An introduction to the variational methods used to formulate and solve mathematical and physical problems, allowing the reader an insight into the systematic use of elementary (partial) convexity of differentiable functions in Euclidian space. By helping students directly characterize the solutions for many minimization problems, the text serves as a prelude to the field theory for sufficiency, laying as it does the groundwork for further explorations in mathematics, physics, mechanical and electrical engineering, as well as computer science.
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8 of 8 people found the following review helpful:
5.0 out of 5 stars
Introductory and readable, yet rigorous,
By Omer Akgiray (Istanbul) - See all my reviews
This review is from: Variational Calculus and Optimal Control: Optimization with Elementary Convexity (Undergraduate Texts in Mathematics) (Hardcover)
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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Inside This Book
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First Sentence:
This chapter presents a brief summary of the standard terminology and basic results related to characterizing the maximal and minimal values of a real valued function f defined on a set D in Euclidean space. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
local extremal point, possible corner points, maximal row rank, implicit function theory, transversal condition, stationary family, stationary functions, extremal function, saddle function, reverse triangle inequality, local extremals, weak local minimum, stationary trajectory, elementary convexity, unique optimal control, strong local minimum, stationary trajectories, exact field, sufficient differentiability, brachistochrone problem, convexity methods, minimizing function, end point conditions, normed linear space, local minimum point Key Phrases - Capitalized Phrases (CAPs): (learn more)
Jakob Bernoulli, Johann Bernoulli, Review of Optimization, Standard Optimization Problems, The Weierstrass-Erdmann Corner Conditions, Construction of Central Fields, The Zenodoros Problem, Variable End Point Problems New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
This chapter presents a brief summary of the standard terminology and basic results related to characterizing the maximal and minimal values of a real valued function f defined on a set D in Euclidean space. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
local extremal point, possible corner points, maximal row rank, implicit function theory, transversal condition, stationary family, stationary functions, extremal function, saddle function, reverse triangle inequality, local extremals, weak local minimum, stationary trajectory, elementary convexity, unique optimal control, strong local minimum, stationary trajectories, exact field, sufficient differentiability, brachistochrone problem, convexity methods, minimizing function, end point conditions, normed linear space, local minimum point Key Phrases - Capitalized Phrases (CAPs): (learn more)
Jakob Bernoulli, Johann Bernoulli, Review of Optimization, Standard Optimization Problems, The Weierstrass-Erdmann Corner Conditions, Construction of Central Fields, The Zenodoros Problem, Variable End Point Problems New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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1
book
cites this book:
- Partial Differential Equations (Applied Mathematical Sciences) (v. 1) by Fritz John in Back Matter (1), Back Matter (2), and Back Matter (3)
- Calculus of Variations (Dover Books on Mathematics) by I. M. Gelfand in Back Matter (1), and Back Matter (2)
- Calculus of Variations (Carus Monograph) by Gilbert Ames Bliss in Back Matter (1), and Back Matter (2)
- Functions of Several Variables (Undergraduate Texts in Mathematics) by Wendell Fleming in Front Matter, and Back Matter
- Calculus of Variations by Rund in Back Matter
See all 100 books this book cites
- Frontiers in Global Optimization (Nonconvex Optimization and Its Applications (closed)) by Christodoulos A. Floudas on page 497
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