Read and Download eBook Full
Author: Hans Sagan
Publisher: Courier Corporation
Published: 2012-04-26
Total Pages: 484
ISBN-13: 048613802X
DOWNLOAD EBOOKProvides 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.
Author: Bernard Dacorogna
Publisher: Imperial College Press
Published: 2009
Total Pages: 241
ISBN-13: 1848163339
DOWNLOAD EBOOKThe calculus of variations is one of the oldest subjects in mathematics, yet is very much alive and is 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, the chapter on regularity has been significantly expanded and 27 new exercises have been added. The book, containing a total of 103 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.
Author: Hansjörg Kielhöfer
Publisher: Springer
Published: 2018-01-25
Total Pages: 242
ISBN-13: 3319711237
DOWNLOAD EBOOKThis 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: L.A. Pars
Publisher: Courier Corporation
Published: 2013-12-10
Total Pages: 358
ISBN-13: 0486165957
DOWNLOAD EBOOKClear, 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: John A. Burns
Publisher: CRC Press
Published: 2013-08-28
Total Pages: 562
ISBN-13: 1466571403
DOWNLOAD EBOOKIntroduction to the Calculus of Variations and Control with Modern Applications provides the fundamental background required to develop rigorous necessary conditions that are the starting points for theoretical and numerical approaches to modern variational calculus and control problems. The book also presents some classical sufficient conditions a
Author: Bruce van Brunt
Publisher: Springer Science & Business Media
Published: 2006-04-18
Total Pages: 295
ISBN-13: 0387216979
DOWNLOAD EBOOKSuitable 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: Frederic Wan
Publisher: CRC Press
Published: 1995-01-01
Total Pages: 660
ISBN-13: 9780412051418
DOWNLOAD EBOOKThis 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.
Author: Charles R. MacCluer
Publisher: Courier Corporation
Published: 2013-05-20
Total Pages: 274
ISBN-13: 0486278301
DOWNLOAD EBOOKFirst 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: Louis Komzsik
Publisher: CRC Press
Published: 2018-09-03
Total Pages: 234
ISBN-13: 1482253607
DOWNLOAD EBOOKThe purpose of the calculus of variations is to find optimal solutions to engineering problems whose optimum may be a certain quantity, shape, or function. Applied Calculus of Variations for Engineers addresses this important mathematical area applicable to many engineering disciplines. Its unique, application-oriented approach sets it apart from the theoretical treatises of most texts, as it is aimed at enhancing the engineer’s understanding of the topic. This Second Edition text: Contains new chapters discussing analytic solutions of variational problems and Lagrange-Hamilton equations of motion in depth Provides new sections detailing the boundary integral and finite element methods and their calculation techniques Includes enlightening new examples, such as the compression of a beam, the optimal cross section of beam under bending force, the solution of Laplace’s equation, and Poisson’s equation with various methods Applied Calculus of Variations for Engineers, Second Edition extends the collection of techniques aiding the engineer in the application of the concepts of the calculus of variations.
Author: Filip Rindler
Publisher: Springer
Published: 2018-06-20
Total Pages: 446
ISBN-13: 3319776371
DOWNLOAD EBOOKThis 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.
