**Author**: Mariano Giaquinta

**Publisher:**Springer Science & Business Media

**ISBN:**9783540506256

**Size**: 34.96 MB

**Format:**PDF, Docs

**Category :**Mathematics

**Languages :**en

**Pages :**474

**View:**1922

**Book Description:**This two-volume treatise is a standard reference in the field. It pays special attention to the historical aspects and the origins partly in applied problems—such as those of geometric optics—of parts of the theory. It contains an introduction to each chapter, section, and subsection and an overview of the relevant literature in the footnotes and bibliography. It also includes an index of the examples used throughout the book.

## Calculus Of Variations

**Author**: Hansjörg Kielhöfer

**Publisher:**Springer

**ISBN:**3319711237

**Size**: 25.50 MB

**Format:**PDF, Mobi

**Category :**Mathematics

**Languages :**en

**Pages :**227

**View:**5190

**Book Description:**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.

## Introduction To The Calculus Of Variations

**Author**: Hans Sagan

**Publisher:**Courier Corporation

**ISBN:**048613802X

**Size**: 31.39 MB

**Format:**PDF, ePub, Mobi

**Category :**Mathematics

**Languages :**en

**Pages :**480

**View:**4687

**Book Description:**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**: I. M. Gelfand

**Publisher:**Courier Corporation

**ISBN:**0486135012

**Size**: 22.90 MB

**Format:**PDF

**Category :**Mathematics

**Languages :**en

**Pages :**240

**View:**6357

**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.

## Calculus Of Variations

**Author**: Robert Weinstock

**Publisher:**Courier Corporation

**ISBN:**0486141063

**Size**: 75.27 MB

**Format:**PDF, Docs

**Category :**Mathematics

**Languages :**en

**Pages :**352

**View:**4874

**Book Description:**Basic introduction covering isoperimetric problems, theory of elasticity, quantum mechanics, electrostatics, geometrical optics, particle dynamics, more. Exercises throughout. "A very useful book." — J. L. Synge, American Mathematical Monthly.

## An Introduction To The Calculus Of Variations

**Author**: Charles Fox

**Publisher:**Courier Corporation

**ISBN:**9780486654997

**Size**: 14.79 MB

**Format:**PDF, Mobi

**Category :**Mathematics

**Languages :**en

**Pages :**271

**View:**3250

**Book Description:**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

**Author**: Filip Rindler

**Publisher:**Springer

**ISBN:**3319776371

**Size**: 58.59 MB

**Format:**PDF, ePub

**Category :**Mathematics

**Languages :**en

**Pages :**444

**View:**1777

**Book Description:**This textbook provides a comprehensive introduction to the classical and modern calculus of variations, serving as a useful reference to advanced undergraduate and graduate students as well as researchers in the field. Starting from ten motivational examples, the book begins with the most important aspects of the classical theory, including the Direct Method, the Euler-Lagrange equation, Lagrange multipliers, Noether’s Theorem and some regularity theory. Based on the efficient Young measure approach, the author then discusses the vectorial theory of integral functionals, including quasiconvexity, polyconvexity, and relaxation. In the second part, more recent material such as rigidity in differential inclusions, microstructure, convex integration, singularities in measures, functionals defined on functions of bounded variation (BV), and Γ-convergence for phase transitions and homogenization are explored. While predominantly designed as a textbook for lecture courses on the calculus of variations, this book can also serve as the basis for a reading seminar or as a companion for self-study. The reader is assumed to be familiar with basic vector analysis, functional analysis, Sobolev spaces, and measure theory, though most of the preliminaries are also recalled in the appendix.

## Calculus Of Variations

**Author**: Charles R. MacCluer

**Publisher:**Courier Corporation

**ISBN:**0486278301

**Size**: 55.19 MB

**Format:**PDF, Kindle

**Category :**Mathematics

**Languages :**en

**Pages :**272

**View:**5338

**Book Description:**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.

## Calculus Of Variations

**Author**: Jurgen Jost

**Publisher:**Cambridge University Press

**ISBN:**9780521642033

**Size**: 10.34 MB

**Format:**PDF, Docs

**Category :**Mathematics

**Languages :**en

**Pages :**323

**View:**6977

**Book Description:**Publisher Description

## A First Course In The Calculus Of Variations

**Author**: Mark Kot

**Publisher:**American Mathematical Society

**ISBN:**1470414953

**Size**: 45.91 MB

**Format:**PDF, ePub

**Category :**Mathematics

**Languages :**en

**Pages :**298

**View:**204

**Book Description:**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.