The only monograph on the topic, this book concerns geometric methods in the theory of differential equations with quadratic right-hand sides, closely related to the calculus of variations and optimal control theory. Based on the author’s lectures, the book is addressed to undergraduate and graduate students, and scientific researchers.
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Editorial Reviews
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".... This book was written by a master expositor and is required reading for anyone who is intersted in pursuing a serious study of the Riccati equation. The first four chapters should be required reading for every graduate student who is thinking about studying geometric or mathematical control theory. I do not know of a better overview of the matheamtics required to do modern geometric control theory. Every control theorist should have a well-worn copy of this book on his bookshelf. ... Zelikin has written a book that will be well read for many years...." Siam Review, Vol. 43/1, March 2001 "... The text requires good background, but will be a useful reference." Mathematika 2002, Issue 93-94
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Inside This Book
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First Sentence:
In 1696, J. Bernoulli posed the brachistochrone problem to the mathematical community promising "to give his due to the mathematician who would succeed in its solution." Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
homogeneity domain, involutive isometry, stationary subgroup, conformal mapping theory, geodesic symmetry, first quadratic form, semiopen interval, symmetrical spaces, skew symmetrical, analytic automorphisms, geodesic submanifolds, strong minimum, double ratio, closed differential form, infinitely distant point, totally geodesic submanifold, nxn matrices, involutive automorphism, brachistochrone problem, symmetrical matrices, nontrivial intersection, positive semidefiniteness, isolated fixed point, isometry group, space tangent Key Phrases - Capitalized Phrases (CAPs): (learn more)
Reducing the Dirichlet Integral, Systems Associated, Three Approaches New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In 1696, J. Bernoulli posed the brachistochrone problem to the mathematical community promising "to give his due to the mathematician who would succeed in its solution." Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
homogeneity domain, involutive isometry, stationary subgroup, conformal mapping theory, geodesic symmetry, first quadratic form, semiopen interval, symmetrical spaces, skew symmetrical, analytic automorphisms, geodesic submanifolds, strong minimum, double ratio, closed differential form, infinitely distant point, totally geodesic submanifold, nxn matrices, involutive automorphism, brachistochrone problem, symmetrical matrices, nontrivial intersection, positive semidefiniteness, isolated fixed point, isometry group, space tangent Key Phrases - Capitalized Phrases (CAPs): (learn more)
Reducing the Dirichlet Integral, Systems Associated, Three Approaches 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 25
books:
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- Lectures on the Calculus of Variations and Optimal Control Theory by Laurence Chisholm Young in Back Matter
- Methods of Algebraic Geometry: Volume 1 (Cambridge Mathematical Library) by W. V. D. Hodge in Back Matter
- Nicht-Euklidische Geometrie by Felix Klein in Back Matter
- Geometric Measure Theory (Classics in Mathematics) by Herbert Federer in Back Matter
- Morse Theory (Annals of Mathematic Studies AM-51) by John Milnor in Back Matter
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