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.
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.
Описание: This well-written, advanced-level text introduces students toFourier analysis and some of its applications. The self-contained treatment covers Fourier series, orthogonal systems, Fourier and Laplace transforms, Bessel functions, and partial differential equations of the first and second orders. Over260 exercises with solutions reinforce students' grasp of the material. 1970 edition."
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
Описание: This advanced graduate-level text examines variational methods in partial differential equations and illustrates their applications to a number of free-boundary problems. Detailed statements of the standard theory of elliptic and parabolic operators make this treatment readable for engineers, students, and nonspecialists alike. The text's first two chapters can be used for a single-semester graduate course in variational inequalities or partial differential equations. The succeeding chapters -- covering jets and cavities, variational problems with potentials, and free-boundary problems not in variational form -- are more specialized and self-contained. Readers who have mastered chapters 1 and 2 will be able to conduct research on the problems explored in subsequent chapters. Bibliographic remarks conclude each chapter, along with several problems and exercises.
Автор: Smith, Donald R. Название: Variational methods in optimization ISBN: 0486404552 ISBN-13(EAN): 9780486404554 Издательство: Dover Рейтинг: Цена: 1668 р. Наличие на складе: Поставка под заказ.
Описание: Fostering an increased appreciation of the fundamental theorem of calculus, this highly readable text elucidates applications of the chain rule of differentiation, integration by parts, parametric curves, line integrals, double integrals, and elementary differential equations. A clear and well-illustrated treatment of techniques for solving a wide variety of optimization problems arising in a diverse array of fields, this volume requires only an elementary knowledge of calculus and can be used either by itself or as a supplementary text in a variety of courses. 1974 edition.
Автор: Prenter P. Название: Splines and Variational Methods ISBN: 0486469026 ISBN-13(EAN): 9780486469027 Издательство: Dover Рейтинг: Цена: 1668 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Автор: Lanczos, Cornelius Название: The Variational Principles of Mechanics ISBN: 0486650677 ISBN-13(EAN): 9780486650678 Издательство: Dover Рейтинг: Цена: 1919 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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.
Автор: Bleecker David Название: Gauge Theory and Variational Principles ISBN: 0486445461 ISBN-13(EAN): 9780486445465 Издательство: Dover Рейтинг: Цена: 1083 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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.
Автор: Moiseiwitsch B. Название: Variational Principles ISBN: 0486438171 ISBN-13(EAN): 9780486438177 Издательство: Dover Рейтинг: Цена: 1501 р. Наличие на складе: Есть у поставщика Поставка под заказ.
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.
Описание: This text provides an introduction to partial differential equations and boundary value problems, including Fourier series. The treatment offers students a smooth transition from a course in elementary ordinary differential equations to more advanced topics in a first course in partial differential equations. This widely adopted and successful book also serves as a valuable reference for engineers and other professionals. The approach emphasizes applications, with particular stress on physics and engineering applications. Rich in proofs and examples, the treatment features many exercises in each section. Relevant Mathematica files are available for download from author Nakhl Asmar's website; however, the book is completely usable without computer access. The Students' Solutions Manual can be downloaded for free from the Dover website, and the Instructor's Solutions Manual is available upon request for professors and potential teachers. The text is suitable for undergraduates in mathematics, physics, engineering, and other fields who have completed a course in ordinary differential equations.
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