The Calculus Direct

This book takes no prior knowledge of mathematics for granted as it takes the student slowly and surely from addition all the way to a basic understanding of the calculus in the least painful and most efficient path possible.

Author: John Weiss

Publisher: CreateSpace

ISBN: 1452854912

Category: Mathematics

Page: 98

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This book takes no prior knowledge of mathematics for granted as it takes the student slowly and surely from addition all the way to a basic understanding of the calculus in the least painful and most efficient path possible. The calculus is not a hard subject, and this book proves this through an easy to read, obvious approach spanning only 100 pages. This book is written with the following type of student in mind; the non-traditional student returning to college after a long break, a notoriously weak student in math who just needs to get past calculus to obtain a degree, and the garage tinkerer who wishes to understand a little more about the technical subjects. This book is meant to address the many fundamental thought-blocks that keep the average 'mathaphobe' (or just an interested person who doesn't have the time to enroll in a course) from excelling in mathematics in a clear and concise manner. It is my sincerest hope that this book helps you with your needs.

Direct Methods in the Calculus of Variations

This book is developed for the study of vectorial problems in the calculus of variations. The subject is a very active one and almost half of the book consists of new material.

Author: Bernard Dacorogna

Publisher: Springer

ISBN: 1441922598

Category: Mathematics

Page: 622

View: 964

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This book is developed for the study of vectorial problems in the calculus of variations. The subject is a very active one and almost half of the book consists of new material. This is a new edition of the earlier book published in 1989 and it is suitable for graduate students. The book has been updated with some new material and examples added. Applications are included.

Direct Methods in the Calculus of Variations

This book is developed for the study of vectorial problems in the calculus of variations. The subject is a very active one and almost half of the book consists of new material.

Author: Bernard Dacorogna

Publisher: Springer Science & Business Media

ISBN: 9780387552491

Category: Mathematics

Page: 622

View: 452

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This book is developed for the study of vectorial problems in the calculus of variations. The subject is a very active one and almost half of the book consists of new material. This is a new edition of the earlier book published in 1989 and it is suitable for graduate students. The book has been updated with some new material and examples added. Applications are included.

Direct Methods in the Calculus of Variations

This book provides a comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order.

Author: Enrico Giusti

Publisher: World Scientific

ISBN: 9789812380432

Category: Mathematics

Page: 403

View: 936

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This book provides a comprehensive discussion on the existence and regularity of minima of regular integrals in the calculus of variations and of solutions to elliptic partial differential equations and systems of the second order. While direct methods for the existence of solutions are well known and have been widely used in the last century, the regularity of the minima was always obtained by means of the Euler equation as a part of the general theory of partial differential equations. In this book, using the notion of the quasi-minimum introduced by Giaquinta and the author, the direct methods are extended to the regularity of the minima of functionals in the calculus of variations, and of solutions to partial differential equations. This unified treatment offers a substantial economy in the assumptions, and permits a deeper understanding of the nature of the regularity and singularities of the solutions. The book is essentially self-contained, and requires only a general knowledge of the elements of Lebesgue integration theory.

Introduction to the Calculus of Variations

12 Introduction to the direct methods of the calculus of variations Only in relatively few cases is the Euler differential equation easy to solve . If an exact solution to the Euler differential equation with the prescribed boundary ...

Author: U. Brechteken-Mandersch

Publisher: CRC Press

ISBN: 0412366908

Category: Mathematics

Page: 208

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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.

Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems AM 105 Volume 105

The direct methods in the Calculus of Variations The methods used in Section 3 for proving the existence of a minimum point for the functional J[u] are known as direct methods in the Calculus of Variations. As we have seen the idea is ...

Author: Mariano Giaquinta

Publisher: Princeton University Press

ISBN: 9781400881628

Category: Mathematics

Page: 296

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The description for this book, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105, will be forthcoming.

Introduction To The Calculus of Variations And Its Applications

Direct. Methods. 1. The. Raylelgh-Rltz. Method. Exact solutions for problems in the calculus of variations are available only for relatively simple problems. Fortunately, accurate approximate solutions often suffice for many ...

Author: Frederic Wan

Publisher: Routledge

ISBN: 9781351436526

Category: Mathematics

Page: 640

View: 906

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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.

Cartesian Currents in the Calculus of Variations II

D. Applying the direct methods of Calculus of Variations just means trying to use Theorem 1. More precisely, when dealing with a minimum problem, in principle no topology or convergence is given a priori: the problem of proving ...

Author: Mariano Giaquinta

Publisher: Springer Science & Business Media

ISBN: 9783662062180

Category: Mathematics

Page: 700

View: 373

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Non-scalar variational problems appear in different fields. In geometry, for in stance, we encounter the basic problems of harmonic maps between Riemannian manifolds and of minimal immersions; related questions appear in physics, for example in the classical theory of a-models. Non linear elasticity is another example in continuum mechanics, while Oseen-Frank theory of liquid crystals and Ginzburg-Landau theory of superconductivity require to treat variational problems in order to model quite complicated phenomena. Typically one is interested in finding energy minimizing representatives in homology or homotopy classes of maps, minimizers with prescribed topological singularities, topological charges, stable deformations i. e. minimizers in classes of diffeomorphisms or extremal fields. In the last two or three decades there has been growing interest, knowledge, and understanding of the general theory for this kind of problems, often referred to as geometric variational problems. Due to the lack of a regularity theory in the non scalar case, in contrast to the scalar one - or in other words to the occurrence of singularities in vector valued minimizers, often related with concentration phenomena for the energy density - and because of the particular relevance of those singularities for the problem being considered the question of singling out a weak formulation, or completely understanding the significance of various weak formulations becames non trivial.

Cartesian Currents in the Calculus of Variations II

Applying the direct methods of Calculus of Variations just means trying to use Theorem 1. More precisely , when dealing with a minimum problem , in principle no topology or convergence is given a priori : the problem of proving ...

Author: Both in the Department of Mathematics Mariano Giaquinta

Publisher: Springer Science & Business Media

ISBN: 354064010X

Category: Mathematics

Page: 700

View: 461

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This monograph (in two volumes) deals with non scalar variational problems arising in geometry, as harmonic mappings between Riemannian manifolds and minimal graphs, and in physics, as stable equilibrium configuations in nonlinear elasticity or for liquid crystals. The presentation is selfcontained and accessible to non specialists. Topics are treated as far as possible in an elementary way, illustrating results with simple examples; in principle, chapters and even sections are readable independently of the general context, so that parts can be easily used for graduate courses. Open questions are often mentioned and the final section of each chapter discusses references to the literature and sometimes supplementary results. Finally, a detailed Table of Contents and an extensive Index are of help to consult this monograph

Lacroix and the Calculus

In the second edition it was divided into three chapters, and even in the first edition we can see clearly the three parts corresponding to those future chapters: direct calculus of differences; inverse calculus of differences of ...

Author: João Caramalho Domingues

Publisher: Springer Science & Business Media

ISBN: 376438638X

Category: Mathematics

Page: 468

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Silvestre François Lacroix was not a prominent mathematical researcher, but he was certainly a most influential mathematical book author. His most famous work is the three-volume Traité du calcul différentiel et du calcul intégral, which is an encyclopedic appraisal of 18th-century calculus that remained the standard reference on the subject through much of the 19th century. This book provides the first global and detailed study of Lacroix's Traité Traité du calcul.

The Calculus of Consent

DIRECT DEMOCRACY AND REPRESENTATIVE GOVERNMENT The approach proceeds from the calculus of the individual , and it is , therefore , more concise and understandable if the individual is presumed to choose directly among the alternatives ...

Author: James M. Buchanan

Publisher: University of Michigan Press

ISBN: 0472061003

Category: Business & Economics

Page: 361

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A scientific study of the political and economic factors influencing democratic decision making

Dictionary of Analysis Calculus and Differential Equations

Note also that every direct method for the solution of a variation problem is also an approximation method for ... The Rayleigh - Ritz is another direct method in the calculus of variations . the origin : positive numbers are used for ...

Author: Douglas N. Clark

Publisher: CRC Press

ISBN: 1420049992

Category: Mathematics

Page: 288

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Clear, rigorous definitions of mathematical terms are crucial to good scientific and technical writing-and to understanding the writings of others. Scientists, engineers, mathematicians, economists, technical writers, computer programmers, along with teachers, professors, and students, all have the occasional-if not frequent-need for comprehensible, working definitions of mathematical expressions. To meet that need, CRC Press proudly introduces its Dictionary of Analysis, Calculus, and Differential Equations - the first published volume in the CRC Comprehensive Dictionary of Mathematics. More than three years in development, top academics and professionals from prestigious institutions around the world bring you more than 2,500 detailed definitions, written in a clear, readable style and complete with alternative meanings, and related references.

Nature s Patterns and the Fractional Calculus

We note in passing that Leibniz was the first to implement a fractional derivative, so the fractional calculus is as old as fluxions and the differential calculus. Direct answers to such questions are not forthcoming, but it appears ...

Author: Bruce J. West

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 9783110534276

Category: Mathematics

Page: 213

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Complexity increases with increasing system size in everything from organisms to organizations. The nonlinear dependence of a system’s functionality on its size, by means of an allometry relation, is argued to be a consequence of their joint dependency on complexity (information). In turn, complexity is proven to be the source of allometry and to provide a new kind of force entailed by a system‘s information gradient. Based on first principles, the scaling behavior of the probability density function is determined by the exact solution to a set of fractional differential equations. The resulting lowest order moments in system size and functionality gives rise to the empirical allometry relations. Taking examples from various topics in nature, the book is of interest to researchers in applied mathematics, as well as, investigators in the natural, social, physical and life sciences. Contents Complexity Empirical allometry Statistics, scaling and simulation Allometry theories Strange kinetics Fractional probability calculus

Quantum Variational Calculus

IntJNon-Linear Mech 2:55–59 Leitmann G (2001a) On a class of direct optimization problems. J Optim Theory Appl 108(3):467– 481 Leitmann G (2001b) Some extensions to a direct optimization method. J Optim Theory Appl 111(1):1–6 Leitmann G ...

Author: Agnieszka B. Malinowska

Publisher: Springer Science & Business Media

ISBN: 9783319027470

Category: Mathematics

Page: 84

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This Brief puts together two subjects, quantum and variational calculi by considering variational problems involving Hahn quantum operators. The main advantage of its results is that they are able to deal with nondifferentiable (even discontinuous) functions, which are important in applications. Possible applications in economics are discussed. Economists model time as continuous or discrete. Although individual economic decisions are generally made at discrete time intervals, they may well be less than perfectly synchronized in ways discrete models postulate. On the other hand, the usual assumption that economic activity takes place continuously, is nothing else than a convenient abstraction that in many applications is far from reality. The Hahn quantum calculus helps to bridge the gap between the two families of models: continuous and discrete. Quantum Variational Calculus is self-contained and unified in presentation. It provides an opportunity for an introduction to the quantum calculus of variations for experienced researchers but may be used as an advanced textbook by graduate students and even ambitious undergraduates as well. The explanations in the book are detailed to capture the interest of the curious reader, and complete to provide the necessary background material needed to go further into the subject and explore the rich research literature, motivating further research activity in the area.

Calculus of Variations

Direct. Method. Fundamental to all of the existence theorems in this book is the conceptually simple, yet powerful, Direct Method of the calculus of variations. It is called “direct” since we prove the existence of solutions to ...

Author: Filip Rindler

Publisher: Springer

ISBN: 9783319776378

Category: Mathematics

Page: 444

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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.

Plateau s Problem and the Calculus of Variations MN 35

The direct methods in the calculus of variations. We now proceed to derive the existence of a minimizer of D on C(T)-and hence of a solution to Plateau's problem (1.1) - (1.3), cp. Remark 2.4. iii) - from the following general ...

Author: Michael Struwe

Publisher: Princeton University Press

ISBN: 9781400860210

Category: Mathematics

Page: 160

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This book is meant to give an account of recent developments in the theory of Plateau's problem for parametric minimal surfaces and surfaces of prescribed constant mean curvature ("H-surfaces") and its analytical framework. A comprehensive overview of the classical existence and regularity theory for disc-type minimal and H-surfaces is given and recent advances toward general structure theorems concerning the existence of multiple solutions are explored in full detail. The book focuses on the author's derivation of the Morse-inequalities and in particular the mountain-pass-lemma of Morse-Tompkins and Shiffman for minimal surfaces and the proof of the existence of large (unstable) H-surfaces (Rellich's conjecture) due to Brezis-Coron, Steffen, and the author. Many related results are covered as well. More than the geometric aspects of Plateau's problem (which have been exhaustively covered elsewhere), the author stresses the analytic side. The emphasis lies on the variational method. Originally published in 1989. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.