Calculus of Variations

Author: I. M. Gelfand,S. V. Fomin

Publisher: Courier Corporation

ISBN: 0486135012

Category: Mathematics

Page: 240

View: 9820

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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.

An Introduction to the Calculus of Variations

Author: Charles Fox

Publisher: Courier Corporation

ISBN: 9780486654997

Category: Mathematics

Page: 271

View: 9428

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In this highly regarded text for advanced undergraduate and graduate students, the author develops the calculus of variations both for its intrinsic interest and for its powerful applications to modern mathematical physics. Topics include first and second variations of an integral, generalizations, isoperimetrical problems, least action, special relativity, elasticity, more. 1963 edition.

Calculus of Variations

Mechanics, Control and Other Applications

Author: Charles R. MacCluer

Publisher: Courier Corporation

ISBN: 0486278301

Category: Mathematics

Page: 272

View: 7899

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First truly up-to-date treatment offers a simple introduction to optimal control, linear-quadratic control design, and more. Broad perspective features numerous exercises, hints, outlines, and appendixes, including a practical discussion of MATLAB. 2005 edition.

Introduction to the Calculus of Variations

Author: Hans Sagan

Publisher: Courier Corporation

ISBN: 048613802X

Category: Mathematics

Page: 480

View: 3352

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Provides a thorough understanding of calculus of variations and prepares readers for the study of modern optimal control theory. Selected variational problems and over 400 exercises. Bibliography. 1969 edition.

Calculus of Variations

Author: Lev D. Elsgolc

Publisher: Courier Corporation

ISBN: 0486154939

Category: Mathematics

Page: 192

View: 7693

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This text offers an introduction to the fundamentals and standard methods of the calculus of variations, covering fixed and movable boundaries, plus solutions of variational problems. 1961 edition.

Calculus of Variations

With Applications to Physics and Engineering

Author: Robert Weinstock

Publisher: Courier Corporation

ISBN: 9780486630694

Category: Mathematics

Page: 326

View: 3117

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This text is basically divided into two parts. Chapters 1–4 include background material, basic theorems and isoperimetric problems. Chapters 5–12 are devoted to applications, geometrical optics, particle dynamics, the theory of elasticity, electrostatics, quantum mechanics, and other topics. Exercises in each chapter. 1952 edition.

An Introduction to the Calculus of Variations

Author: L.A. Pars

Publisher: Courier Corporation

ISBN: 0486165957

Category: Mathematics

Page: 368

View: 9533

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Clear, rigorous introductory treatment covers applications to geometry, dynamics, and physics. It focuses upon problems with one independent variable, connecting abstract theory with its use in concrete problems. 1962 edition.

The Variational Principles of Mechanics

Author: Cornelius Lanczos

Publisher: Courier Corporation

ISBN: 0486134709

Category: Science

Page: 464

View: 5594

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Philosophic, less formalistic approach to analytical mechanics offers model of clear, scholarly exposition at graduate level with coverage of basics, calculus of variations, principle of virtual work, equations of motion, more.

The Calculus of Variations

Author: Bruce van Brunt

Publisher: Springer Science & Business Media

ISBN: 0387216979

Category: Mathematics

Page: 292

View: 4200

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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.

Lectures on Linear Algebra

Author: I. M. Gelfand

Publisher: Courier Corporation

ISBN: 9780486660820

Category: Mathematics

Page: 185

View: 2604

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Prominent Russian mathematician's concise, well-written exposition considers n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, and an introduction to tensors. While not designed as an introductory text, the book's well-chosen topics, brevity of presentation, and the author's reputation will recommend it to all students, teachers, and mathematicians working in this sector.

Introduction To The Calculus of Variations And Its Applications, Second Edition

Author: Frederic Wan

Publisher: Routledge

ISBN: 1351436511

Category: Mathematics

Page: 640

View: 9323

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This comprehensive text provides all information necessary for an introductory course on the calculus of variations and optimal control theory. Following a thorough discussion of the basic problem, including sufficient conditions for optimality, the theory and techniques are extended to problems with a free end point, a free boundary, auxiliary and inequality constraints, leading to a study of optimal control theory.

Integral Equations

Author: F. G. Tricomi

Publisher: Courier Corporation

ISBN: 0486158306

Category: Mathematics

Page: 256

View: 2174

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Authoritative, well-written treatment of extremely useful mathematical tool with wide applications. Topics include Volterra Equations, Fredholm Equations, Symmetric Kernels and Orthogonal Systems of Functions, more. Advanced undergraduate to graduate level. Exercises. Bibliography.

Variational Methods in Optimization

Author: Donald R. Smith

Publisher: Courier Corporation

ISBN: 9780486404554

Category: Mathematics

Page: 378

View: 5096

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Highly readable text elucidates applications of the chain rule of differentiation, integration by parts, parametric curves, line integrals, double integrals, and elementary differential equations. 1974 edition.

A Primer on the Calculus of Variations and Optimal Control Theory

Author: Mike Mesterton-Gibbons

Publisher: American Mathematical Soc.

ISBN: 0821847724

Category: Mathematics

Page: 252

View: 8993

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The calculus of variations is used to find functions that optimize quantities expressed in terms of integrals. Optimal control theory seeks to find functions that minimize cost integrals for systems described by differential equations. This book is an introduction to both the classical theory of the calculus of variations and the more modern developments of optimal control theory from the perspective of an applied mathematician. It focuses on understanding concepts and how to apply them. The range of potential applications is broad: the calculus of variations and optimal control theory have been widely used in numerous ways in biology, criminology, economics, engineering, finance, management science, and physics. Applications described in this book include cancer chemotherapy, navigational control, and renewable resource harvesting. The prerequisites for the book are modest: the standard calculus sequence, a first course on ordinary differential equations, and some facility with the use of mathematical software. It is suitable for an undergraduate or beginning graduate course, or for self study. It provides excellent preparation for more advanced books and courses on the calculus of variations and optimal control theory.

Functional Analysis, Calculus of Variations and Optimal Control

Author: Francis Clarke

Publisher: Springer Science & Business Media

ISBN: 1447148207

Category: Mathematics

Page: 591

View: 1423

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Functional analysis owes much of its early impetus to problems that arise in the calculus of variations. In turn, the methods developed there have been applied to optimal control, an area that also requires new tools, such as nonsmooth analysis. This self-contained textbook gives a complete course on all these topics. It is written by a leading specialist who is also a noted expositor. This book provides a thorough introduction to functional analysis and includes many novel elements as well as the standard topics. A short course on nonsmooth analysis and geometry completes the first half of the book whilst the second half concerns the calculus of variations and optimal control. The author provides a comprehensive course on these subjects, from their inception through to the present. A notable feature is the inclusion of recent, unifying developments on regularity, multiplier rules, and the Pontryagin maximum principle, which appear here for the first time in a textbook. Other major themes include existence and Hamilton-Jacobi methods. The many substantial examples, and the more than three hundred exercises, treat such topics as viscosity solutions, nonsmooth Lagrangians, the logarithmic Sobolev inequality, periodic trajectories, and systems theory. They also touch lightly upon several fields of application: mechanics, economics, resources, finance, control engineering. Functional Analysis, Calculus of Variations and Optimal Control is intended to support several different courses at the first-year or second-year graduate level, on functional analysis, on the calculus of variations and optimal control, or on some combination. For this reason, it has been organized with customization in mind. The text also has considerable value as a reference. Besides its advanced results in the calculus of variations and optimal control, its polished presentation of certain other topics (for example convex analysis, measurable selections, metric regularity, and nonsmooth analysis) will be appreciated by researchers in these and related fields.

Tensors, Differential Forms, and Variational Principles

Author: David Lovelock,Hanno Rund

Publisher: Courier Corporation

ISBN: 048613198X

Category: Mathematics

Page: 400

View: 8315

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Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.

Introduction to the Calculus of Variations

Third Edition

Author: Bernard Dacorogna

Publisher: World Scientific Publishing Company

ISBN: 178326554X

Category: Mathematics

Page: 324

View: 7600

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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.

Calculus of Variations

An Introduction to the One-Dimensional Theory with Examples and Exercises

Author: Hansjörg Kielhöfer

Publisher: Springer

ISBN: 3319711237

Category: Mathematics

Page: 227

View: 6609

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This clear and concise textbook provides a rigorous introduction to the calculus of variations, depending on functions of one variable and their first derivatives. It is based on a translation of a German edition of the book Variationsrechnung (Vieweg+Teubner Verlag, 2010), translated and updated by the author himself. Topics include: the Euler-Lagrange equation for one-dimensional variational problems, with and without constraints, as well as an introduction to the direct methods. The book targets students who have a solid background in calculus and linear algebra, not necessarily in functional analysis. Some advanced mathematical tools, possibly not familiar to the reader, are given along with proofs in the appendix. Numerous figures, advanced problems and proofs, examples, and exercises with solutions accompany the book, making it suitable for self-study. The book will be particularly useful for beginning graduate students from the physical, engineering, and mathematical sciences with a rigorous theoretical background.

Calculus of Variations

Author: Jürgen Jost,Xianqing Li-Jost

Publisher: Cambridge University Press

ISBN: 9780521642033

Category: Mathematics

Page: 323

View: 6464

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This textbook on the calculus of variations covers from the basics to the modern aspects of the theory.