Calculus Of Variations Ii

Author : Mariano Giaquinta
Publisher : Springer Science & Business Media
ISBN 13 : 3662032783
Total Pages : 498 pages
Book Rating : 4.87/5 ( download)

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Download or read book Calculus of Variations I written by Mariano Giaquinta and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Filip Rindler
Publisher : Springer
ISBN 13 : 3319776371
Total Pages : 444 pages
Book Rating : 4.78/5 ( download)

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Download or read book Calculus of Variations written by Filip Rindler and published by Springer. This book was released on 2018-06-20 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Charles R. MacCluer
Publisher : Courier Corporation
ISBN 13 : 0486278301
Total Pages : 272 pages
Book Rating : 4.08/5 ( download)

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Download or read book Calculus of Variations written by Charles R. MacCluer and published by Courier Corporation. This book was released on 2013-05-20 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Mark Kot
Publisher : American Mathematical Society
ISBN 13 : 1470414953
Total Pages : 311 pages
Book Rating : 4.55/5 ( download)

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Download or read book A First Course in the Calculus of Variations written by Mark Kot and published by American Mathematical Society. This book was released on 2014-10-06 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Hansjörg Kielhöfer
Publisher : Springer
ISBN 13 : 3319711237
Total Pages : 227 pages
Book Rating : 4.32/5 ( download)

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Download or read book Calculus of Variations written by Hansjörg Kielhöfer and published by Springer. This book was released on 2018-01-25 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : I. M. Gelfand
Publisher : Courier Corporation
ISBN 13 : 0486135012
Total Pages : 240 pages
Book Rating : 4.14/5 ( download)

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Download or read book Calculus of Variations written by I. M. Gelfand and published by Courier Corporation. This book was released on 2012-04-26 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Bruce van Brunt
Publisher : Springer Science & Business Media
ISBN 13 : 0387216979
Total Pages : 295 pages
Book Rating : 4.73/5 ( download)

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Download or read book The Calculus of Variations written by Bruce van Brunt and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : L.A. Pars
Publisher : Courier Corporation
ISBN 13 : 0486165957
Total Pages : 368 pages
Book Rating : 4.50/5 ( download)

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Download or read book An Introduction to the Calculus of Variations written by L.A. Pars and published by Courier Corporation. This book was released on 2013-12-10 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Irene Fonseca
Publisher : Springer Science & Business Media
ISBN 13 : 0387690069
Total Pages : 602 pages
Book Rating : 4.63/5 ( download)

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Download or read book Modern Methods in the Calculus of Variations written by Irene Fonseca and published by Springer Science & Business Media. This book was released on 2007-08-22 with total page 602 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of two books on methods and techniques in the calculus of variations. Contemporary arguments are used throughout the text to streamline and present in a unified way classical results, and to provide novel contributions at the forefront of the theory. This book addresses fundamental questions related to lower semicontinuity and relaxation of functionals within the unconstrained setting, mainly in L^p spaces. It prepares the ground for the second volume where the variational treatment of functionals involving fields and their derivatives will be undertaken within the framework of Sobolev spaces. This book is self-contained. All the statements are fully justified and proved, with the exception of basic results in measure theory, which may be found in any good textbook on the subject. It also contains several exercises. Therefore,it may be used both as a graduate textbook as well as a reference text for researchers in the field. Irene Fonseca is the Mellon College of Science Professor of Mathematics and is currently the Director of the Center for Nonlinear Analysis in the Department of Mathematical Sciences at Carnegie Mellon University. Her research interests lie in the areas of continuum mechanics, calculus of variations, geometric measure theory and partial differential equations. Giovanni Leoni is also a professor in the Department of Mathematical Sciences at Carnegie Mellon University. He focuses his research on calculus of variations, partial differential equations and geometric measure theory with special emphasis on applications to problems in continuum mechanics and in materials science.

Author : Frederic Wan
Publisher : Routledge
ISBN 13 : 1351436511
Total Pages : 381 pages
Book Rating : 4.19/5 ( download)

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Download or read book Introduction To The Calculus of Variations And Its Applications written by Frederic Wan and published by Routledge. This book was released on 2017-10-19 with total page 381 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.