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The Table of Integrals, Series, and Products is the essential reference for integrals in the English language. Mathematicians, scientists, and engineers, rely on it when identifying and subsequently solving extremely complex problems. Since publication of the first English-language edition in 1965, it has been thoroughly revised and enlarged on a regular basis, with substantial additions and, where necessary, existing entries corrected or revised. The seventh edition includes a fully searchable CD-Rom.- Fully searchable CD that puts information at your fingertips included with text- Most up to date listing of integrals, series andproducts - Provides accuracy and efficiency in work
Table of Integrals, Series, and Products provides information pertinent to the fundamental aspects of integrals, series, and products. This book provides a comprehensive table of integrals. Organized into 17 chapters, this book begins with an overview of elementary functions and discusses the power of binomials, the exponential function, the logarithm, the hyperbolic function, and the inverse trigonometric function. This text then presents some basic results on vector operators and coordinate systems that are likely to be useful during the formulation of many problems. Other chapters consider inequalities that range from basic algebraic and functional inequalities to integral inequalities and fundamental oscillation and comparison theorems for ordinary differential equations. This book discusses as well the important part played by integral transforms. The final chapter deals with Fourier and Laplace transforms that provides so much information about other integrals. This book is a valuable resource for mathematicians, engineers, scientists, and research workers.
An extensive summary of mathematical functions that occur in physical and engineering problems
Biography of Howard Aiken, a major figure of the early digital era, by a major historian of science who was also a colleague of Aiken's at Harvard. Howard Hathaway Aiken (1900-1973) was a major figure of the early digital era. He is best known for his first machine, the IBM Automatic Sequence Controlled Calculator or Harvard Mark I, conceived in 1937 and put into operation in 1944. But he also made significant contributions to the development of applications for the new machines and to the creation of a university curriculum for computer science. This biography of Aiken, by a major historian of science who was also a colleague of Aiken's at Harvard, offers a clear and often entertaining introduction to Aiken and his times. Aiken's Mark I was the most intensely used of the early large-scale, general-purpose automatic digital computers, and it had a significant impact on the machines that followed. Aiken also proselytized for the computer among scientists, scholars, and businesspeople and explored novel applications in data processing, automatic billing, and production control. But his most lasting contribution may have been the students who received degrees under him and then took prominent positions in academia and industry. I. Bernard Cohen argues convincingly for Aiken's significance as a shaper of the computer world in which we now live.
Asymptotics and Special Functions provides a comprehensive introduction to two important topics in classical analysis: asymptotics and special functions. The integrals of a real variable and contour integrals are discussed, along with the Liouville-Green approximation and connection formulas for solutions of differential equations. Differential equations with regular singularities are also considered, with emphasis on hypergeometric and Legendre functions. Comprised of 14 chapters, this volume begins with an introduction to the basic concepts and definitions of asymptotic analysis and special functions, followed by a discussion on asymptotic theories of definite integrals containing a parameter. Contour integrals as well as integrals of a real variable are described. Subsequent chapters deal with the analytic theory of ordinary differential equations; differential equations with regular and irregular singularities; sums and sequences; and connection formulas for solutions of differential equations. The book concludes with an evaluation of methods used in estimating (as opposed to bounding) errors in asymptotic approximations and expansions. This monograph is intended for graduate mathematicians, physicists, and engineers.
A massive compendium of useful information, this volume represents a valuable tool for applied mathematicians in many areas of academia and industry. A dozen useful tables supplement the text. 1962 edition.