Introduction To The Mathematics Of Variation

Author : Taha Sochi
Publisher : Taha Sochi
Page : 246 pages
File Size : 53,6 Mb
Release : 2022-08-16
Category : Mathematics
ISBN : 8210379456XXX

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Introduction to the Mathematics of Variation by Taha Sochi Pdf

This book is about the calculus of variations which is a subject concerned mainly with optimization of functionals. However, because part of it is based on using ordinary calculus in solving optimization problems, "Calculus of Variations" in its original title is modified to become “Mathematics of Variation”. In fact, the book is essentially a collection of solved problems with rather modest theoretical background and hence it is based on the method of "learning by example and practice" which in our view is the most effective way for learning mathematics and overcoming its difficulties. The main merit of the book is its clarity, intuitive structure and rather inclusiveness as it includes the main topics and applications of this subject. The materials in this book require decent background in general mathematics (mostly in single-variable and multi-variable differential and integral calculus). The book can be used as a text or as a reference for an introductory course on this subject as part of an undergraduate curriculum in physics or engineering or applied mathematics. The book can also be used as a source of supplementary pedagogical materials used in tutorial sessions associated with such a course.

Author : Hans Sagan
Publisher : Courier Corporation
Page : 484 pages
File Size : 43,5 Mb
Release : 2012-04-26
Category : Mathematics
ISBN : 9780486138022

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Introduction to the Calculus of Variations by Hans Sagan Pdf

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.

Author : L.A. Pars
Publisher : Courier Corporation
Page : 368 pages
File Size : 51,9 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.

Author : Bernard Dacorogna
Publisher : World Scientific Publishing Company
Page : 241 pages
File Size : 48,7 Mb
Release : 2008-12-10
Category : Mathematics
ISBN : 9781911298496

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Introduction to the Calculus of Variations by Bernard Dacorogna Pdf

The 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. Request Inspection Copy Contents:PreliminariesClassical MethodsDirect Methods: ExistenceDirect Methods: RegularityMinimal SurfacesIsoperimetric InequalitySolutions to the Exercises Readership: Graduate and undergraduate students in analysis and differential equations.

Author : Frederic Wan
Publisher : Routledge
Page : 640 pages
File Size : 52,6 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351436526

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Introduction To The Calculus of Variations And Its Applications by Frederic Wan Pdf

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.

Author : Frederic Wan
Publisher : Routledge
Page : 381 pages
File Size : 51,9 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351436519

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Introduction To The Calculus of Variations And Its Applications by Frederic Wan Pdf

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.

Author : John A. Burns
Publisher : CRC Press
Page : 562 pages
File Size : 50,8 Mb
Release : 2013-08-28
Category : Mathematics
ISBN : 9781466571402

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Introduction to the Calculus of Variations and Control with Modern Applications by John A. Burns Pdf

Introduction 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 : Hansjörg Kielhöfer
Publisher : Springer
Page : 227 pages
File Size : 54,9 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 : Anonim
Publisher : Unknown
Page : 271 pages
File Size : 47,7 Mb
Release : 1950
Category : Calculus of variations
ISBN : LCCN:51003039

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An Introduction to the Calculus of Variations by Anonim Pdf

Author : Agnieszka B Malinowska,Delfim F M Torres
Publisher : World Scientific Publishing Company
Page : 292 pages
File Size : 46,7 Mb
Release : 2012-09-14
Category : Mathematics
ISBN : 9781848169685

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Introduction to the Fractional Calculus of Variations by Agnieszka B Malinowska,Delfim F M Torres Pdf

This invaluable book provides a broad introduction to the fascinating and beautiful subject of Fractional Calculus of Variations (FCV). In 1996, FVC evolved in order to better describe non-conservative systems in mechanics. The inclusion of non-conservatism is extremely important from the point of view of applications. Forces that do not store energy are always present in real systems. They remove energy from the systems and, as a consequence, Noether's conservation laws cease to be valid. However, it is still possible to obtain the validity of Noether's principle using FCV. The new theory provides a more realistic approach to physics, allowing us to consider non-conservative systems in a natural way. The authors prove the necessary Euler–Lagrange conditions and corresponding Noether theorems for several types of fractional variational problems, with and without constraints, using Lagrangian and Hamiltonian formalisms. Sufficient optimality conditions are also obtained under convexity, and Leitmann's direct method is discussed within the framework of FCV. The book is self-contained and unified in presentation. It may be used as an advanced textbook by graduate students and ambitious undergraduates in mathematics and mechanics. It provides an opportunity for an introduction to FCV for experienced researchers. The explanations in the book are detailed, in order to capture the interest of the curious reader, and the book provides the necessary background material required to go further into the subject and explore the rich research literature.

Author : Charles Fox
Publisher : Courier Corporation
Page : 308 pages
File Size : 45,8 Mb
Release : 1987-01-01
Category : Mathematics
ISBN : 0486654990

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An Introduction to the Calculus of Variations by Charles Fox Pdf

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.

Author : Bruce van Brunt
Publisher : Springer Science & Business Media
Page : 295 pages
File Size : 41,9 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 : U. Brechteken-Mandersch
Publisher : CRC Press
Page : 216 pages
File Size : 52,7 Mb
Release : 1991-06-01
Category : Mathematics
ISBN : 0412366908

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Introduction to the Calculus of Variations by U. Brechteken-Mandersch Pdf

This text provides a clear, concise introduction to the calculus of variations. The introductory chapter provides a general sense of the subject through a discussion of several classical and contemporary examples of the subject's use.

Author : George Leitmann
Publisher : Springer Science & Business Media
Page : 313 pages
File Size : 48,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781489903334

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The Calculus of Variations and Optimal Control by George Leitmann Pdf

When the Tyrian princess Dido landed on the North African shore of the Mediterranean sea she was welcomed by a local chieftain. He offered her all the land that she could enclose between the shoreline and a rope of knotted cowhide. While the legend does not tell us, we may assume that Princess Dido arrived at the correct solution by stretching the rope into the shape of a circular arc and thereby maximized the area of the land upon which she was to found Carthage. This story of the founding of Carthage is apocryphal. Nonetheless it is probably the first account of a problem of the kind that inspired an entire mathematical discipline, the calculus of variations and its extensions such as the theory of optimal control. This book is intended to present an introductory treatment of the calculus of variations in Part I and of optimal control theory in Part II. The discussion in Part I is restricted to the simplest problem of the calculus of variations. The topic is entirely classical; all of the basic theory had been developed before the turn of the century. Consequently the material comes from many sources; however, those most useful to me have been the books of Oskar Bolza and of George M. Ewing. Part II is devoted to the elementary aspects of the modern extension of the calculus of variations, the theory of optimal control of dynamical systems.

Author : I. M. Gelfand,S. V. Fomin
Publisher : Courier Corporation
Page : 240 pages
File Size : 40,5 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.