CRC Standard Mathematical Tables and Formulae, 32nd Edition: 32nd Edition (Hardback) book cover

CRC Standard Mathematical Tables and Formulae, 32nd Edition

Edited by Daniel Zwillinger

© 2011 – CRC Press

833 pages | 71 B/W Illus.

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Hardback: 9781439835487
pub: 2011-06-22
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pub: 2011-06-22
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About the Book

With over 6,000 entries, CRC Standard Mathematical Tables and Formulae, 32nd Edition continues to provide essential formulas, tables, figures, and descriptions, including many diagrams, group tables, and integrals not available online. This new edition incorporates important topics that are unfamiliar to some readers, such as visual proofs and sequences, and illustrates how mathematical information is interpreted. Material is presented in a multisectional format, with each section containing a valuable collection of fundamental tabular and expository reference material.

New to the 32nd Edition

  • A new chapter on Mathematical Formulae from the Sciences that contains the most important formulae from a variety of fields, including acoustics, astrophysics, epidemiology, finance, statistical mechanics, and thermodynamics
  • New material on contingency tables, estimators, process capability, runs test, and sample sizes
  • New material on cellular automata, knot theory, music, quaternions, and rational trigonometry
  • Updated and more streamlined tables

Retaining the successful format of previous editions, this comprehensive handbook remains an invaluable reference for professionals and students in mathematical and scientific fields.


Praise for Previous Editions:

An excellent reference resource for all readership levels, this guide offers easy navigation through a browseable table of contents and an extensive index. It follows a natural progression for those studying the subject. It is logical, useful, and affordable. Summing up: Highly Recommended.

—CHOICE, September 2003

The 31st Edition of the CRC Standard Mathematical Tables and Formulae is, without a doubt, the new and improved bible of mathematics. It is an outstanding reference book, containing more than 30 new sections, covering more than 3,000 items, and including tables, properties, etc. The index has been revamped to make it faster and easier to find results.

Author Daniel Zwillinger has done an excellent job keeping the same successful format that has characterized earlier editions of the handbook. …

Mathematicians will find this handbook indispensable — an absolute must-have desk reference. The ready access of tables that may be needed in mathematical endeavors will make life much easier for engineers, scientists, mathematicians, or even for those who are in the process of studying these and related subjects.

John Vacca, former computer security official for NASA's space station program (Freedom), The Barnes & Noble Review

Table of Contents

Numbers and Elementary Mathematics

Proofs without words


Special numbers

Number theory

Series and products


Elementary algebra


Vector algebra

Linear and matrix algebra

Abstract algebra

Discrete Mathematics

Set theory



Combinatorial design theory

Difference equations


Euclidean geometry

Coordinate systems in the plane

Plane symmetries or isometries

Other transformations of the plane



Surfaces of revolution: the torus


Spherical geometry and trigonometry


Special plane curves

Coordinate systems in space

Space symmetries or isometries

Other transformations of space

Direction angles and direction cosines


Lines in space




Differential geometry


Differential calculus

Differential forms


Table of indefinite integrals

Table of definite integrals

Ordinary differential equations

Partial differential equations

Integral equations

Tensor analysis

Orthogonal coordinate systems

Interval analysis

Real analysis

Generalized functions

Complex analysis

Special Functions

Ceiling and floor functions


Logarithmic functions

Exponential function

Trigonometric functions

Circular functions and planar triangles

Tables of trigonometric functions

Angle conversion

Inverse circular functions

Hyperbolic functions

Inverse hyperbolic functions

Gudermannian function

Orthogonal polynomials

Gamma function

Beta function

Error functions

Fresnel integrals

Sine, cosine, and exponential integrals


Hypergeometric functions

Legendre functions

Bessel functions

Elliptic integrals

Jacobian elliptic functions

Clebsch–Gordan coefficients

Integral transforms: Preliminaries

Fourier integral transform

Discrete Fourier transform (DFT)

Fast Fourier transform (FFT)

Multidimensional Fourier transforms

Laplace transform

Hankel transform

Hartley transform

Mellin transform

Hilbert transform


Tables of transforms

Probability and Statistics

Probability theory

Classical probability problems

Probability distributions

Queuing theory

Markov chains

Random number generation

Control charts and reliability


Confidence intervals

Tests of hypotheses

Linear regression

Analysis of variance (ANOVA)

Sample size

Contingency tables

Probability tables

Scientific Computing

Basic numerical analysis

Numerical linear algebra

Numerical integration and differentiation

Mathematical Formulae from the Sciences



Atmospheric physics

Atomic physics

Basic mechanics

Beam dynamics

Classical mechanics

Coordinate systems – Astronomical

Coordinate systems – Terrestrial

Earthquake engineering

Electromagnetic transmission

Electrostatics and magnetism

Electronic circuits



Fluid mechanics

Fuzzy logic

Human body

Image processing matrices


Modeling physical systems


Population genetics

Quantum mechanics


Relativistic mechanics

Solid mechanics

Statistical mechanics



Calendar computations

Cellular automata

Communication theory

Control theory

Computer languages


Discrete dynamical systems and chaos

Electronic resources

Elliptic curves

Financial formulae

Game theory

Knot theory


Moments of inertia


Operations research

Recreational mathematics

Risk analysis and decision rules

Signal processing

Symbolic logic


Voting power

Greek alphabet

Braille code

Morse code

List of References

List of Figures

List of Notation


About the Editor

Daniel Zwillinger has more than 25 years of proven technical expertise in numerous areas of engineering and the physical sciences. He earned a Ph.D. in applied mathematics from the California Institute of Technology.

About the Series

Advances in Applied Mathematics

Learn more…

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Mathematical Physics