Ebook Calculus of Variations: Mechanics, Control and Other Applications (Dover Books on Mathematics), by Charles R. MacCluer
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Calculus of Variations: Mechanics, Control and Other Applications (Dover Books on Mathematics), by Charles R. MacCluer
Ebook Calculus of Variations: Mechanics, Control and Other Applications (Dover Books on Mathematics), by Charles R. MacCluer
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The first truly up-to-date treatment of the calculus of variations, this text is also the first to offer a simple introduction to such key concepts as optimal control and linear-quadratic control design. Suitable for junior/senior–level students of math, science, and engineering, this volume also serves as a useful reference for engineers, chemists, and forest/environmental managers. Its broad perspective features numerous exercises, hints, outlines, and comments, plus several appendixes, including a practical discussion of MATLAB.
Students will appreciate the text's reader-friendly style, which features gradual advancements in difficulty and starts by developing technique rather than focusing on technical details. The examples and exercises offer many citations of engineering-based applications, and the exercises range from elementary to graduate-level projects, including longer projects and those related to classic papers.
- Sales Rank: #1757573 in eBooks
- Published on: 2013-05-20
- Released on: 2013-05-20
- Format: Kindle eBook
About the Author
Charles R. MacCluer is Professor of Mathematics and director of the industrial mathematics program at Michigan State University. His first interest was algebraic number theory but later turned to the more practical disciplines of control theory, signal processing, building science, and industrial problems. He is the author of "Industrial Mathematics, Boundary Value Problems and Fourier Expansions," and "Calculus of Variations."
Most helpful customer reviews
6 of 7 people found the following review helpful.
The provenance of this book (by the author)
By Amazon Customer
I wrote this book to be used as the text for our senior capstone course for mathematics majors at Michigan State University. The mission of our capstone courses is to ask the student to integrate several sub-disciplines of mathematics (and if possible other disciplines) into a significant technical writing product. My version of the capstone incorporated ideas from engineering --- Lagrange mechanics and optimal control --- as well as the classical problems proposed by the Bernoulli brothers, Newton, Leibniz, Euler, and other early mathematicians, the problems that gave birth to this earliest of fields. The book has an unusually large number of illustrations of mechanical applications, which may account for its high adoption rate by engineering instructors.
The charm of this subject is found in its classical applications accessible to any student with calculus. I have attempted to downplay (at first) the technical details, to instead develop technique. As a result, even a modestly equipped student can carry away a strong understanding of the subject based on practice with the calculations. The starred proofs employ advanced machinery but are sketched in an expository style that may be comprehensible to undergraduates.
The difficulty of the book ramps up gradually --- Chapter 8 is at a strong senior level, while Chapters 9 and 10 (Weak and Strong Sufficiency) and Chapter 11 (Corner Points) are more abstract and at very strong senior or graduate level.
There is no modern text at this level that is accessible to students armed only with calculus. There are of course the fine classic Dover editions of Fox, Sagan, Weinstock, Ewing, and Gelfand/Fomin. But these books are all showing their age, and, unlike our book, none of these incorporate a simple introduction to optimal control, the bang-bang theorem, Pontryagin's maximum principle, or linear-quadratic control design. Some of the most entertaining applications of the calculus of variations are found in optimal control.
3 of 3 people found the following review helpful.
Decent
By ScienceThinker
This book can be useful for someone who wishes to glance over the main ideas of optimal control. It is easy to read and it contains a good number of exercises, many of which relate to details and extensions of the theory discussed in the book. However a demanding mathematician may find it unsatisfying. Although the focus is towards precise mathematics, some rigor has been sacrificed in order to make it more accessible. On the other hand, scientists and engineers will probable find it unappealing since the book deals with the math formalism more than describing and finding solutions to as many physical situations as possible. Also, they care very little for weak and strong sufficiency conditions; they usually prefer a reasoning that is based on physical arguments (even if it is not the most robust and rigorous). Therefore, the book is written with a style that will discourage people in almost every discipline to use. My personal view is that the book would have been much better if the author had targeted one particular group (either mathematicians or physicists or engineers). Each of these groups has different attitude towards the subject and it is virtually impossible to satisfy all of them. For attempting such a herculean task (i.e. satisfying everyone), I believe that the book came descent and each group can learn something if it is willing to read it.
However, this is not the right book to learn calculus of variations; I would have preferred a different title such as `Introduction to Optimization Problems' to make its content more obvious. Since the books selects several topics to present, one can hardly get a global picture for the traditional material of calculus of variations. Although the author says that the classics on the topic show their age, with all my apologies to him, I do actually prefer them. Among them, my favorite ones are Calculus of Variations (Dover Books on Mathematics) by Elsgolc, Calculus of Variations: with Applications to Physics and Engineering by Weinstock and Calculus of Variations (Dover Books on Mathematics) by Gelfand and Fomin.
Finally, another little thing I do not like with the book is the insertion of Mathematica and MATLAB code at various places. It is not really a big problem but I do not like to see them in a book that is apparently abstract. They also have a negative aesthetics effect. I would have preferred to have all of the coding placed in a chapter at the end of the book. (In fact, the author does include an appendix entitled MATLAB Cookbook!)
2 of 2 people found the following review helpful.
incomplete, not for self-study
By Turtleman
Note that this book is geared toward proof, rather than computation.
The table of contents may seem that this book is for application in science / engineering.
This book is definitely NOT for self-study.
In the book, so many proof are incomplete.
It explains proof up to the half way, then rest of the proof are left as "exercise" for readers.
I really don't see what is the purpose of the book.
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