Lectures on the Calculus of Variations
Author : Oskar Bolza
Publisher : University of Michigan Library
Page : 306 pages
File Size : 34,11 MB
Release : 1904
Category : Mathematics
ISBN :
Calculus of Variations
Author : I. M. Gelfand
Publisher : Courier Corporation
Page : 260 pages
File Size : 19,12 MB
Release : 2012-04-26
Category : Mathematics
ISBN : 0486135012
Book Description
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.
Lecture Notes On Calculus Of Variations
Author : Kung-ching Chang
Publisher : World Scientific
Page : 325 pages
File Size : 32,88 MB
Release : 2016-09-16
Category : Mathematics
ISBN : 981314470X
Book Description
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.
Calculus of Variations and Optimal Control Theory
Author : Daniel Liberzon
Publisher : Princeton University Press
Page : 255 pages
File Size : 20,39 MB
Release : 2012
Category : Mathematics
ISBN : 0691151873
Book Description
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
Classical Mechanics with Calculus of Variations and Optimal Control
Author : Mark Levi
Publisher : American Mathematical Soc.
Page : 322 pages
File Size : 15,42 MB
Release : 2014-03-07
Category : Mathematics
ISBN : 0821891383
Book Description
This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox"; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book.
Lectures on Functional Equations and Their Applications
Author : J. Aczel
Publisher : Courier Corporation
Page : 548 pages
File Size : 27,94 MB
Release : 2006-02-01
Category : Mathematics
ISBN : 0486445232
Book Description
Numerous detailed proofs highlight this treatment of functional equations. Starting with equations that can be solved by simple substitutions, the book then moves to equations with several unknown functions and methods of reduction to differential and integral equations. Also includes composite equations, equations with several unknown functions of several variables, vector and matrix equations, more. 1966 edition.
Lectures on the Coupling Method
Author : Torgny Lindvall
Publisher : Courier Corporation
Page : 292 pages
File Size : 17,59 MB
Release : 2012-08-15
Category : Mathematics
ISBN : 048615324X
Book Description
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.
The Calculus of Variations
Author : Bruce van Brunt
Publisher : Springer Science & Business Media
Page : 295 pages
File Size : 26,36 MB
Release : 2006-04-18
Category : Mathematics
ISBN : 0387216979
Book Description
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.
Introduction To The Calculus Of Variations (3rd Edition)
Author : Bernard Dacorogna
Publisher : World Scientific Publishing Company
Page : 322 pages
File Size : 48,76 MB
Release : 2014-08-13
Category : Mathematics
ISBN : 178326554X
Book Description
The calculus of variations is one of the oldest subjects in mathematics, and it is very much alive and 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, several new exercises have been added. The book, containing a total of 119 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.
Lectures on the Calculus of Variations
Author : G.A. Bliss
Publisher :
Page : pages
File Size : 30,58 MB
Release : 1951
Category :
ISBN :
