeping the subject mainstream for mathematicians and for physicists. He has attempted, he writes, to adhere to the principle of minimal generality, according to which every idea should first be clearly understood in the simplest situation!
This is successfully done, so that this book should prove attractive in length and in scope to its target readership. In this new excellent text are included a large number of interesting problems; at the end of the book there is a full set of problems from examinations given in Moscow. This book aims to cover the most basic parts of the subject ….
The book can serve as a nonstandard, geometrically motivated introduction to PDEs for students …. It is, probably, worth mentioning that the introduction contains some general philosophical views of the author on the subject of PDEs and modern mathematics as a whole and will be of interest to a broad mathematical audience. It is … based on a course delivered to third-year students of mathematics.
Lectures on Partial Differential Equations | Vladimir I. Arnold | Springer
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Lectures on Analytic Differential Equations
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