Introduction to the Calculus of Variations

Nonfiction, Science & Nature, Mathematics, Calculus
Cover of the book Introduction to the Calculus of Variations by Hans Sagan, Dover Publications
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Hans Sagan ISBN: 9780486138022
Publisher: Dover Publications Publication: April 26, 2012
Imprint: Dover Publications Language: English
Author: Hans Sagan
ISBN: 9780486138022
Publisher: Dover Publications
Publication: April 26, 2012
Imprint: Dover Publications
Language: English

". . . eminently suitable as a text for an introductory course: the style is pleasant; the prerequisites are kept to a minimum . . . and the pace of the development is appropriate for most students at the senior or first year graduate level." — American Mathematical Monthly
The purpose of this text is to lay a broad foundation for an understanding of the problems of the calculus of variations and its many methods and techniques, and to prepare readers for the study of modern optimal control theory.* *The treatment is limited to a thorough discussion of single-integral problems in one or more unknown functions, where the integral is employed in the riemannian sense.
The first three chapters deal with variational problems without constraints. Chapter 4 is a self-contained treatment of the homogeneous problem in the two-dimensional plane. In Chapter 5, the minimum principle of Pontryagin as it applies to optimal control problems of nonpredetermined duration, where the state variables satisfy an autonomous system of first-order equations, is developed to the extent possible by classical means within the general framework of the Hamilton-Jacobi theory. Chapter 6 is devoted to a derivation of the multiplier rule for the problem of Mayer with fixed and variable endpoints and its application to the problem of Lagrange and the isoperimetric problem. In the last chapter, Legendre's necessary condition for a weak relative minimum and a sufficient condition for a weak relative minimum are derived within the framework of the theory of the second variation.
This book, which includes many strategically placed problems and over 400 exercises, is directed to advanced undergraduate and graduate students with a background in advanced calculus and intermediate differential equations, and is adaptable to either a one- or two-semester course on the subject.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

". . . eminently suitable as a text for an introductory course: the style is pleasant; the prerequisites are kept to a minimum . . . and the pace of the development is appropriate for most students at the senior or first year graduate level." — American Mathematical Monthly
The purpose of this text is to lay a broad foundation for an understanding of the problems of the calculus of variations and its many methods and techniques, and to prepare readers for the study of modern optimal control theory.* *The treatment is limited to a thorough discussion of single-integral problems in one or more unknown functions, where the integral is employed in the riemannian sense.
The first three chapters deal with variational problems without constraints. Chapter 4 is a self-contained treatment of the homogeneous problem in the two-dimensional plane. In Chapter 5, the minimum principle of Pontryagin as it applies to optimal control problems of nonpredetermined duration, where the state variables satisfy an autonomous system of first-order equations, is developed to the extent possible by classical means within the general framework of the Hamilton-Jacobi theory. Chapter 6 is devoted to a derivation of the multiplier rule for the problem of Mayer with fixed and variable endpoints and its application to the problem of Lagrange and the isoperimetric problem. In the last chapter, Legendre's necessary condition for a weak relative minimum and a sufficient condition for a weak relative minimum are derived within the framework of the theory of the second variation.
This book, which includes many strategically placed problems and over 400 exercises, is directed to advanced undergraduate and graduate students with a background in advanced calculus and intermediate differential equations, and is adaptable to either a one- or two-semester course on the subject.

More books from Dover Publications

Cover of the book The Man Who Would Be King by Hans Sagan
Cover of the book The Phenomenology of Mind by Hans Sagan
Cover of the book Graphic Worlds of Peter Bruegel the Elder by Hans Sagan
Cover of the book Infamous Pirates by Hans Sagan
Cover of the book Easy-to-Master Mental Magic by Hans Sagan
Cover of the book Magicians' Tricks by Hans Sagan
Cover of the book Great Drawings of Nudes by Hans Sagan
Cover of the book Women in Love by Hans Sagan
Cover of the book Uncle Vanya by Hans Sagan
Cover of the book The Great Anarchists by Hans Sagan
Cover of the book Probability by Hans Sagan
Cover of the book Taos Tales by Hans Sagan
Cover of the book Introduction to Hilbert Space and the Theory of Spectral Multiplicity by Hans Sagan
Cover of the book The Fitzwilliam Virginal Book, Volume Two by Hans Sagan
Cover of the book Late Victorian Interiors and Interior Details by Hans Sagan
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy