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

4.6 4.6 out of 5 stars 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.


 

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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 ‏ : ‎ 3.45 pounds
  • Dimensions ‏ : ‎ 8.25 x 1.75 x 10.75 inches
  • Customer Reviews:
    4.6 4.6 out of 5 stars 150 ratings

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Milton Abramowitz
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Customer reviews

4.6 out of 5 stars
150 global ratings

Customers say

Customers find the book an excellent reference book with lots of formulas. They also describe the structure as very extensive and organized. Opinions are mixed on readability, with some finding it well-put together and others saying it was put together without care for readability.

AI-generated from the text of customer reviews

20 customers mention "Content"20 positive0 negative

Customers find the book an excellent reference book with awesome stuff. They also say it's very useful, indispensable, and a good reference for formulas. Readers also say the book is great to have around, offering tons of solutions to integrals, series, functions, and more.

"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..." Read more

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

"Great text for anyone in an engineering, science or math field...." Read more

"This book is a well-known classic which deserves all praises.I used the volume available in my work's library during many years...." Read more

3 customers mention "Structure"3 positive0 negative

Customers find the book very extensive, organized, and concise. They also say the tables greatly facilitate hard work.

"...The list of special functions is impressive and it also contains many other useful tables." Read more

"...present the results in an elegant, concise and tables greatly facilitate the hard work. A serious and comprehensive work" Read more

"...Even in the age of Internet, this book is very extensive organized and can help find useful relations one was not aware of." Read more

6 customers mention "Readability"3 positive3 negative

Customers are mixed about the readability. Some mention that the book is put together well, very professional, and presents the results in an elegant, concise manner. However, others say that it was produced without care for readability and as a poor quality eBook.

"...Overall the book is put together well. The list of special functions is impressive and it also contains many other useful tables." Read more

"...the equations in the graphics are of poor quality and sometimes barely readable. Kindle ought to be better but they continue to suck at graphics." Read more

"excellent, very professional, present the results in an elegant, concise and tables greatly facilitate the hard work. A serious and comprehensive work" Read more

"...But this publisher just spat out this edition without care for readability. I wasted my money buying this edition. Don't waste yours." Read more

3 customers mention "Visuals"0 positive3 negative

Customers find the visuals in the book not good.

"...the eBook is a collection of scanned pages and the resolution of the pages isn't high enough to resolve the mathematical formulas clearly...." Read more

"Kindle graphics not good..." Read more

"Unreadable, poorly-defined graphics..." Read more

Top reviews from the United States

Reviewed in the United States on January 21, 2016
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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Reviewed in the United States on November 13, 2021
A very excellent book. Just like new. Thank you very much!!
Reviewed in the United States on November 28, 2012
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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Reviewed in the United States on April 11, 2015
Great text for anyone in an engineering, science or math field. Although most personal computers have processors capable of evaluating these tables, there is still no comparison to being able to reference the value instantly. Especially useful for quick checks. I can always get more accurate results online or with interpolation, but I bask park answer helps you know if the extra work is required. Overall the book is put together well. The list of special functions is impressive and it also contains many other useful tables.
Reviewed in the United States on January 25, 2017
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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Reviewed in the United States on February 19, 2013
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.
Reviewed in the United States on May 5, 2012
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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Reviewed in the United States on November 12, 2012
I used this book as an undergrad, and now that I'm a professor, I use it again and recommend it to my students. It's a great resource for physicists and engineers who deal with complex functions and would rather get to the heart of the matter than waste time re-deriving an integral.

Top reviews from other countries

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Guilherme
5.0 out of 5 stars Livro de referência muito bom para áreas de exatas e engenharias
Reviewed in Brazil on January 12, 2024
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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Guilherme
5.0 out of 5 stars Livro de referência muito bom para áreas de exatas e engenharias
Reviewed in Brazil on January 12, 2024
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
5.0 out of 5 stars Superb reference text for physics, engineering and more!
Reviewed in Canada on August 30, 2023
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!
Cliente Amazon
5.0 out of 5 stars Excellent
Reviewed in Italy on February 14, 2024
Everything ok, shipping on time and book in excellent condition.
Un scientifique
5.0 out of 5 stars Indispensable en analyse
Reviewed in France on September 3, 2022
C'est un atlas complet des fonctions speciales. Vraiment tres utiles.
arianna
5.0 out of 5 stars Per chi desidera avere una raccolta completa di formule e tabelle matematiche.
Reviewed in Italy on June 10, 2020
Una completissima raccolta di formule tabelle numeriche con molti decimali a disposizione ed indicazioni per l'interpolazione dei valori. E' difficile raggiungere una precisione simile con calcolatrici da tavolo o semplici programmi. Sono presenti tra i tanti le funzioni di Bessel, Ipergeometrica, integrali ellittici, funzione theta,
polinomi ortogonali, analisi cominatoria ... trasformate di Laplace.
Sicuramente utilizzabile da fisici e matematici che devono fare calcoli.
Potrebbe essere stato utile a Katherine Johnson (vedi film HiddenFigures- Il diritto di contare).

Questa ristampa della Dover Publications nonostane le sue dimensioni più di 1000 pagine è molto robusta nella rilegatura.