Calculus of Variations

With Applications to Physics and Engineering

Author: Robert Weinstock

Publisher: Courier Corporation

ISBN: 9780486630694

Category: Mathematics

Page: 326

View: 5074

This text is basically divided into two parts. Chapters 1–4 include background material, basic theorems and isoperimetric problems. Chapters 5–12 are devoted to applications, geometrical optics, particle dynamics, the theory of elasticity, electrostatics, quantum mechanics, and other topics. Exercises in each chapter. 1952 edition.
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Calculus of Variations, Applications and Computations

Author: C Bandle,Michel Chipot,J Saint Jean Paulin,Josef Bemelmans,I Shafrir

Publisher: CRC Press

ISBN: 9780582239623

Category: Mathematics

Page: 296

View: 6792

This research presents some important domains of partial differential equations and applied mathematics including calculus of variations, control theory, modelling, numerical analysis and various applications in physics, mechanics and engineering. These topics are now part of many areas of science and have experienced tremendous development during the last decades.
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Calculus of Variations with Applications

Author: George McNaught Ewing

Publisher: Courier Corporation

ISBN: 0486648567

Category: Mathematics

Page: 343

View: 2968

Applications-oriented introduction to variational theory develops insight and promotes understanding of specialized books and research papers. Suitable for advanced undergraduate and graduate students as a primary or supplementary text. 1969 edition.
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CALCULUS OF VARIATIONS WITH APPLICATIONS

Author: A. S. GUPTA

Publisher: PHI Learning Pvt. Ltd.

ISBN: 8120311205

Category: Mathematics

Page: 256

View: 3666

Calculus of variations is one of the most important mathematical tools of great scientific significance used by scientistis and engineers. Unfortunately, a few books that are available are written at a level which is not easily comprehensible for postgraduate students.This book, written by a highly respected academic, presents the materials in a lucid manner so as to be within the easy grasp of the students with some background in calculus, differential equations and functional analysis. The aim is to give a thorough and systematic analysis of various aspects of calculus of variations.
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Real Analysis and Applications

Including Fourier Series and the Calculus of Variations

Author: Frank Morgan

Publisher: American Mathematical Soc.

ISBN: 9780821886113

Category: Mathematics

Page: 197

View: 8498

Real Analysis and Applications starts with a streamlined, but complete, approach to real analysis. It finishes with a wide variety of applications in Fourier series and the calculus of variations, including minimal surfaces, physics, economics, Riemannian geometry, and general relativity. The basic theory includes all the standard topics: limits of sequences, topology, compactness, the Cantor set and fractals, calculus with the Riemann integral, a chapter on the Lebesgue theory, sequences of functions, infinite series, and the exponential and Gamma functions. The applications conclude with a computation of the relativistic precession of Mercury's orbit, which Einstein called "convincing proof of the correctness of the theory [of General Relativity]." The text not only provides clear, logical proofs, but also shows the student how to derive them. The excellent exercises come with select solutions in the back. This is a text that makes it possible to do the full theory and significant applications in one semester. Frank Morgan is the author of six books and over one hundred articles on mathematics. He is an inaugural recipient of the Mathematical Association of America's national Haimo award for excellence in teaching. With this applied version of his Real Analysis text, Morgan brings his famous direct style to the growing numbers of potential mathematics majors who want to see applications along with the theory. The book is suitable for undergraduates interested in real analysis.
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Calculus of Variations

Author: I. M. Gelfand,S. V. Fomin

Publisher: Courier Corporation

ISBN: 0486135012

Category: Mathematics

Page: 240

View: 962

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.
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The Calculus of Variations

Author: Bruce van Brunt

Publisher: Springer Science & Business Media

ISBN: 0387216979

Category: Mathematics

Page: 292

View: 2903

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.
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Lecture Notes on Calculus of Variations

Author: Kung Ching Chang

Publisher: World Scientific

ISBN: 981314470X

Category: Mathematics

Page: 324

View: 2885

This is based on the course "Calculus of Variations" taught at Peking University from 2006 to 2010 for advanced undergraduate to graduate students majoring in mathematics. The book contains 20 lectures covering both the theoretical background material as well as an abundant collection of applications. Lectures 1–8 focus on the classical theory of calculus of variations. Lectures 9–14 introduce direct methods along with their theoretical foundations. Lectures 15–20 showcase a broad collection of applications. The book offers a panoramic view of the very important topic on calculus of variations. This is a valuable resource not only to mathematicians, but also to those students in engineering, economics, and management, etc.
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Calculus of Variations and Differential Equations

Author: Alexander Ioffe,Simeon Reich,I Shafrir

Publisher: CRC Press

ISBN: 9780849306051

Category: Mathematics

Page: 272

View: 4603

The calculus of variations is a classical area of mathematical analysis-300 years old-yet its myriad applications in science and technology continue to hold great interest and keep it an active area of research. These two volumes contain the refereed proceedings of the international conference on Calculus of Variations and Related Topics held at the Technion-Israel Institute of Technology in March 1998. The conference commemorated 300 years of work in the field and brought together many of its leading experts. The papers in the first volume focus on critical point theory and differential equations. The other volume deals with variational aspects of optimal control. Together they provide a unique opportunity to review the state-of-the-art of the calculus of variations, as presented by an international panel of masters in the field.
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Nonstandard Methods in the Calculus of Variations

Author: Curtis Tuckey

Publisher: CRC Press

ISBN: 9780582231801

Category: Mathematics

Page: 112

View: 7208

This monograph is unique in its treatment of the application of methods of nonstandard analysis to the theory of curves in the calculus of variations. It will be of particular value to researchers in the calculus of variations and optimal control theory.
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The Calculus of Variations and Functional Analysis

With Optimal Control and Applications in Mechanics

Author: L. P. Lebedev,Michael J. Cloud

Publisher: World Scientific

ISBN: 9812794999

Category: Mathematics

Page: 436

View: 7199

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.
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Variational Methods

Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Third Edition

Author: Michael Struwe

Publisher: Springer Science & Business Media

ISBN: 9783540664796

Category: Mathematics

Page: 274

View: 2314

Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Rad??. The book gives a concise introduction to variational methods and presents an overview of areas of current research in the field. The third edition gives a survey on new developments in the field. References have been updated and a small number of mistakes have been rectified.
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Calculus of Variations

Author: L. E. Elsgolc

Publisher: Elsevier

ISBN: 1483137562

Category: Mathematics

Page: 178

View: 4998

Calculus of Variations aims to provide an understanding of the basic notions and standard methods of the calculus of variations, including the direct methods of solution of the variational problems. The wide variety of applications of variational methods to different fields of mechanics and technology has made it essential for engineers to learn the fundamentals of the calculus of variations. The book begins with a discussion of the method of variation in problems with fixed boundaries. Subsequent chapters cover variational problems with movable boundaries and some other problems; sufficiency conditions for an extremum; variational problems of constrained extrema; and direct methods of solving variational problems. Each chapter is illustrated by a large number of problems some of which are taken from existing textbooks. The solutions to the problems in each chapter are provided at the end of the book.
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Introduction to the Calculus of Variations and Control with Modern Applications

Author: John A. Burns

Publisher: CRC Press

ISBN: 146657139X

Category: Mathematics

Page: 562

View: 8235

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 and discusses the importance of distinguishing between the necessary and sufficient conditions. In the first part of the text, the author develops the calculus of variations and provides complete proofs of the main results. He explains how the ideas behind the proofs are essential to the development of modern optimization and control theory. Focusing on optimal control problems, the second part shows how optimal control is a natural extension of the classical calculus of variations to more complex problems. By emphasizing the basic ideas and their mathematical development, this book gives you the foundation to use these mathematical tools to then tackle new problems. The text moves from simple to more complex problems, allowing you to see how the fundamental theory can be modified to address more difficult and advanced challenges. This approach helps you understand how to deal with future problems and applications in a realistic work environment.
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A Course in Mathematical Analysis Volume 3

Variation of Solutions; Partial Differential Equations of the Second Order; Integral Equations; Calculus of Variations

Author: Edouard Goursat,Howard G. Bergmann

Publisher: Courier Corporation

ISBN: 0486446522

Category: Mathematics

Page: 752

View: 9306

Classic three-volume study. Volume 1 covers applications to geometry, expansion in series, definite integrals, and derivatives and differentials. Volume 2 explores functions of a complex variable and differential equations. Volume 3 surveys variations of solutions and partial differential equations of the second order and integral equations and calculus of variations.
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Calculus of Variations and Partial Differential Equations

Topics on Geometrical Evolution Problems and Degree Theory

Author: Luigi Ambrosio,Norman Dancer

Publisher: Springer Science & Business Media

ISBN: 9783540648031

Category: Mathematics

Page: 348

View: 5842

At the summer school in Pisa in September 1996, Luigi Ambrosio and Norman Dancer each gave a course on the geometric problem of evolution of a surface by mean curvature, and degree theory with applications to PDEs respectively. This self-contained presentation accessible to PhD students bridged the gap between standard courses and advanced research on these topics. The resulting book is divided accordingly into 2 parts, and neatly illustrates the 2-way interaction of problems and methods. Each of the courses is augmented and complemented by additional short chapters by other authors describing current research problems and results.
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Calculus of Variations and Optimal Control

Technion 1998

Author: Alexander Ioffe,Simeon Reich,I Shafrir

Publisher: CRC Press

ISBN: 9781584880240

Category: Mathematics

Page: 280

View: 454

The calculus of variations is a classical area of mathematical analysis-300 years old-yet its myriad applications in science and technology continue to hold great interest and keep it an active area of research. These two volumes contain the refereed proceedings of the international conference on Calculus of Variations and Related Topics held at the Technion-Israel Institute of Technology in March 1998. The conference commemorated 300 years of work in the field and brought together many of its leading experts. The papers in the first volume focus on critical point theory and differential equations. The other volume deals with variational aspects of optimal control. Together they provide a unique opportunity to review the state-of-the-art of the calculus of variations, as presented by an international panel of masters in the field.
Release