Fluid dynamics, the behavior of liquids and gases, is a field of broad impact -- in physics, engineering, oceanography, and meteorology for example -- yet full understanding demands fluency in higher mathematics, the only language fluid dynamics speaks. Dr. Richard Meyer's work is indeed introductory, while written for advanced undergraduate and graduate students in applied mathematics, engineering, and the physical sciences. A knowledge of calculus and vector analysis is presupposed. The author develops basic concepts from a semi-axiomatic foundation, noting that "for mathematics students such a treatment helps to dispel the all too common impression that the whole subject is built on a quicksand of assorted intuitions." Contents include: Kinematics: Lagrangian and Eulerian descriptions, Circulation and Vorticity. Momentum Principle and Ideal Fluid: Conservation examples, Euler equations, D'Alembert's and Kelvin's theorems. Newtonian Fluid: Constitutive and Kinetic theories, exact solutions. Fluids of Small Viscosity: Singular Perturbation, Boundary Layers. Some Aspects of Rotating Fluids: Rossby number, Ekman layer, Taylor-Proudman Blocking. Some Effects of Compressibility: Thermodynamics, Waves, Shock relations and structure, Navier-Stokes equations. Dr. Meyer writes, "This core of our knowledge concerns the relation between inviscid and viscous fluids, and the bulk of this book is devoted to a discussion of that relation."
Автор: Rubinow S. I. Название: Introduction to Mathematical Biology ISBN: 0486425320 ISBN-13(EAN): 9780486425320 Издательство: Dover Рейтинг: Цена: 2868 р. Наличие на складе: Поставка под заказ.
Описание: Designed to explore the applications of mathematical techniques and methods related to biology, this text explores five areas: cell growth, enzymatic reactions, physiological tracers, biological fluid dynamics and diffusion. Topics essentially follow a course in elementary differential equations - some linear algebra and graph theory; requires only a knowledge of elementary calculus.
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: Thomson, William Tyrrell Название: Introduction to Space Dynamics ISBN: 0486651134 ISBN-13(EAN): 9780486651132 Издательство: Dover Рейтинг: Цена: 2178 р. Наличие на складе: Поставка под заказ.
Автор: Curry Haskell B. Название: Foundations of Mathematical Logic ISBN: 0486634620 ISBN-13(EAN): 9780486634623 Издательство: Dover Рейтинг: Цена: 2868 р. Наличие на складе: Поставка под заказ.
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: McLeod, Jr., Edward B. Название: Introduction to Fluid Dynamics ISBN: 0486807053 ISBN-13(EAN): 9780486807058 Издательство: Dover Рейтинг: Цена: 1833 р. Наличие на складе: Поставка под заказ.
Описание: Concise, unified, and logical, this introduction to the study of the basic principles of fluid dynamics emphasizes the statement of problems in mathematical language. In addition to its value as a reference for professional engineers, this volume is suitable for advanced undergraduates and graduate students of mathematics and engineering. Some familiarity with the algebra of vector fields is assumed, and a useful appendix provides a succinct review of vector algebra. An introductory chapter covers fundamental notions from the continuum hypothesis to steady-state flow. Succeeding chapters explore conservation of mass, forces acting on a fluid in equilibrium, dynamic equations of motion, irrotational motion, integration of Euler's equation in special cases, and flows representable by harmonic functions. Additional topics include two dimensional flows, rectilinear vortices, general vortex motion, flows with a free boundary, and compressible fluids.
Описание: Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects. Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text.
What are the laws of physics, and how did they develop? This reader-friendly guide offers illustrative examples of the rules of physical science and how they were formulated. It was written by Francis Bitter, a distinguished teacher and inventor who revolutionized the use of resistive magnets with his development of the Bitter plate. Dr. Bitter shares his scientific expertise in direct, nontechnical terminology as he explains methods of fact gathering, analysis, and experimentation. The four-part treatment begins with an introductory section on physical measurement. An overview of the basics of data assembly leads to the path of scientific investigation, which is exemplified by observations on planetary motions such as those of Earth, Venus, and Mercury. The heart of the book explores analytic methods: topics include the role of mathematics as the language of physics; the nature of mechanical vibrations; harmonic motion and shapes; the geometry of the laws of motion; and the geometry of oscillatory motions. A final section surveys experimentation and its procedures, with explanations of magnetic fields, the fields of coils, and variables involved in coil design. Appropriate for anyone with a grasp of high-school-level mathematics, this book is as well suited to classroom use as it is to self-study.
Автор: Hodel, Richard Название: An Introduction to Mathematical Logic ISBN: 0486497852 ISBN-13(EAN): 9780486497853 Издательство: Dover Рейтинг: Цена: 3443 р. Наличие на складе: Поставка под заказ.
Описание: Widely praised for its clarity and thorough coverage, this comprehensive overview of mathematical logic is suitable for readers of many different backgrounds. Designed primarily for advanced undergraduates and graduate students of mathematics, the treatment also contains much of interest to advanced students in computer science and philosophy. An introductory section prepares readers for successive chapters on propositional logic and first-order languages and logic. Subsequent chapters shift in emphasis from an approach to logic from a mathematical point of view to the interplay between mathematics and logic. Topics include the theorems of Godel, Church, and Tarski on incompleteness, undecidability, and indefinability; a rigorous treatment of recursive functions and recursive relations; computability theory; and Hilbert's Tenth Problem. Numerous exercises appear throughout the text, and an appendix offers helpful background on number theory.