Автор: Oden J. Название: An Introduction to the Mathematical Theory of Finite Elements ISBN: 0486462994 ISBN-13(EAN): 9780486462998 Издательство: Dover Рейтинг: Цена: 24820.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This introduction to the theory of Sobolev spaces and Hilbert space methods in partial differential equations is geared toward readers of modest mathematical backgrounds. It offers coherent, accessible demonstrations of the use of these techniques in developing the foundations of the theory of finite element approximations. J. T. Oden is Director of the Institute for Computational Engineering & Sciences (ICES) at the University of Texas at Austin, and J. N. Reddy is a Professor of Engineering at Texas A&M University. They developed this essentially self-contained text from their seminars and courses for students with diverse educational backgrounds. Their effective presentation begins with introductory accounts of the theory of distributions, Sobolev spaces, intermediate spaces and duality, the theory of elliptic equations, and variational boundary value problems. The second half of the text explores the theory of finite element interpolation, finite element methods for elliptic equations, and finite element methods for initial boundary value problems. Detailed proofs of the major theorems appear throughout the text, in addition to numerous examples.
Автор: Smullyan, Raymond Название: A Beginner`s Guide to Mathematical Logic ISBN: 0486492370 ISBN-13(EAN): 9780486492377 Издательство: Dover Рейтинг: Цена: 20640.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. He highlights each subject with inventive explanations and unique problems. Smullyan's accessible narrative provides memorable examples of concepts related to proofs, propositional logic and first-order logic, incompleteness theorems, and incompleteness proofs. Additional topics include undecidability, combinatoric logic, and recursion theory. Suitable for undergraduate and graduate courses, this book will also amuse and enlighten mathematically minded readers. 2014 edition.
Автор: Curry Haskell B. Название: Foundations of Mathematical Logic ISBN: 0486634620 ISBN-13(EAN): 9780486634623 Издательство: Dover Рейтинг: Цена: 24780.00 T Наличие на складе: Невозможна поставка. Описание: This book is a thoroughly documented and comprehensive account of the constructive theory of the first-order predicate calculus. This is a calculus that is central to modern mathematical logic and important for mathematicians, philosophers, and scientists whose work impinges upon logic. Professor Curry begins by asking a simple question: What is mathematical logic? If we can define logic as "the analysis and criticism of thought" (W. E. Johnson), then mathematical logic is, according to Curry, "a branch of mathematics which has much the same relation to the analysis and criticism of thought as geometry does to the science of space." The first half of the book gives the basic principles and outlines of the field. After a general introduction to the subject, the author discusses formal methods including algorithms and epitheory. A brief treatment of the Markov treatment of algorithms is included here. The elementary facts about lattices and similar algebraic systems are then covered. In the second half of the book Curry investigates the possibility for a formulation that expresses the meaning to be attached to the logical connectives and to develop the properties that follow from the assumptions so motivated. The author covers positive connectives: implication, conjunction, and alternation. He then goes on to negation and quantification, and concludes with modal operations. Extensive use is made in these latter chapters of the work of Gentzen. Lists of exercises are included. Haskell B. Curry, Evan Pugh Research Professor, Emeritus, at Pennsylvania State University, was a member of the Institute for Advanced Study, Princeton; a former Director of the Institute for Foundational Research, the University of Amsterdam; and President of the Association for Symbolic Logic. His book avoids a doctrinaire stance, presenting various interpretations of logical systems, and offers philosophical and reflective as well as mathematical perspectives.
Автор: Khinchin, A. Ya. Название: Mathematical Foundations of Statistical Mechanics ISBN: 0486601471 ISBN-13(EAN): 9780486601472 Издательство: Dover Рейтинг: Цена: 12370.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The translation of this important book brings to the English-speaking mathematician and mathematical physicist a thoroughly up-to-date introduction to statistical mechanics. It offers a precise and mathematically rigorous formulation of the problems of statistical mechanics, as opposed to the non-rigorous discussion presented in most other works. It provides analytical tools needed to replace many of the cumbersome concepts and devices commonly used for establishing basic formulae, and it furnishes the mathematician with a logical step-by-step introduction, which will enable him to master the elements of statistical mechanics in the shortest possible time. After a historical sketch, the author discusses the geometry and kinematics of the phase space, with the theorems of Liouville and Birkhoff; the ergodic problem (in the sense of replacing time averages by phase averages); the theory of probability; central limit theorem; ideal monatomic gas; foundation of thermodynamics, and dispersion and distribution of sum functions. "An excellent introduction to the difficult and important discipline of Statistical Mechanics. It is clear, concise, and rigorous. There is a very good chapter on the ergodic theorem (with a complete proof ) and . . . a highly lucid chapter on statistical foundations of thermodynamics . . . useful to teachers . . . and to mathematicians." ― M. Kac, "Quarterly of Applied Mathematics. "
Автор: Johnsonbaugh Richard Название: Foundations of Mathematical Analysis ISBN: 0486477665 ISBN-13(EAN): 9780486477664 Издательство: Dover Рейтинг: Цена: 28910.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This classroom-tested volume offers a definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. Upper-level undergraduate students with a background in calculus will benefit from its teachings, along with beginning graduate students seeking a firm grounding in modern analysis. A self-contained text, it presents the necessary background on the limit concept, and the first seven chapters could constitute a one-semester introduction to limits. Subsequent chapters discuss differential calculus of the real line, the Riemann-Stieltjes integral, sequences and series of functions, transcendental functions, inner product spaces and Fourier series, normed linear spaces and the Riesz representation theorem, and the Lebesgue integral. Supplementary materials include an appendix on vector spaces and more than 750 exercises of varying degrees of difficulty. Hints and solutions to selected exercises, indicated by an asterisk, appear at the back of the book.
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