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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 over100 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.

Statistical physics, and more specifically, the theory of transitions between states of matter, more or less defines what we know about 'everyday' matter and its transformations.

The major aim of this serial is to provide review articles that can serve as standard references for research workers in the field, and for graduate students and others wishing to obtain reliable information on important recent developments.

Organized into eight chapters, this volume starts with an overview of the functional analysis in the study of several concrete models. This book then discusses how to generalize the Lebesgue integral to work with functions on the real line and with Borel sets. This text also explores the properties of finite-dimensional vector spaces. Other chapters discuss the normed linear spaces, which have the property of being complete. This monograph further examines the general class of topologized vector spaces and the spaces of distributions that arise in a wide variety of physical problems and functional situations.

This book is a valuable resource for mathematicians and physicists. Students and researchers in the field of geometry will also find this book extremely useful.

Methods for approximating functions on the real line are treated first, as they provide the foundations for the methods on the sphere and the ball and are useful for the analysis of time-dependent (spherical) problems. The author then examines the transfer of these spherical methods to problems on the ball, such as the modeling of the Earth’s or the brain’s interior. Specific topics covered include:

* the advantages and disadvantages of Fourier, spline, and wavelet methods

* theory and numerics of orthogonal polynomials on intervals, spheres, and balls

* cubic splines and splines based on reproducing kernels

* multiresolution analysis using wavelets and scaling functions

This textbook is written for students in mathematics, physics, engineering, and the geosciences who have a basic background in analysis and linear algebra. The work may also be suitable as a self-study resource for researchers in the above-mentioned fields.

- From the Preface to the Second Edition

Although the exponential growth of computer power has advanced the importance of simulations and visualization tools for elaborating new models, designs and technologies, the discipline of fluid mechanics is still large, and turbulence in flows remains a challenging problem in classical physics. Like its predecessor, the revised and expanded Second Edition of this book addresses the basic principles of fluid mechanics and solves fluid flow problems where viscous effects are the dominant physical phenomena.

Much progress has occurred in the half a century that has passed since the edition of 1964. As predicted, aspects of hydrodynamics once considered offbeat have risen to importance. For example, the authors have worked on problems where variations in viscosity and surface tension cannot be ignored. The advent of nanotechnology has broadened interest in the hydrodynamics of thin films, and hydromagnetic effects and radiative heat transfer are routinely encountered in materials processing. This monograph develops the basic equations, in the three most important coordinate systems, in a way that makes it easy to incorporate these phenomena into the theory.

The book originally described by Prof. Langlois as "a monograph on theoretical hydrodynamics, written in the language of applied mathematics" offers much new coverage including the second principle of thermodynamics, the Boussinesq approximation, time dependent flows, Marangoni convection, Kovasznay flow, plane periodic solutions, Hele-Shaw cells, Stokeslets, rotlets, finite element methods, Wannier flow, corner eddies, and analysis of the Stokes operator.

In-depth explorations of the Dirac theory of the electron and of radiative effects include brief accounts of relevant experiments. The specific application of general field-theoretic results to atomic systems also receives a thorough examination. Author Hans A. Bethe (1906–2005), Professor of Physics at Cornell University, won the Nobel Prize in Physics in 1967. Co-author Edwin E. Salpeter is James Gilbert White Distinguished Professor of the Physical Sciences at Cornell University.

Timeless and collectible, the lectures are essential reading, not just for students of physics but for anyone seeking an introduction to the field from the inimitable Feynman.

The fifth problem of algebraic regression, the system of conditional equations of homogeneous and inhomogeneous type, is formulated. An analogue is the inhomogeneous general linear Gauss-Markov model with fixed and random effects, also called mixed model. Collocation is an example. Another speciality is our sixth problem of probabilistic regression, the model "errors-in-variable”, also called Total Least Squares, namely SIMEX and SYMEX developed by Carroll-Cook-Stefanski-Polzehl-Zwanzig. Another speciality is the treatment of the three-dimensional datum transformation and its relation to the Procrustes Algorithm. The sixth problem of generalized algebraic regression is the system of conditional equations with unknowns, also called Gauss-Helmert model. A new method of an algebraic solution technique, the concept of Groebner Basis and Multipolynomial Resultant is finally presented, illustrating polynomial nonlinear equations.

A great part of the work is presented in four Appendices. Appendix A is a treatment, of tensor algebra, namely linear algebra, matrix algebra and multilinear algebra. Appendix B is devoted to sampling distributions and their use in terms of confidence intervals and confidence regions. Appendix C reviews the elementary notions of statistics, namely random events and stochastic processes. Appendix D introduces the basics of Groebner basis algebra, its careful definition, the Buchberger Algorithm, especially the C. F. Gauss combinatorial algorithm

Throughout we give numerous examples and present various test computations. Our reference list includes more than 3000 references, books and papers.

This book is a source of knowledge and inspiration not only for geodesists and mathematicians, but also for engineers in general, as well as natural scientists and economists. Inference on effects which result in observations via linear and nonlinear functions is a general task in science. The authors provide a comprehensive in-depth treatise on the analysis and solution of such problems. I wish all readers of this brilliant encyclopaedic book this pleasure and much benefit.

Prof. Dr. Harro Walk

Institute of Stochastics and Applications, Universität Stuttgart, Germany.

This book contains six chapters and begins with a discussion of the basic principles and limitations of numerical integration. The succeeding chapters present the approximate integration rules and formulas over finite and infinite intervals. These topics are followed by a review of error analysis and estimation, as well as the application of functional analysis to numerical integration. A chapter describes the approximate integration in two or more dimensions. The final chapter looks into the goals and processes of automatic integration, with particular attention to the application of Tschebyscheff polynomials.

This book will be of great value to theoreticians and computer programmers.

The book provides a discussion on the phenomenon in fluid mechanics and their intercorrelations, such as heat transfer, diffusion in fluids, acoustics, theory of combustion, dynamics of superfluids, and relativistic fluid dynamics.

The text will be of great interest to researchers whose work involves or concerns fluid mechanics.

Among a wealth of enhancements, this edition analyzes, updates, and validates molecular formulas and weights, boiling and melting points, densities, and refractive indexes in the Physical Constants of Organic Compounds Table through comparisons with critically evaluated data from the NIST Thermodynamics Research Center.

New Tables:Analytical Chemistry

Abbreviations Used In Analytical Chemistry Basic Instrumental Techniques of Analytical Chemistry Correlation Table for Ultraviolet Active Functionalities Detection of Outliers in Measurements

Polymer Properties

Second Virial Coefficients of Polymer Solutions

Updated Tables:

Properties of the Elements and Inorganic Compounds

Update of the Melting, Boiling, Triple, and Critical Points of the Elements

Fluid Properties

Major update and expansion of Viscosity of Gases table Major update and expansion of Thermal Conductivity of Gases table Major update of Properties of Cryogenic Fluids Major update of Recommended Data for Vapor-Pressure Calibration Expansion of table on the Viscosity of Liquid Metals Update of Permittivity (Dielectric Constant) of Gases table Added new refrigerant R-1234yf to Thermophysical Properties of Selected Fluids at Saturation table

Molecular Structure and Spectroscopy

Major update of Atomic Radii of the Elements Update of Bond Dissociation Energies Update of Characteristic Bond Lengths in Free Molecules

Atomic, Molecular, and Optical Physics

Update of Electron Affinities Update of Atomic and Molecular Polarizabilities

Nuclear and Particle Physics

Major update of the Table of the Isotopes

Properties of Solids

Major update and expansion of the Electron Inelastic Mean Free Paths table Update of table on Semiconducting Properties of Selected Materials

Geophysics, Astronomy, and Acoustics

Update of the Global Temperature Trend table to include 2010 data

Health and Safety Information

Major update of Threshold Limits for Airborne Contaminants

The Handbook is also available as an eBook.

This revision is a cover-to-cover expansion and renovation of the third edition. It now includes an introduction to tensor computations and brand new sections on • fast transforms• parallel LU• discrete Poisson solvers• pseudospectra• structured linear equation problems• structured eigenvalue problems• large-scale SVD methods• polynomial eigenvalue problems

Matrix Computations is packed with challenging problems, insightful derivations, and pointers to the literature—everything needed to become a matrix-savvy developer of numerical methods and software.

This book presents a most lucid introduction to the Rayleigh-Bénard problem: it has also been applauded for its thorough, clear coverage of the theory of instabilities causing convection.

Dr. Chandrasekhar considers most of the typical problems in hydromagnetic stability, with the exception of viscous shear flow; a specialized domain deserving a book unto itself. Contents include: Rotation; Stability of More General Flows; Bénard Problem; Gravitational Equilibrium and Instability; Stability of a Magnetic Field; Thermal Instability of a Layer of Fluid heated from Below; Rayleigh-Taylor Instability; Kelvin-Helmholtz Instability; and Onset of Thermal Instability in Fluid Spheres and Spherical Shells.

Each chapter is accompanied by a section of bibliographical notes: indexes locating definitions and theorems are also provided. Graduate students in theoretical and experimental physics, as well as physicists in diverse fields, will immediately remark upon the clear exposition, and be glad this book is now so readily available.

This high-level treatment by a noted mathematician considers one-dimensional singular integral equations involving Cauchy principal values. Its coverage includes such topics as the Hölder condition, Hilbert and Riemann-Hilbert problems, the Dirichlet problem, inversion formulas for arcs, and many other areas. Intended for graduate students, applied and pure mathematicians, engineers, physicists, and researchers in a variety of scientific and industrial fields, this text is accessible to students acquainted with the basic theory of functions of a complex variable and the theory of Fredholm integral equations.

This revision will make this book mroe attractive as a textbook in functional analysis. Further refinement of coverage of physical topics will also reinforce its well-established use as a course book in mathemtical physics.