Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (Dover Books on Mathematics) by Milton Abramowitz (PDF)

Description

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 othersEach 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 low-cost 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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Hard to understand. But useful.

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

⭐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

⭐have provided me with many useful analytic solutions to very difficult integrals and functions which appear in engineering, I highly recommend both books.

⭐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.

⭐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:–

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⭐(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.

⭐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.

⭐This is a classic reference manual for special functions. Everyone who works in science or engineering should keep a copy of this book around as a reference. You never know when you need to look up the definition of some special function, which may have more than one convention, and its relationship to some other special function. I know first hand that many of the special functions defined in the R Statistical Computing language are defined according to this book, and the R help references these definitions. Dover Publication also produces a paperback version of this book.

⭐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 addedmaterial, but this Handbook is good enough.Carlos Alberto Dantas Moura

⭐This is an excellent, and one of the standar, reference books for functions and formulae. If you do much applied mathematics at all, then this book can save a large amount of time with its large list of properties of the various functions.Large coverage of functions such as bessel functions, and hypergeometric functions.It should be on the desks of most physicists and engineers.

⭐this book is a must have for anyone who works in applied math, and a used copy is a good buy

⭐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.If you’re looking for this you probably know what your looking for. It’s not a text book…it won’t teach you calculus/relativity or solving equations…what it does have is a “gigantic” library of functions/approximations and old school log tables (as well as pages of other tyopes of tables…exp, powers etc…). Graphs, pictures of functions, Reimann functions…the list goes on…5 stars seems a bit silly…I wouldnt say “I love it”…but it does what it says and is the one stop shop (I guess) for anything to do with mathematical functions…

⭐Es el libro de referencia de funciones matemáticas y constantes físicas y matemáticas por excelencia. Además, el precio es más que razonable por su tamaño. Sólo tengo una queja, y es que en algunas fórmulas los caracteres son tan pequeños que son prácticamente ilegibles. Por ejemplo, en algunas fórmulas es muy difícil distinguir un 2 de una “a”. Esperaba que este error fuese subsanado en esta edición moderna, pero sigue estando. Las constantes físicas tampoco han sido actualizadas.

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