The Calculus Of Variations And Functional Analysis

Author : Francis Clarke
Publisher : Springer Science & Business Media
Page : 589 pages
File Size : 53,8 Mb
Release : 2013-02-06
Category : Mathematics
ISBN : 9781447148203

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Functional Analysis, Calculus of Variations and Optimal Control by Francis Clarke Pdf

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.

Author : L. P. Lebedev,Michael J. Cloud
Publisher : World Scientific
Page : 435 pages
File Size : 49,9 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812794994

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The Calculus of Variations and Functional Analysis by L. P. Lebedev,Michael J. Cloud Pdf

This volume is aimed at those who are concerned about Chinese medicine - how it works, what its current state is and, most important, how to make full use of it. The audience therefore includes clinicians who want to serve their patients better and patients who are eager to supplement their own conventional treatment. The authors of the book belong to three different fields, modern medicine, Chinese medicine and pharmacology. They provide information from their areas of expertise and concern, attempting to make it comprehensive for users. The approach is macroscopic and philosophical; readers convinced of the philosophy are to seek specific assistance.

Author : L. P. Lebedev,Michael J. Cloud
Publisher : World Scientific
Page : 435 pages
File Size : 53,8 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812385819

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The Calculus of Variations and Functional Analysis by L. P. Lebedev,Michael J. Cloud Pdf

In this book, Sam helps his goose sisters fly to safety to looking for familiar landforms.

Author : Lebedev Leonid P,Cloud Michael J
Publisher : World Scientific
Page : 436 pages
File Size : 54,9 Mb
Release : 2003-12-23
Category : Technology & Engineering
ISBN : 9789814485173

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Calculus Of Variations And Functional Analysis, The: With Optimal Control And Applications In Mechanics by Lebedev Leonid P,Cloud Michael J Pdf

This is a book for those who want to understand the main ideas in the theory of optimal problems. It provides a good introduction to classical topics (under the heading of “the calculus of variations”) and more modern topics (under the heading of “optimal control”). It employs the language and terminology of functional analysis to discuss and justify the setup of problems that are of great importance in applications. The book is concise and self-contained, and should be suitable for readers with a standard undergraduate background in engineering mathematics.

Author : L. P. Lebedev,Michael J. Cloud,Victor A. Eremeyev
Publisher : World Scientific
Page : 500 pages
File Size : 43,6 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814390477

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Advanced Engineering Analysis by L. P. Lebedev,Michael J. Cloud,Victor A. Eremeyev Pdf

Advanced Engineering Analysis: The Calculus of Variations and Functional Analysis with Applications in Mechanics Advanced Engineering Analysis is a textbook on modern engineering analysis, covering the calculus of variations, functional analysis, and control theory, as well as applications of these disciplines to mechanics. The book offers a brief and concise, yet complete explanation of essential theory and applications. It contains exercises with hints and solutions, ideal for self-study. Book jacket.

Author : Filip Rindler
Publisher : Springer
Page : 444 pages
File Size : 54,7 Mb
Release : 2018-06-20
Category : Mathematics
ISBN : 9783319776378

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Calculus of Variations by Filip Rindler Pdf

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 : Bruce van Brunt
Publisher : Springer Science & Business Media
Page : 292 pages
File Size : 45,9 Mb
Release : 2006-04-18
Category : Mathematics
ISBN : 9780387216973

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The Calculus of Variations by Bruce van Brunt Pdf

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 : I. M. Gelfand,S. V. Fomin
Publisher : Courier Corporation
Page : 240 pages
File Size : 55,7 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486135014

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Calculus of Variations by I. M. Gelfand,S. V. Fomin Pdf

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 : Mike Mesterton-Gibbons
Publisher : American Mathematical Soc.
Page : 274 pages
File Size : 51,5 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821847725

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A Primer on the Calculus of Variations and Optimal Control Theory by Mike Mesterton-Gibbons Pdf

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.

Author : Springer
Publisher : Unknown
Page : 608 pages
File Size : 50,6 Mb
Release : 2013-02-05
Category : Electronic
ISBN : 1447148215

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Functional Analysis, Calculus of Variations and Optimal Control by Springer Pdf

Author : Haim Brezis
Publisher : Springer Science & Business Media
Page : 600 pages
File Size : 55,6 Mb
Release : 2010-11-02
Category : Mathematics
ISBN : 9780387709147

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Functional Analysis, Sobolev Spaces and Partial Differential Equations by Haim Brezis Pdf

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover both of these closely connected topics. Since the French book was first published, it has been translated into Spanish, Italian, Japanese, Korean, Romanian, Greek and Chinese. The English edition makes a welcome addition to this list.

Author : Hansjörg Kielhöfer
Publisher : Springer
Page : 227 pages
File Size : 41,9 Mb
Release : 2018-01-25
Category : Mathematics
ISBN : 9783319711232

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Calculus of Variations by Hansjörg Kielhöfer Pdf

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 : Filippo Santambrogio
Publisher : Springer Nature
Page : 354 pages
File Size : 42,6 Mb
Release : 2024-01-18
Category : Mathematics
ISBN : 9783031450365

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A Course in the Calculus of Variations by Filippo Santambrogio Pdf

This book provides an introduction to the broad topic of the calculus of variations. It addresses the most natural questions on variational problems and the mathematical complexities they present. Beginning with the scientific modeling that motivates the subject, the book then tackles mathematical questions such as the existence and uniqueness of solutions, their characterization in terms of partial differential equations, and their regularity. It includes both classical and recent results on one-dimensional variational problems, as well as the adaptation to the multi-dimensional case. Here, convexity plays an important role in establishing semi-continuity results and connections with techniques from optimization, and convex duality is even used to produce regularity results. This is then followed by the more classical Hölder regularity theory for elliptic PDEs and some geometric variational problems on sets, including the isoperimetric inequality and the Steiner tree problem. The book concludes with a chapter on the limits of sequences of variational problems, expressed in terms of Γ-convergence. While primarily designed for master's-level and advanced courses, this textbook, based on its author's instructional experience, also offers original insights that may be of interest to PhD students and researchers. A foundational understanding of measure theory and functional analysis is required, but all the essential concepts are reiterated throughout the book using special memo-boxes.

Author : Daniel Liberzon
Publisher : Princeton University Press
Page : 255 pages
File Size : 43,5 Mb
Release : 2012
Category : Mathematics
ISBN : 9780691151878

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Calculus of Variations and Optimal Control Theory by Daniel Liberzon Pdf

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

Author : L.A. Pars
Publisher : Courier Corporation
Page : 368 pages
File Size : 47,8 Mb
Release : 2013-12-10
Category : Mathematics
ISBN : 9780486165950

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An Introduction to the Calculus of Variations by L.A. Pars Pdf

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.