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Variational Methods for Boundary Value Problems for Systems of Elliptic Equations



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Автор: Lavrent`ev, M. A.
Название:  Variational Methods for Boundary Value Problems for Systems of Elliptic Equations
Издательство: Dover
Классификация:
ISBN: 0486661709
ISBN-13(EAN): 9780486661704
ISBN: 0-486-66170-9
ISBN-13(EAN): 978-0-486-66170-4
Обложка/Формат: Paperback
Страницы: 160
Вес: 0.198 кг.
Дата издания: 20.01.2016
Серия: Mathematics
Язык: English
Размер: 217 x 138 x 9
Основная тема: Applied
Поставляется из: США
Описание: In this famous monograph, a distinguished mathematician presents an innovative approach to classical boundary value problems ― one that may be used by mathematicians as well as by theoreticians in mechanics. The approach is based on a number of geometric properties of conformal and quasi-conformal mappings and employs the general basic scheme for solution of variational problems first suggested by Hilbert and developed by Tonnelli.
The first two chapters cover variational principles of the theory of conformal mapping and behavior of a conformal transformation on the boundary. Chapters 3 and 4 explore hydrodynamic applications and quasiconformal mappings, and the final two chapters address linear systems and the simplest classes of non-linear systems. Mathematicians will take particular interest in the method of the proof of the existence and uniqueness theorems as well as the general theory of quasi-conformal mappings. Theoreticians in mechanics will find the approximate formulas for conformal and quasi-conformal




Variational Methods for Boundary Value Problems: for Systems of Elliptic Equations

Автор: Lavrent`ev M. A.
Название: Variational Methods for Boundary Value Problems: for Systems of Elliptic Equations
ISBN: 0486450783 ISBN-13(EAN): 9780486450780
Издательство: Dover
Цена: 3553 р.
Наличие на складе: Невозможна поставка.

Approximation of Elliptic Boundary-Value Problems

Автор: Aubin Jean-Pierre
Название: Approximation of Elliptic Boundary-Value Problems
ISBN: 0486457915 ISBN-13(EAN): 9780486457918
Издательство: Dover
Рейтинг:
Цена: 1668 р.
Наличие на складе: Поставка под заказ.

Описание: A marriage of the finite-differences method with variational methods for solving boundary-value problems, the finite-element method is superior in many ways to finite-differences alone. This self-contained text for advanced undergraduates and graduate students is intended to imbed this combination of methods into the framework of functional analysis. 1980 edition.

The Variational Theory of Geodesics

Автор: Postnikov M. M.
Название: The Variational Theory of Geodesics
ISBN: 0486495299 ISBN-13(EAN): 9780486495293
Издательство: Dover
Цена: 3135 р.
Наличие на складе: Невозможна поставка.

Gauge Theory and Variational Principles

Автор: Bleecker David
Название: Gauge Theory and Variational Principles
ISBN: 0486445461 ISBN-13(EAN): 9780486445465
Издательство: Dover
Рейтинг:
Цена: 1083 р.
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Описание: This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This well-organized treatment supplements its rigor with intuitive ideas.
Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field equation. Additional topics include free Dirac electron fields; interactions; calculus on frame bundle; and unification of gauge fields and gravitation. The text concludes with references, a selected bibliography, an index of notation, and a general index.

Variational Principles

Автор: Moiseiwitsch B.
Название: Variational Principles
ISBN: 0486438171 ISBN-13(EAN): 9780486438177
Издательство: Dover
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Цена: 1501 р.
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Описание: This graduate-level text's primary objective is to demonstrate the expression of the equations of the various branches of mathematical physics in the succinct and elegant form of variational principles (and thereby illuminate their interrelationship). Its related intentions are to show how variational principles may be employed to determine the discrete eigenvalues for stationary state problems and to illustrate how to find the values of quantities (such as the phase shifts) that arise in the theory of scattering. Chapter-by-chapter treatment consists of analytical dynamics; optics, wave mechanics, and quantum mechanics; field equations; eigenvalue problems; and scattering theory. 1966 edition. Bibliography. Index.

Variational Analysis: Critical Extremals and Sturmian Extensions

Автор: Morse Marston
Название: Variational Analysis: Critical Extremals and Sturmian Extensions
ISBN: 0486457877 ISBN-13(EAN): 9780486457871
Издательство: Dover
Рейтинг:
Цена: 1250 р.
Наличие на складе: Поставка под заказ.

Описание: This text presents extended separation, comparison, and oscillation theorems that replace the classical analysis of Legendre, Jacobi, Hilbert, and others. Its analysis of related quadratic functionals shows how critical extremals can substitute for minimizing extremals.
Author Marston Morse is renowned for his development of a version of variational theory with applications to equilibrium problems in mathematical physics--the theory known as Morse theory, which forms a vital role in global analysis. He begins this treatment of variational analysis with an extended investigation of critical extremals that proceeds to quadratic index forms, advanced and free. Additional topics include focal conditions and Sturm-like theorems, general boundary conditions, and prestructures for characteristic root theory. A helpful pair of appendixes include supplementary information on free linear conditions and subordinate quadratic forms and their complementary forms.

The Variational Principles of Mechanics

Автор: Lanczos, Cornelius
Название: The Variational Principles of Mechanics
ISBN: 0486650677 ISBN-13(EAN): 9780486650678
Издательство: Dover
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Цена: 1919 р.
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Описание:

Analytical mechanics is, of course, a topic of perennial interest and usefulness in physics and engineering, a discipline that boasts not only many practical applications, but much inherent mathematical beauty. Unlike many standard textbooks on advanced mechanics, however, this present text eschews a primarily technical and formalistic treatment in favor of a fundamental, historical, philosophical approach. As the author remarks, there is a tremendous treasure of philosophical meaning" behind the great theories of Euler and Lagrange, Hamilton, Jacobi, and other mathematical thinkers.
Well-written, authoritative, and scholarly, this classic treatise begins with an introduction to the variational principles of mechanics including the procedures of Euler, Lagrange, and Hamilton.
Ideal for a two-semester graduate course, the book includes a variety of problems, carefully chosen to familiarize the student with new concepts and to illuminate the general principles involved. Moreover, it offers excellent grounding for the student of mathematics, engineering, or physics who does not intend to specialize in mechanics, but wants a thorough grasp of the underlying principles.
The late Professor Lanczos (Dublin Institute of Advanced Studies) was a well-known physicist and educator who brought a superb pedagogical sense and profound grasp of the principles of mechanics to this work, now available for the first time in an inexpensive Dover paperback edition. His book will be welcomed by students, physicists, engineers, mathematicians, and anyone interested in a clear masterly exposition of this all-important discipline.

Tensors, Differential Forms, and Variational Principles

Автор: Lovelock, David
Название: Tensors, Differential Forms, and Variational Principles
ISBN: 0486658406 ISBN-13(EAN): 9780486658407
Издательство: Dover
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Цена: 1584 р.
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Описание:

The aim of this book is to present a self-contained, reasonably modern account of tensor analysis and the calculus of exterior differential forms, adapted to the needs of physicists, engineers, and applied mathematicians. In the later, increasingly sophisticated chapters, the interaction between the concept of invariance and the calculus of variations is examined. This interaction is of profound importance to all physical field theories.
Beginning with simple physical examples, the theory of tensors and forms is developed by a process of successive abstractions. This enables the reader to infer generalized principles from concrete situations -- departing from the traditional approach to tensors and forms in terms of purely differential-geometric concepts.
The treatment of the calculus of variations of single and multiple integrals is based ab initio on Carath odory's method of equivalent integrals. Subsequent material explores the effects of invariance postulates on variational principles, focusing ultimately on relativistic field theories. Other discussions include:
- integral invariants
- simple and direct derivations of Noether's theorems
- Riemannian spaces with indefinite metrics
The emphasis in this book is on analytical techniques, with abundant problems, ranging from routine manipulative exercises to technically difficult problems encountered by those using tensor techniques in research activities. A special effort has been made to collect many useful results of a technical nature, not generally discussed in the standard literature. The Appendix, newly revised and enlarged for the Dover edition, presents a reformulation of the principal concepts of the main text within the terminology of current global differential geometry, thus bridging the gap between classical tensor analysis and the fundamentals of more recent global theories.

Variational Principles in Dynamics and Quantum Theory

Автор: Yourgrau Wolfgang
Название: Variational Principles in Dynamics and Quantum Theory
ISBN: 0486458881 ISBN-13(EAN): 9780486458885
Издательство: Dover
Рейтинг:
Цена: 1083 р.
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Описание: Focusing on applications relevant to modern physics, this text for advanced undergraduates and graduate students surveys variational principles, examining their relationship to dynamics and quantum theory. It stresses the history and theory of these concepts rather than their mechanics, providing many insights into the development of quantum mechanics. 1968 edition.

Kernel Functions and Elliptic Differential Equations in Mathematical Physics

Автор: Bergman Stefan
Название: Kernel Functions and Elliptic Differential Equations in Mathematical Physics
ISBN: 0486445534 ISBN-13(EAN): 9780486445533
Издательство: Dover
Рейтинг:
Цена: 2086 р.
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Описание: This text focuses on the theory of boundary value problems in partial differential equations, which plays a central role in various fields of pure and applied mathematics, theoretical physics, and engineering. Geared toward upper-level undergraduates and graduate students, it discusses a portion of the theory from a unifying point of view and provides a systematic and self-contained introduction to each branch of the applications it employs.
The two-part treatment begins with a survey of boundary value problems occurring in certain branches of theoretical physics. It introduces fundamental solutions in a heuristic way and examines their physical significance. Many concepts can be unified by concentrating upon these particular kernels, and the text explains the common mathematical background of widely varying theories, such as those of heat conduction, hydrodynamics, electrostatics, magnetostatics, and elasticity. In addition to its intrinsic interest, this material provides illustrations and exact mathematical formulation of the problems and the methods. The second part is confined to a rather special type of partial differential equation, which is dealt with in the greatest detail so that students can make applications and generalizations to similar problems.

Nonlinear Potential Theory of Degenerate Elliptic Equations

Автор: Heinonen Juha
Название: Nonlinear Potential Theory of Degenerate Elliptic Equations
ISBN: 0486450503 ISBN-13(EAN): 9780486450506
Издательство: Dover
Цена: 1668 р.
Наличие на складе: Поставка под заказ.

Lectures on the Theory of Elliptic Functions

Автор: Hancock Harris
Название: Lectures on the Theory of Elliptic Functions
ISBN: 0486438252 ISBN-13(EAN): 9780486438252
Издательство: Dover
Цена: 6270 р.
Наличие на складе: Невозможна поставка.


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