Lectures on the Calculus of Variations
Author | : Oskar Bolza |
Publisher | : University of Michigan Library |
Total Pages | : 306 |
Release | : 1904 |
Genre | : Mathematics |
ISBN | : |
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Author | : Oskar Bolza |
Publisher | : University of Michigan Library |
Total Pages | : 306 |
Release | : 1904 |
Genre | : Mathematics |
ISBN | : |
Author | : I. M. Gelfand |
Publisher | : Courier Corporation |
Total Pages | : 260 |
Release | : 2012-04-26 |
Genre | : Mathematics |
ISBN | : 0486135012 |
Fresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal for math and physics students.
Author | : Daniel Liberzon |
Publisher | : Princeton University Press |
Total Pages | : 255 |
Release | : 2012 |
Genre | : Mathematics |
ISBN | : 0691151873 |
This textbook offers a concise yet rigorous introduction to calculus of variations and optimal control theory, and is a self-contained resource for graduate students in engineering, applied mathematics, and related subjects. Designed specifically for a one-semester course, the book begins with calculus of variations, preparing the ground for optimal control. It then gives a complete proof of the maximum principle and covers key topics such as the Hamilton-Jacobi-Bellman theory of dynamic programming and linear-quadratic optimal control. Calculus of Variations and Optimal Control Theory also traces the historical development of the subject and features numerous exercises, notes and references at the end of each chapter, and suggestions for further study. Offers a concise yet rigorous introduction Requires limited background in control theory or advanced mathematics Provides a complete proof of the maximum principle Uses consistent notation in the exposition of classical and modern topics Traces the historical development of the subject Solutions manual (available only to teachers) Leading universities that have adopted this book include: University of Illinois at Urbana-Champaign ECE 553: Optimum Control Systems Georgia Institute of Technology ECE 6553: Optimal Control and Optimization University of Pennsylvania ESE 680: Optimal Control Theory University of Notre Dame EE 60565: Optimal Control
Author | : Kung-ching Chang |
Publisher | : World Scientific |
Total Pages | : 325 |
Release | : 2016-09-16 |
Genre | : Mathematics |
ISBN | : 981314470X |
This is based on the course 'Calculus of Variations' taught at Peking University from 2006 to 2010 for advanced undergraduate to graduate students majoring in mathematics. The book contains 20 lectures covering both the theoretical background material as well as an abundant collection of applications. Lectures 1-8 focus on the classical theory of calculus of variations. Lectures 9-14 introduce direct methods along with their theoretical foundations. Lectures 15-20 showcase a broad collection of applications. The book offers a panoramic view of the very important topic on calculus of variations. This is a valuable resource not only to mathematicians, but also to those students in engineering, economics, and management, etc.
Author | : Bruce van Brunt |
Publisher | : Springer Science & Business Media |
Total Pages | : 295 |
Release | : 2006-04-18 |
Genre | : Mathematics |
ISBN | : 0387216979 |
Suitable for advanced undergraduate and graduate students of mathematics, physics, or engineering, this introduction to the calculus of variations focuses on variational problems involving one independent variable. It also discusses more advanced topics such as the inverse problem, eigenvalue problems, and Noether’s theorem. The text includes numerous examples along with problems to help students consolidate the material.
Author | : Bernard Dacorogna |
Publisher | : World Scientific Publishing Company |
Total Pages | : 241 |
Release | : 2008-12-10 |
Genre | : Mathematics |
ISBN | : 1911298496 |
The calculus of variations is one of the oldest subjects in mathematics, yet is very much alive and is still evolving. Besides its mathematical importance and its links to other branches of mathematics, such as geometry or differential equations, it is widely used in physics, engineering, economics and biology. This book serves both as a guide to the expansive existing literature and as an aid to the non-specialist — mathematicians, physicists, engineers, students or researchers — in discovering the subject's most important problems, results and techniques. Despite the aim of addressing non-specialists, mathematical rigor has not been sacrificed; most of the theorems are either fully proved or proved under more stringent conditions. In this new edition, the chapter on regularity has been significantly expanded and 27 new exercises have been added. The book, containing a total of 103 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels. Request Inspection Copy Contents:PreliminariesClassical MethodsDirect Methods: ExistenceDirect Methods: RegularityMinimal SurfacesIsoperimetric InequalitySolutions to the Exercises Readership: Graduate and undergraduate students in analysis and differential equations.
Author | : I. G. Petrovsky |
Publisher | : Courier Corporation |
Total Pages | : 261 |
Release | : 2012-12-13 |
Genre | : Mathematics |
ISBN | : 0486155080 |
Graduate-level exposition by noted Russian mathematician offers rigorous, readable coverage of classification of equations, hyperbolic equations, elliptic equations, and parabolic equations. Translated from the Russian by A. Shenitzer.
Author | : Torgny Lindvall |
Publisher | : Courier Corporation |
Total Pages | : 292 |
Release | : 2012-08-15 |
Genre | : Mathematics |
ISBN | : 048615324X |
Practical and easy-to-use reference progresses from simple to advanced topics, covering, among other topics, renewal theory, Markov chains, Poisson approximation, ergodicity, and Strassen's theorem. 1992 edition.
Author | : Jürgen Moser |
Publisher | : Birkhauser |
Total Pages | : 132 |
Release | : 2003-01-01 |
Genre | : Mathematics |
ISBN | : 9780817621858 |
"These lecture notes describe the Aubry-Mather-Theory within the calculus of variations. The text consists of the translated original lectures of Jurgen Moser and a bibliographic appendix with comments on the current state-of-the-art in this field of interest. Students will find a rapid introduction to the calculus of variations, leading to modern dynamical systems theory. Differential geometric applications are discussed, in particular billiards and minimal geodesics on the two-dimensional torus. Many exercises and open questions make this book a valuable resource for both teaching and research."--BOOK JACKET.
Author | : Laurence Chisholm Young |
Publisher | : American Mathematical Soc. |
Total Pages | : 354 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9780821826904 |
This book is divided into two parts. The first addresses the simpler variational problems in parametric and nonparametric form. The second covers extensions to optimal control theory. The author opens with the study of three classical problems whose solutions led to the theory of calculus of variations. They are the problem of geodesics, the brachistochrone, and the minimal surface of revolution. He gives a detailed discussion of the Hamilton-Jacobi theory, both in the parametric and nonparametric forms. This leads to the development of sufficiency theories describing properties of minimizing extremal arcs. Next, the author addresses existence theorems. He first develops Hilbert's basic existence theorem for parametric problems and studies some of its consequences. Finally, he develops the theory of generalized curves and "automatic" existence theorems. In the second part of the book, the author discusses optimal control problems. He notes that originally these problems were formulated as problems of Lagrange and Mayer in terms of differential constraints. In the control formulation, these constraints are expressed in a more convenient form in terms of control functions. After pointing out the new phenomenon that may arise, namely, the lack of controllability, the author develops the maximum principle and illustrates this principle by standard examples that show the switching phenomena that may occur. He extends the theory of geodesic coverings to optimal control problems. Finally, he extends the problem to generalized optimal control problems and obtains the corresponding existence theorems.