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An Introduction to the Calculus of Variations

An Introduction to the Calculus of Variations

  • Author: Charles Fox
  • Publisher: Courier Corporation
  • ISBN: 9780486654997
  • Category: Mathematics
  • Page: 271
  • View: 3379
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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.

Introduction to the Calculus of Variations

Introduction to the Calculus of Variations

  • Author: Hans Sagan
  • Publisher: Courier Corporation
  • ISBN: 048613802X
  • Category: Mathematics
  • Page: 480
  • View: 9918
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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

Calculus of Variations

  • Author: Izrail Moiseevitch Gelfand,Serge? Vasil?evich Fomin,Richard A. Silverman
  • Publisher: Courier Corporation
  • ISBN: 9780486414485
  • Category: Mathematics
  • Page: 232
  • View: 6153
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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

An Introduction to the Calculus of Variations

  • Author: L.A. Pars
  • Publisher: Courier Corporation
  • ISBN: 0486165957
  • Category: Mathematics
  • Page: 368
  • View: 9745
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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.

Calculus of Variations

Calculus of Variations

With Applications to Physics and Engineering

  • Author: Robert Weinstock
  • Publisher: Courier Corporation
  • ISBN: 9780486630694
  • Category: Mathematics
  • Page: 326
  • View: 5824
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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.

Calculus of Variations

Calculus of Variations

  • Author: Lev D. Elsgolc
  • Publisher: Courier Corporation
  • ISBN: 0486154939
  • Category: Mathematics
  • Page: 192
  • View: 9732
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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

Calculus of Variations

Mechanics, Control and Other Applications

  • Author: Charles R. MacCluer
  • Publisher: Courier Corporation
  • ISBN: 0486278301
  • Category: Mathematics
  • Page: 272
  • View: 9421
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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 And Its Applications, Second Edition

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

  • Author: Frederic Wan
  • Publisher: Routledge
  • ISBN: 1351436511
  • Category: Mathematics
  • Page: 640
  • View: 9391
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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.

Calculus of Variations

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: 2822
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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.

The Variational Principles of Mechanics

The Variational Principles of Mechanics

  • Author: Cornelius Lanczos
  • Publisher: Courier Corporation
  • ISBN: 0486134709
  • Category: Science
  • Page: 464
  • View: 7434
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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.

Introduction to the Calculus of Variations

Introduction to the Calculus of Variations

Third Edition

  • Author: Bernard Dacorogna
  • Publisher: World Scientific Publishing Company
  • ISBN: 178326554X
  • Category: Mathematics
  • Page: 324
  • View: 7183
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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.

The Calculus of Variations

The Calculus of Variations

  • Author: Bruce van Brunt
  • Publisher: Springer Science & Business Media
  • ISBN: 0387216979
  • Category: Mathematics
  • Page: 292
  • View: 6845
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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.

Introduction to Nonlinear Differential and Integral Equations

Introduction to Nonlinear Differential and Integral Equations

  • Author: Harold Thayer Davis
  • Publisher: Courier Corporation
  • ISBN: 9780486609713
  • Category: Mathematics
  • Page: 566
  • View: 7662
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Topics covered include differential equations of the 1st order, the Riccati equation and existence theorems, 2nd order equations, elliptic integrals and functions, nonlinear mechanics, nonlinear integral equations, more. Includes 137 problems.

Functional Analysis, Calculus of Variations and Optimal Control

Functional Analysis, Calculus of Variations and Optimal Control

  • Author: Francis Clarke
  • Publisher: Springer Science & Business Media
  • ISBN: 1447148207
  • Category: Mathematics
  • Page: 591
  • View: 2274
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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.

A Primer on the Calculus of Variations and Optimal Control Theory

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: 3784
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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.

Calculus of Variations

Calculus of Variations

  • Author: Andrew Russell Forsyth
  • Publisher: Cambridge University Press
  • ISBN: 1107640830
  • Category: Mathematics
  • Page: 680
  • View: 3500
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This 1927 book constitutes Scottish mathematician Andrew Russell Forsyth's attempt at a systematic exposition of the calculus of variations.

The Malliavin Calculus

The Malliavin Calculus

  • Author: Denis R. Bell
  • Publisher: Courier Corporation
  • ISBN: 0486152057
  • Category: Mathematics
  • Page: 128
  • View: 5565
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This introductory text presents detailed accounts of the different forms of the theory developed by Stroock and Bismut, discussions of the relationship between these two approaches, and a variety of applications. 1987 edition.

Tensors, Differential Forms, and Variational Principles

Tensors, Differential Forms, and Variational Principles

  • Author: David Lovelock,Hanno Rund
  • Publisher: Courier Corporation
  • ISBN: 048613198X
  • Category: Mathematics
  • Page: 400
  • View: 3335
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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.

Differential Geometry and the Calculus of Variations by Robert Hermann

Differential Geometry and the Calculus of Variations by Robert Hermann

  • Author: N.A
  • Publisher: Elsevier
  • ISBN: 9780080955575
  • Category: Mathematics
  • Page: 322
  • View: 5137
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In this book, we study theoretical and practical aspects of computing methods for mathematical modelling of nonlinear systems. A number of computing techniques are considered, such as methods of operator approximation with any given accuracy; operator interpolation techniques including a non-Lagrange interpolation; methods of system representation subject to constraints associated with concepts of causality, memory and stationarity; methods of system representation with an accuracy that is the best within a given class of models; methods of covariance matrix estimation; methods for low-rank matrix approximations; hybrid methods based on a combination of iterative procedures and best operator approximation; and methods for information compression and filtering under condition that a filter model should satisfy restrictions associated with causality and different types of memory. As a result, the book represents a blend of new methods in general computational analysis, and specific, but also generic, techniques for study of systems theory ant its particular branches, such as optimal filtering and information compression. - Best operator approximation, - Non-Lagrange interpolation, - Generic Karhunen-Loeve transform - Generalised low-rank matrix approximation - Optimal data compression - Optimal nonlinear filtering

A First Course in the Calculus of Variations

A First Course in the Calculus of Variations

  • Author: Mark Kot
  • Publisher: American Mathematical Society
  • ISBN: 1470414953
  • Category: Mathematics
  • Page: 298
  • View: 5369
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This book is intended for a first course in the calculus of variations, at the senior or beginning graduate level. The reader will learn methods for finding functions that maximize or minimize integrals. The text lays out important necessary and sufficient conditions for extrema in historical order, and it illustrates these conditions with numerous worked-out examples from mechanics, optics, geometry, and other fields. The exposition starts with simple integrals containing a single independent variable, a single dependent variable, and a single derivative, subject to weak variations, but steadily moves on to more advanced topics, including multivariate problems, constrained extrema, homogeneous problems, problems with variable endpoints, broken extremals, strong variations, and sufficiency conditions. Numerous line drawings clarify the mathematics. Each chapter ends with recommended readings that introduce the student to the relevant scientific literature and with exercises that consolidate understanding.