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Variational Calculus and Optimal Control: Optimization with Elementary Convexity (Undergraduate Texts in Mathematics) (Englisch) Gebundene Ausgabe – 21. Dezember 1995

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Synopsis

The text provides an introduction to the variational methods used to formulate and solve mathematical and physical problems and gives the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize then the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency. It lays the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, and computer science.

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This book supplies a broad-based introduction to variational methods for formulating and solving problems in mathematics and the applied sciences. It refines and extends the author's earlier text on variational calculus and a supplement on optimal control. It is the only current introductory text that uses elementary partial convexity of differentiable functions to characterize directly the solutions of some minimization problems before exploring necessary conditions for optimality or field theory methods of sufficiency. Through effective notation, it combines rudiments of analysis in (normed) linear spaces with simpler aspects of convexity to offer a multilevel strategy for handling such problems. It also employs convexity considerations to broaden the discussion of Hamilton's principle in mechanics and to introduce Pontjragin's principle in optimal control. It is mathematically self-contained but it uses applications from many disciplines to provide a wealth of examples and exercises. The book is accessible to upper-level undergraduates and should help its user understand theories of increasing importance in a society that values optimal performance.

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Format: Gebundene Ausgabe
I had read/studied most of this book when I was a graduate student in chemical engineering at Syracuse University (in 1987-88). I also took two courses on the subject from Professor Troutman. I strongly recommend this book to any "newcomer" to the subject. The author is a mathematician, and a large fraction of the book consists of theorems, lemmas, propositions, corollaries (and their rigorous proofs). The book also contains, however, a good number of illustrative examples and exercises which make it useful to engineers and scientists as well as to students of mathematics who want to learn more about applications of mathematics to physical sciences.
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5.0 von 5 Sternen Very complete book! 11. März 2014
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5.0 von 5 Sternen Introductory and readable, yet rigorous 7. Mai 2000
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Format: Gebundene Ausgabe
I had read/studied most of this book when I was a graduate student in chemical engineering at Syracuse University (in 1987-88). I also took two courses on the subject from Professor Troutman. I strongly recommend this book to any "newcomer" to the subject. The author is a mathematician, and a large fraction of the book consists of theorems, lemmas, propositions, corollaries (and their rigorous proofs). The book also contains, however, a good number of illustrative examples and exercises which make it useful to engineers and scientists as well as to students of mathematics who want to learn more about applications of mathematics to physical sciences.
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