Calculus of Variations: with Applications to Physics and Engineering by Robert Weinstock (PDF)

Description

This book by Robert Weinstock was written to fill the need for a basic introduction to the calculus of variations. Simply and easily written, with an emphasis on the applications of this calculus, it has long been a standard reference of physicists, engineers, and applied mathematicians. The author begins slowly, introducing the reader to the calculus of variations, and supplying lists of essential formulae and derivations. Later chapters cover isoperimetric problems, geometrical optics, Fermat’s principle, dynamics of particles, the Sturm-Liouville eigenvalue-eigenfunction problem, the theory of elasticity, quantum mechanics, and electrostatics. Each chapter ends with a series of exercises which should prove very useful in determining whether the material in that chapter has been thoroughly grasped.The clarity of exposition makes this book easily accessible to anyone who has mastered first-year calculus with some exposure to ordinary differential equations. Physicists and engineers who find variational methods evasive at times will find this book particularly helpful. “I regard this as a very useful book which I shall refer to frequently in the future.” J. L. Synge, Bulletin of the American Mathematical Society.

User’s Reviews

Editorial Reviews: About the Author Robert Weinstock: Mathematical Memories Robert Weinstock’s Calculus of Variations, first published by McGraw-Hill in 1952 and reprinted by Dover in 1974, is one of Dover’s longest-running books in mathematics. In a memoir written in the 1990s, Weinstock recalled how, after he received his PhD in physics from Stanford in 1943, he worked for a time at Harvard’s Radar Research Laboratory as part of the war effort. Describing himself then as an idealistic 26-year-old, he came up with the idea that he could do more for humanity and humanity’s problems as a working man than as a physicist, and so went to work for some months in 1946 as a seaman on two merchant ships. Back in the United States, Weinstock responded to a call for qualified mathematics instructors at Stanford (then, like most American colleges and universities, dealing with a major influx of new students supported by the GI Bill). He planned at the time to return to academia for only a short time. But, as it turned out, a long teaching career at Stanford, Notre Dame, and finally Oberlin ensued, concluding in 1990 after about fifty years. In the Author’s Own Words:”From January into September 1946, I was a wiper (an engine-room worker who did painting, cleaning, and other maintenance) on a succession of two merchant ships. These took me twice through the Panama Canal and provided visits to all three World War Two enemy nations: Italy, Germany, and Japan. I experienced what were surely the most fascinating eight months of my life. I’m convinced, in retrospect, that I was in 1946 the only wiper in the U.S.Merchant Marine with a PhD in physics.” — Robert Weinstock

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

⭐The item arrived on time in good condition. Thanks.

⭐Good explanations throughout the proof and theory. Obvious that it’s a old book, written kind of old fashioned but pretty good anyway. It’s worth the money. Cheap!

⭐We used this for Calc Var course in 1962, I wanted a fresh copy. Excellent and a standard for serious Math Physics

⭐Don’t understand the content. Maybe book is good but is not for me. I bouhgt it by mistake and because it was cheap.

⭐Muito bom! Very good!

⭐This book will make you fall in love with the beauty of this branch of mathematics.

⭐As a warning to the readers, I would like to say that my review was initially written for Elsgolc’s book

⭐. However, it is a comparative review between the two books and, thus, I have added it here.I used to think that Weinstock’s book was the best introduction to Calculus of Variations for scientists. I had discovered it as an undergrad student and, since then, I kept it at the top of my list. It is a well written book on a mathematical subject of great importance to scientists. But, recently, I discovered Elsgole’s book and I must admit that it has to replace Weinstock’s book at the top of the list.Weinstock’s book is written at the right level for scientists – not highly abstract, but not imprecise for mathematicians. It contains all the right topics from calculus of variations and lots – really lots – of applications from science. However, I always felt that all these applications are more of distraction for someone who wants to learn just the topic of calculus of variations and then apply it in his/her own discipline. After all, the majority of the applications material in Weinstock’s book can easily be found in physics and engineering books; and in these applications the calculus of variations part is only a small step to get a differential equation for the phenomenon under consideration. But the actual theory of the calculus of variations cannot be found so easily in the science books. Usually, these books devote a brief chapter to the topic of calculus of variations discussing only the main problem (which is often solved in a very unsatisfying way) and then state that other problems can be handled similarly, essentially asking the reader to discover the remaining techniques on his/her own.My point in the previous paragraph is that scientists are in need to read a presentation of the various calculus of variations techniques in a crystal clear way, not read a copy of their mechanics text. And Elsgole’s book is exactly this: a careful, clean presentation of the theory without extremely long and unnecessary excursions to physics. It is written at the same level as Weinstock’s book and it does contain simple examples to clarify the theory. One nice feature of the book is many two-column pages in which the author shows to the reader how the ideas of calculus of variations are similar to the ideas of the traditional calculus (of functions). The beginners will find this feature very valuable. The book is thinner than Weinstock’s and yet it contains more topics than Weinstock’s: Weinstock does not discuss extremals with cusps, neither he deals with sufficiency conditions for an extremum. Elsgole’s book does contain some applications (section 7 of chapter 1) to make the connection with science but they are too quick – the other extreme. The reader will find Weinstock’s end-of-chapter problems more interesting and exciting but Elsgole’s are not bad. They are made to fit exactly the contents of the corresponding chapter. Most probably, beginners will find Elsgole’s problems more useful just because they are fine-tuned to the material. Weinstock’s book also contains a chapter reviewing important ideas and results from calculus which are to be used later in the book; Elsgole’s does not. I am not bothered by such an omission as I never cared for such reviews. However, readers who value them will find Weinstock’s chapter nice and useful.Elsgole’s book is a good reading for mathematicians too. In fact, mathematicians will be turned off by Weinstock’s book. The extensive applications make the math scant. So, Elsgole’s book is the right choice for them.Overall, I think that you want to have both books in your bookcase. If you want to learn the topic and you want to focus on a single book, I recommend Elsgole’ book as first reading and then Weinstock’s. If you have some little extra time, a combined study of both books would be highly beneficial and it will enrich your knowledge greatly.

⭐thanks

⭐This is an excellent book on the calculus of variations ! It is very well written, always with a pedagogical viewpoint. The only pre-requisite is ordinary calculus. Besides the theoretic development, a huge number of examples and applications are illustrated, ranging from pure mathematics to physics (including classical mechanics, strings, membranes, elasticity theory, quantum mechanics). Many special topics are also included, such as the existence of finite (or differential) constraints, eigenvalue- eigenfunction problems, free or constrained end points conditions. So this book covers much of the topic; maybe the only missing point is the inverse problem of the calculus of variations: when a given system of partial differential equations can be considered as the Euler-Lagrange equations of any functional ? And, if so, can we get to that functional somehow ? This point is of course of much importance in physics. But, in any case, this book is certainly one of the best to dive into the topic.

⭐Este livro é uma impressão de uma digitalização de outro livro usado e riscado. A impressão tem falhas, manchas. ,,This book should cost less than 500. Also packaging was not good

⭐Un clasique sur le calcul des variations…Bien. Le sujet est vaste et plein d epièges, mais bien traité par l’auteur.

⭐

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