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Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover Books on Mathematics) 0009-Revised Edition

by Milton Abramowitz (Editor), Irene A. Stegun (Editor)

4.5 150 ratings

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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.

Despite the increasing use of computers, the basic need for mathematical tables continues. Tables serve a vital role in preliminary surveys of problems before programming for machine operation, and they are indispensable to thousands of engineers and scientists without access to machines. Because of automatic computers, however, and because of recent scientific advances, a greater variety of functions and a higher accuracy of tabulation than have been available until now are required.

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.

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 over 100 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 edition contains every page of the original government publication.

Dover is widely recognized for a magnificent mathematics list featuring such world-class theorists as Paul J. Cohen (Set Theory and the Continuum Hypothesis), Alfred Tarski (Undecidable Theories), Gary Chartrand (Introductory Graph Theory), Hermann Weyl (The Concept of a Riemann Surface), Shlomo Sternberg (Dynamical Systems), and multiple works by C. R. Wylie in geometry, plus Stanley J. Farlow's Partial Differential Equations for Scientists and Engineers.

ISBN-10

0486612724
ISBN-13

978-0486612720
Edition

0009-Revised
Publisher

Dover Publications
Publication date

June 1, 1965
Language

English
Dimensions

8.25 x 1.75 x 10.75 inches
Print length

1046 pages
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Product details

Publisher ‏ : ‎ Dover Publications; 0009-Revised edition (June 1, 1965)
Language ‏ : ‎ English
Paperback ‏ : ‎ 1046 pages
ISBN-10 ‏ : ‎ 0486612724
ISBN-13 ‏ : ‎ 978-0486612720
Item Weight ‏ : ‎ 3.17 pounds
Dimensions ‏ : ‎ 8.25 x 1.75 x 10.75 inches

Best Sellers Rank: #606,631 in Books (See Top 100 in Books)
- #54 in Functional Analysis Mathematics
- #145 in Mathematics Reference (Books)
- #395 in Mathematics Study & Teaching (Books)

Customer Reviews:
4.5 150 ratings

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4.5 out of 5

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AnalogJoe

Comprehensive and accurate

Reviewed in the United States on January 21, 2016

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This book is great to have around, it offers tons of solutions to integrals, series, functions, etc... this is a must have for every scientist or engineer, however there are a lot of numerical tables which are by now completely obsolete, for instance Bessel function values, most of those tables are easily and more accurately calculated by Matlab. What is really useful in this book are not the numerical but the analyitical solutions to many, many functions.

Event today with software like Mathematica this book will still be useful, specially in those cases in which the software just doesnt give you the correct or expected answer. Im an EE grad student, and this book by Abramowitz coupled with Table of Integrals, Series, and Products, Eighth Edition have provided me with many useful analytic solutions to very difficult integrals and functions which appear in engineering, I highly recommend both books.

8 people found this helpful

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Amazon Customer

A Member of The Big Four...

Reviewed in the United States on November 28, 2012

Verified Purchase

This wonderful volume is one of four works I always keep in digital or desk drawer reach while reading/studying/ referencing any other math book or journal article, the complete list being:

-- Encyclopedia Of Mathematics (Science Encyclopedia)

-- The Princeton Companion to Mathematics

-- Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover Books on Mathematics)

-- NIST Handbook of Mathematical Functions (Being of course the 2010 update of the Abramowitz classic above).

Given these four, there is hardly a topic from among the current 495 math fields of study that isn't at least explained in enough detail to save LOTS of time on link expeditions. At minimum, these give head starts on alphabetized keywords that will quickly fill holes in any research project, class, or syllabus.

8 people found this helpful

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Miguel Angel Aguilar

Very nice book!

Reviewed in the United States on November 13, 2021

Verified Purchase

A very excellent book. Just like new. Thank you very much!!

Reviewed in the United States on September 23, 2021

Verified Purchase

Hard to understand. But useful.

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Amazon Customer

but this Handbook is good enough. Carlos Alberto Dantas Moura

Reviewed in the United States on January 25, 2017

Verified Purchase

This book is a well-known classic which deserves all praises.
I used the volume available in my work's library during many years.
However, I retired recently and rushed to get my own copy.
There seems to be be other similar books, some with added
material, but this Handbook is good enough.
Carlos Alberto Dantas Moura

One person found this helpful

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RM in AZ

A classic, and still useful.

Reviewed in the United States on February 19, 2013

Verified Purchase

My granddaughter, a university student, wanted her own copy of this old book, which I have had for years. She and her friends were fascinated by the tables, and my account of how we used them before scientific calculators were available to everyone. This is still a useful reference, with lots of formulas. I'll probably get a more recent handbook, but this was a good deal.

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WillH

Great content, poor quality eBook

Reviewed in the United States on May 5, 2012

Verified Purchase

I bought this book for its section on statistical distributions. It is among the few resources available for somebody who wants to numerically calculate these sorts of things and not resort to look up tables or programs somebody else has written. It is very heavy on the math with virtually no explanation in laymans terms; It's exactly what I was looking for.

Unfortunately the eBook is a collection of scanned pages and the resolution of the pages isn't high enough to resolve the mathematical formulas clearly. On my iPad 2 I have to zoom right in and squint to try and figure out what symbol the blob of pixels represents.

Navigation is also a problem. Each page has two scanned images, despite each image being of the same page. Forget about clicking references or jumping to a page number.

As a book, the content is unsurpassed, but I wouldn't recommend the eBook version because of the poor quality conversion. I wish I had the paper copy.

5 people found this helpful

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Tang Xiaping

nice feedback experience from seller

Reviewed in the United States on April 2, 2011

Verified Purchase

The book I bought from the seller is not satisfied at first. As I didn't know that the book is in "acceptable" condition. So I give a bad feedback for the book. The seller contacts with me very quickly after I gave the feedback. We solve the problem very quickly. And I am very satisfied with the final result. Nice seller to choose.

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Guilherme

Livro de referência muito bom para áreas de exatas e engenharias

Reviewed in Brazil on January 12, 2024

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Manual matemático interessante e útil para a realização de muitos tipos de cálculo, ainda que o atual nível tecnológico da computação certamente já tenha colocado todo o seu conteúdo em “softwares” para aplicações científico-tecnológicas. A edição do livro data de 1965 e a reimpressão, com diversas correções, é de 1970.
O manual, ao lado de inúmeras equações de diversos campos da matemática, traz uma quantidade significativa de gráficos e de tabelas numéricas para viabilizar cálculos práticos em problemas que utilizam as referidas equações. Destaco a presença de exemplos demonstrando a utilização das tabelas.
Para quem estuda e/ou trabalha com exatas e engenharias, este livro funciona muito bem com a famosa “Tabela Schaum” (Manual de Fórmulas, Métodos e Tabelas de Matemática, do autor Murray Spiegel e editado pela McGraw-Hill).
O exemplar adquirido é usado e, ainda que trazendo marcas de frequente utilização, está em bom estado :-)
A entrega ocorreu em prazo mais rápido que o previsto, mesmo sendo compra internacional, e o vendedor foi cuidadoso, embalando o livro num pacote plástico adicional, totalmente vedado, além da caixa-padrão, para protegê-lo até a chegada. Estou bem satisfeito com a aquisição :-D

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Darren Hennig

Superb reference text for physics, engineering and more!

Reviewed in Canada on August 30, 2023

Verified Purchase

Very nice 1000 page book - has formulae and calculated (to 10 digits + in transcendentals and connstants).

Alloows one to use a calculator or slide rule (!!) in lieu of a computer if doing field remote calcs, or the power dies! Also useful to add iterations into spreadsheets for determining values. A must-have for those needing an excellent reference with tables, calcs, formulae, and more. Highly recommended!

DZ

Ottimo

Reviewed in Italy on May 2, 2023

Verified Purchase

Per chi preferisce essere almeno un po indipendente dai fogli elettronici.

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Un scientifique

Indispensable en analyse

Reviewed in France on September 3, 2022

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C'est un atlas complet des fonctions speciales. Vraiment tres utiles.

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Cliente de Amazon

Excelente libro de consulta

Reviewed in Mexico on September 21, 2017

Verified Purchase

Soy alumno doctoral en estadística aplicada. Este libro está sobrado para usarse como libro de consulta. La edición se me hace aceptable aunque la letra puede ser considerada un poco chica. Aún así, una excelente herramienta para mi trabajo.

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