Описание: This book was written to help mathematics students and those in the physical sciences learn modern mathematical techniques for setting up and analyzing problems. The mathematics used is rigorous, but not overwhelming, while the authors carefully model physical situations, emphasizing feedback among a beginning model, physical experiments, mathematical predictions, and the subsequent refinement and reevaluation of the physical model itself. Chapter 1 begins with a discussion of various physical problems and equations that play a central role in applications. The following chapters take up the theory of partial differential equations, including detailed discussions of uniqueness, existence, and continuous dependence questions, as well as techniques for constructing conclusions. Specifically, Chapters 2 through 6 deal with problems in one spatial dimension. Chapter 7 is a detailed introduction to the theory of integral equations; then Chapters 8 through 12 treat problems in more spatial variables. Each chapter begins with a discussion of problems that can be treated by elementary means, such as separation of variables or integral transforms, and which lead to explicit, analytical representations of solutions. The minimal mathematical prerequisites for a good grasp of the material in this book are a course in advanced calculus, or an advanced course in science or engineering, and a basic exposure to matrix methods. Students of mathematics, physics, engineering, and other disciplines will find here an excellent guide to mathematical problem-solving techniques with a broad range of applications. For this edition the authors have provided a new section of Solutions and Hints to selected Problems. Suggestions for further reading complete the text.

Автор: Friedman Avner Название: Generalized Functions and Partial Differential Equations ISBN: 0486446107 ISBN-13(EAN): 9780486446103 Издательство: Dover Рейтинг: Цена: 1668 р. Наличие на складе: Есть у поставщика Поставка под заказ.

Описание: This self-contained treatment develops the theory of generalized functions and the theory of distributions, and it systematically applies them to solving a variety of problems in partial differential equations. A major portion of the text is based on material included in the books of L. Schwartz, who developed the theory of distributions, and in the books of Gelfand and Shilov, who deal with generalized functions of any class and their use in solving the Cauchy problem. In addition, the author provides applications developed through his own research. Geared toward upper-level undergraduates and graduate students, the text assumes a sound knowledge of both real and complex variables. Familiarity with the basic theory of functional analysis, especially normed spaces, is helpful but not necessary. An introductory chapter features helpful background on topological spaces. Applications to partial differential equations include a treatment of the Cauchy problem, the Goursat problem, fundamental solutions, existence and differentiality of solutions of equations with constants, coefficients, and related topics. Supplementary materials include end-of-chapter problems, bibliographical remarks, and a bibliography.

Despite the increasing use of computers, the basic need for mathematical tables continues. Tables serve a vital role in preliminary surveys of problems before programming for machine operation, and they are indispensable to thousands of engineers and scientists without access to machines. Because of automatic computers, however, and because of recent scientific advances, a greater variety of functions and a higher accuracy of tabulation than have been available until now are required. In 1954, a conference on mathematical tables, sponsored by M.I.T. and the National Science Foundation, met to discuss a modernization and extension of Jahnke and Emde's classical tables of functions. This volume, published 10 years later by the U.S. Department of Commerce, is the result. Designed to include a maximum of information and to meet the needs of scientists in all fields, it is a monumental piece of work, a comprehensive and self-contained summary of the mathematical functions that arise in physical and engineering problems. The book contains 29 sets of tables, some to as high as 20 places: mathematical constants; physical constants and conversion factors (6 tables); exponential integral and related functions (7); error function and Fresnel integrals (12); Bessel functions of integer (12) and fractional (13) order; integrals of Bessel functions (2); Struve and related functions (2); confluent hypergeometric functions (2); Coulomb wave functions (2); hypergeometric functions; Jacobian elliptic and theta functions (2); elliptic integrals {9); Weierstrass elliptic and related functions; parabolic cylinder functions {3); Mathieu functions (2); spheroidal wave functions (5); orthogonal polynomials (13); combinatorial analysis (9); numerical interpolation, differentiation and integration (11); probability functions (ll); scales of notation (6); miscellaneous functions (9); Laplace transforms (2); and others. Each of these sections is prefaced by a list of related formulas and graphs: differential equations, series expansions, special functions, and other basic relations. These constitute an unusually valuable reference work in themselves. The prefatory material also includes an explanation "of "the numerical methods involved in using the tables that follow and a bibliography. Numerical examples illustrate the use of each table and explain the computation of function values which lie outside its range, while the editors' introduction describes higher-order interpolation procedures. Well over""100 figures illustrate the text. In all, this is one of the most ambitious and useful books of its type ever published, an essential aid in all scientific and engineering research, problem solving, experimentation and field work. This low-cost edition contains every page of the original government publication.

Автор: Hochstadt, Harry Название: The Functions of Mathematical Physics ISBN: 0486652149 ISBN-13(EAN): 9780486652146 Издательство: Dover Цена: 1417 р. Наличие на складе: Поставка под заказ.

Описание:

A modern classic, this clearly written, incisive textbook provides a comprehensive, detailed survey of the functions of mathematical physics, a field of study straddling the somewhat artificial boundary between pure and applied mathematics. In the 18th and 19th centuries, the theorists who devoted themselves to this field pioneers such as Gauss, Euler, Fourier, Legendre, and Bessel were searching for mathematical solutions to physical problems. Today, although most of the functions have practical applications, in areas ranging from the quantum-theoretical model of the atom to the vibrating membrane, some, such as those related to the theory of discontinuous groups, still remain of purely mathematical interest. Chapters One and Two examine orthogonal polynomials, with sections on such topics as the recurrence formula, the Christoffel-Darboux formula, the Weierstrass approximation theorem, and the application of Hermite polynomials to quantum mechanics. Chapter Three is devoted to the principal properties of the gamma function, including asymptotic expansions and Mellin-Barnes integrals. Chapter Four covers hypergeometric functions, including a review of linear differential equations with regular singular points, and a general method for finding integral representations. Chapters Five and Six are concerned with the Legendre functions and their use in the solutions of Laplace's equation in spherical coordinates, as well as problems in an "n"-dimension setting. Chapter Seven deals with confluent hypergeometric functions, and Chapter Eight examines, at length, the most important of these the Bessel functions. Chapter Nine covers Hill's equations, including the expansion theorems. "

Описание: This high-level treatment by a noted mathematician considers one-dimensional singular integral equations involving Cauchy principal values. Intended for graduate students and professionals, its coverage includes such topics as the Holder condition, Hilbert and Riemann-Hilbert problems, the Dirichlet problem, inversion formulas for arcs, and many other areas. 1992 edition.

Автор: Tikhonov, A. N. Название: Equations of Mathematical Physics ISBN: 048678634X ISBN-13(EAN): 9780486786346 Издательство: Dover Цена: 5012 р. Наличие на складе: Поставка под заказ.

Описание: One of the definitive works in game theory, this fascinating volume offers an original look at methods of obtaining solutions for conflict situations. Combining the principles of game theory, the calculus of variations, and control theory, the author considers and solves an amazing array of problems: military, pursuit and evasion, games of firing and maneuver, athletic contests, and many other problems of conflict. Beginning with general definitions and the basic mathematics behind differential game theory, the author proceeds to examinations of increasingly specific techniques and applications: dispersal, universal, and equivocal surfaces; the role of game theory in warfare; development of an effective theory despite incomplete information; and more. All problems and solutions receive clearly worded, illuminating discussions, including detailed examples and numerous formal calculations. The product of fifteen years of research by a highly experienced mathematician and engineer, this volume will acquaint students of game theory with practical solutions to an extraordinary range of intriguing problems.

Описание: A general theory of the functions depending on a continuous set of values of another function, this volume is based on the author's fundamental notion of the transition from a finite number of variables to a continually infinite number. Deals primarily with integral equations, and also addresses the calculus of variations. 1930 edition.

Описание: Intended for use in a beginning one-semester course in differential equations, this text is designed for students of pure and applied mathematics with a working knowledge of algebra, trigonometry, and elementary calculus. Its mathematical rigor is balanced by complete but simple explanations that appeal to readers' physical and geometric intuition. Starting with an introduction to differential equations, the text proceeds to examinations of first- and second-order differential equations, series solutions, the Laplace transform, systems of differential equations, difference equations, nonlinear differential equations and chaos, and partial differential equations. Numerous figures, problems with solutions, and historical notes clarify the text.

Описание: Approximately 1,000 problems -- with answers and solutions included at the back of the book -- illustrate such topics as random events, random variables, limit theorems, Markov processes, and much more.

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.

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