Quantum Mechanics and Path Integrals: Emended Edition
Автор: Bleistein Norman Название: Asymptotic Expansions of Integrals ISBN: 0486650820 ISBN-13(EAN): 9780486650821 Издательство: Dover Рейтинг: Цена: 1564 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Asymptotic analysis, that branch of mathematics devoted to the study of the behavior of functions within chosen limits, was once thought of more as a specialized art than a necessary discipline. Now, a solid foundation in the theory and technique of asymptotic expansion of integrals is at the heart of the education of every student concentrating in applied mathematics. It is also an invaluable asset to scientists in many other fields.This excellent introductory text, written by two experts in the field, offers students of applied mathematics and researchers and workersin other fields a coherent and systematic presentation of the principles and methods of asymptotic expansions of integrals. Students will find each of the nine chapters useful and easy to comprehend; each begins with elementary material or informal introductions and concludes with an abundant selection of applicable problems and exercises. All that is needed is a basic understanding of calculus, differential equations, and complex variables.Practiced users of asymptotics will find the work a valuable reference with an extensive index locating all the functions covered in the text and every formula associated with the major techniques. Subjects include integration by parts, Watson's lemma, Laplace's method, stationary phase, and steepest descents. Also treated are the Mellin transform method and less elementary aspects of steepest descent. Each chapter is carefully illustrated with helpful diagrams and tables.Used for years as a text in classrooms throughout the country, the book has been revised and corrected for this inexpensive paperback edition. Any student or teacher looking for a suitable text for a year's or semester's course in asymptotics will value this affordable volume as the only comprehensive introduction available; scientists and researchers will undoubtedly refer to it again and again."
Автор: Swanson, Mark Название: Path Integrals and Quantum Processes ISBN: 0486493067 ISBN-13(EAN): 9780486493060 Издательство: Dover Рейтинг: Цена: 1955 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This text offers a systematic presentation of the path integral approach to calculating transition elements, partition functions, and source functionals. The treatment contains a set of logical connections and applications which represent the scope of problems that the path integral can solve. Readers receive sufficient background to advance to related books and articles at the frontiers of theoretical physics. An introductory section covers mathematical preliminaries, progressing to examinations of quantum mechanical path integrals, an evaluation of the path integral, and an exploration of further applications. Subsequent chapters cover Grassmann variables, field theory and gauge field theory, perturbation theory, and nonperturbative results. Suitable for advanced undergraduates and graduate students of physics, the text requires only some familiarity with quantum mechanics. Exercises and lists of references throughout the book make it ideal for supplementary reading and self-study.
Описание: 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.
Описание: This compact guide emphasizes the relationship between physics and mathematics, introducing Fourier series in the way that Fourier himself used them: as solutions of the heat equation in a disk. 1966 edition.
Автор: Yudell L. Luke Название: Integrals of Bessel Functions ISBN: 0486789691 ISBN-13(EAN): 9780486789699 Издательство: Dover Рейтинг: Цена: 1955 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Integrals of Bessel Functions concerns definite and indefinite integrals, the evaluation of which is necessary to numerous applied problems. A massive compendium of useful information, this volume represents a resource for applied mathematicians in many areas of academia and industry as well as an excellent text for advanced undergraduates and graduate students of mathematics. Starting with an extensive introductory chapter on basic formulas, the treatment advances to indefinite integrals, examining them in terms of Lommel and Bessel functions. Subsequent chapters explore airy functions, incomplete gamma function and related functions, repeated integrals of Bessel functions, and integrals involving Struve functions. Additional topics include Schwarz functions and generalizations, miscellaneous indefinite integrals involving Bessel functions, and definite integrals. A dozen useful tables supplement the text.
Автор: Krylov V. Название: Approximate Calculation of Integrals ISBN: 0486445798 ISBN-13(EAN): 9780486445793 Издательство: Dover Рейтинг: Цена: 1564 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A systematic introduction to the principal ideas and results of the contemporary theory of approximate integration, this volume approaches its subject from the viewpoint of functional analysis. In addition, it offers a useful reference for practical computations. Its primary focus lies in the problem of approximate integration of functions of a single variable, rather than the more difficult problem of approximate integration of functions of more than one variable. The three-part treatment begins with concepts and theorems encountered in the theory of quadrature. The second part is devoted to the problem of calculation of definite integrals. This section considers three basic topics: the theory of the construction of mechanical quadrature formulas for sufficiently smooth integrand functions, the problem of increasing the precision of quadratures, and the convergence of the quadrature process. The final part explores methods for the calculation of indefinite integrals, and the text concludes with helpful appendixes.
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