Introduction To The Mathematics Of Variation

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Introduction to the Mathematics of Variation

Author : Taha Sochi
Publisher : Taha Sochi
ISBN 13 :
Total Pages : 246 pages
Book Rating : 4./5 ( download)

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Book Synopsis Introduction to the Mathematics of Variation by : Taha Sochi

Download or read book Introduction to the Mathematics of Variation written by Taha Sochi and published by Taha Sochi. This book was released on 2022-08-16 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to the Calculus of Variations

Author : Hans Sagan
Publisher : Courier Corporation
ISBN 13 : 048613802X
Total Pages : 484 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Introduction to the Calculus of Variations by : Hans Sagan

Download or read book Introduction to the Calculus of Variations written by Hans Sagan and published by Courier Corporation. This book was released on 2012-04-26 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to the Calculus of Variations

Author : L.A. Pars
Publisher : Courier Corporation
ISBN 13 : 0486165957
Total Pages : 358 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis An Introduction to the Calculus of Variations by : L.A. Pars

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 358 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.

Calculus of Variations

Author : Hansjörg Kielhöfer
Publisher : Springer
ISBN 13 : 3319711237
Total Pages : 242 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Calculus of Variations by : Hansjörg Kielhöfer

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 242 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.

Introduction To The Calculus of Variations And Its Applications

Author : Frederic Wan
Publisher : Routledge
ISBN 13 : 135143652X
Total Pages : 640 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Introduction To The Calculus of Variations And Its Applications by : Frederic Wan

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 640 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.

An Introduction to the Calculus of Variations

Author :
Publisher :
ISBN 13 :
Total Pages : 271 pages
Book Rating : 4.:/5 (51 download)

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Book Synopsis An Introduction to the Calculus of Variations by :

Download or read book An Introduction to the Calculus of Variations written by and published by . This book was released on 1950 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Calculus of Variations

Author : I. M. Gelfand
Publisher : Courier Corporation
ISBN 13 : 0486135012
Total Pages : 260 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Calculus of Variations by : I. M. Gelfand

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 260 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.

A First Course in the Calculus of Variations

Author : Mark Kot
Publisher : American Mathematical Society
ISBN 13 : 1470414953
Total Pages : 311 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis A First Course in the Calculus of Variations by : Mark Kot

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.

The Calculus of Variations

Author : Bruce van Brunt
Publisher : Springer Science & Business Media
ISBN 13 : 0387216979
Total Pages : 295 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis The Calculus of Variations by : Bruce van Brunt

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.

Classical Mechanics with Calculus of Variations and Optimal Control

Author : Mark Levi
Publisher : American Mathematical Soc.
ISBN 13 : 0821891383
Total Pages : 322 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Classical Mechanics with Calculus of Variations and Optimal Control by : Mark Levi

Download or read book Classical Mechanics with Calculus of Variations and Optimal Control written by Mark Levi and published by American Mathematical Soc.. This book was released on 2014-03-07 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an intuitively motivated presentation of many topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are: an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the "tennis racket paradox"; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between the dynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin's Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theorems. With minimal prerequisites consisting of basic calculus and basic undergraduate physics, this book is suitable for courses from an undergraduate to a beginning graduate level, and for a mixed audience of mathematics, physics and engineering students. Much of the enjoyment of the subject lies in solving almost 200 problems in this book.

An Introduction to the Calculus of Variations

Author : Charles Fox
Publisher : Courier Corporation
ISBN 13 : 9780486654997
Total Pages : 308 pages
Book Rating : 4.6/5 (549 download)

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Book Synopsis An Introduction to the Calculus of Variations by : Charles Fox

Download or read book An Introduction to the Calculus of Variations written by Charles Fox and published by Courier Corporation. This book was released on 1987-01-01 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to the Calculus of Variations and Control with Modern Applications

Author : John A. Burns
Publisher : CRC Press
ISBN 13 : 1466571403
Total Pages : 562 pages
Book Rating : 4.4/5 (665 download)

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

Download or read book Introduction to the Calculus of Variations and Control with Modern Applications written by John A. Burns and published by CRC Press. This book was released on 2013-08-28 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Calculus of Variations

Author : Charles R. MacCluer
Publisher : Courier Corporation
ISBN 13 : 0486278301
Total Pages : 274 pages
Book Rating : 4.4/5 (862 download)

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Book Synopsis Calculus of Variations by : Charles R. MacCluer

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 274 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.

A Modern Theory of Random Variation

Author : Patrick Muldowney
Publisher : John Wiley & Sons
ISBN 13 : 1118345940
Total Pages : 493 pages
Book Rating : 4.1/5 (183 download)

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Book Synopsis A Modern Theory of Random Variation by : Patrick Muldowney

Download or read book A Modern Theory of Random Variation written by Patrick Muldowney and published by John Wiley & Sons. This book was released on 2013-04-26 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: A ground-breaking and practical treatment of probability and stochastic processes A Modern Theory of Random Variation is a new and radical re-formulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering, and quantum mechanics. Setting aside the classical theory of probability measure spaces, the book utilizes a mathematically rigorous version of the theory of random variation that bases itself exclusively on finitely additive probability distribution functions. In place of twentieth century Lebesgue integration and measure theory, the author uses the simpler concept of Riemann sums, and the non-absolute Riemann-type integration of Henstock. Readers are supplied with an accessible approach to standard elements of probability theory such as the central limmit theorem and Brownian motion as well as remarkable, new results on Feynman diagrams and stochastic integrals. Throughout the book, detailed numerical demonstrations accompany the discussions of abstract mathematical theory, from the simplest elements of the subject to the most complex. In addition, an array of numerical examples and vivid illustrations showcase how the presented methods and applications can be undertaken at various levels of complexity. A Modern Theory of Random Variation is a suitable book for courses on mathematical analysis, probability theory, and mathematical finance at the upper-undergraduate and graduate levels. The book is also an indispensible resource for researchers and practitioners who are seeking new concepts, techniques and methodologies in data analysis, numerical calculation, and financial asset valuation. Patrick Muldowney, PhD, served as lecturer at the Magee Business School of the UNiversity of Ulster for over twenty years. Dr. Muldowney has published extensively in his areas of research, including integration theory, financial mathematics, and random variation.

Functional Analysis, Calculus of Variations and Optimal Control

Author : Francis Clarke
Publisher : Springer Science & Business Media
ISBN 13 : 1447148207
Total Pages : 589 pages
Book Rating : 4.4/5 (471 download)

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Book Synopsis Functional Analysis, Calculus of Variations and Optimal Control by : Francis Clarke

Download or read book Functional Analysis, Calculus of Variations and Optimal Control written by Francis Clarke and published by Springer Science & Business Media. This book was released on 2013-02-06 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction To The Calculus Of Variations (3rd Edition)

Author : Bernard Dacorogna
Publisher : World Scientific Publishing Company
ISBN 13 : 178326554X
Total Pages : 322 pages
Book Rating : 4.7/5 (832 download)

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Book Synopsis Introduction To The Calculus Of Variations (3rd Edition) by : Bernard Dacorogna

Download or read book Introduction To The Calculus Of Variations (3rd Edition) written by Bernard Dacorogna and published by World Scientific Publishing Company. This book was released on 2014-08-13 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: The calculus of variations is one of the oldest subjects in mathematics, and it is very much alive and 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, several new exercises have been added. The book, containing a total of 119 exercises with detailed solutions, is well designed for a course at both undergraduate and graduate levels.

Calculus of Variations and Optimal Control Theory

Author : Daniel Liberzon
Publisher : Princeton University Press
ISBN 13 : 0691151873
Total Pages : 255 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Calculus of Variations and Optimal Control Theory by : Daniel Liberzon

Download or read book Calculus of Variations and Optimal Control Theory written by Daniel Liberzon and published by Princeton University Press. This book was released on 2012 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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