Handbook of mathematical formulas and integrals / Alan Jeffrey.

Format:

Book

Author/Creator:

Jeffrey, Alan.

Language:

English

Subjects (All):

Mathematics--Tables.

Mathematics.

Mathematics--Formulae.

Physical Description:

1 online resource (461 p.)

Edition:

3rd ed.

Place of Publication:

Amsterdam ; Boston : Elsevier Academic Press, c2004.

Language Note:

English

Summary:

The updated Handbook is an essential reference for researchers and students in applied mathematics, engineering, and physics. It provides quick access to important formulas, relations, and methods from algebra, trigonometric and exponential functions, combinatorics, probability, matrix theory, calculus and vector calculus, ordinary and partial differential equations, Fourier series, orthogonal polynomials, and Laplace transforms. Many of the entries are based upon the updated sixth edition of Gradshteyn and Ryzhik's Table of Integrals, Series, and Products and other important ref

Contents:

Front Cover; MATHEMATICAL FORMULAS AND INTEGRALS; Copyright Page; Contents; Preface; Preface to the Second Edition; Index of Special Functions and Notations; Chapter 0. Quick Reference List of Frequently Used Data; 0.1 Useful Identities; 0.2 Complex Relationships; 0.3 Constants; 0.4 Derivatives of Elementary Functions; 0.5 Rules of Differentiation and Integration; 0.6 Standard Integrals; 0.7 Standard Series; 0.8 Geometry; Chapter 1. Numerical, Algebraic, and Analytical Results for Series and Calculus; 1.1 Algebraic Results Involving Real and Complex Numbers; 1.2 Finite Sums

1.3 Bernoulli and Euler Numbers and Polynomials1.4 Determinants; 1.5 Matrices; 1.6 Permutations and Combinations; 1.7 Partial Fraction Decomposition; 1.8 Convergence of Series; 1.9 Infinite Products; 1.10 Functional Series; 1.11 Power Series; 1.12 Taylor Series; 1.13 Fourier Series; 1.14 Asymptotic Expansions; 1.15 Basic Results from the Calculus; Chapter 2. Functions and Identities; 2.1 Complex Numbers and Trigonometric and Hyperbolic Functions; 2.2 Logarithms and Exponentials; 2.3 The Exponential Function; 2.4 Trigonometric Identities; 2.5 Hyperbolic Identities; 2.6 The Logarithm

2.7 Inverse Trigonometric and Hyperbolic Functions2.8 Series Representations of Trigonometric and Hyperbolic Functions; 2.9 Useful Limiting Values and Inequalities Involving Elementary Functions; Chapter 3. Derivatives of Elementary Functions; 3.1 Derivatives of Algebraic, Logarithmic, and Exponential Functions; 3.2 Derivatives of Trigonometric Functions; 3.3 Derivatives of Inverse Trigonometric Functions; 3.4 Derivatives of Hyperbolic Functions; 3.5 Derivatives of Inverse Hyperbolic Functions; Chapter 4. Indefinite Integrals of Algebraic Functions

4.1 Algebraic and Transcendental Functions4.2 Indefinite Integrals of Rational Functions; 4.3 Nonrational Algebraic Functions; Chapter 5 Indefinite Integrals of Exponential Functions; 5.1 Basic Results; Chapter 6. Indefinite Integrals of Logarithmic Functions; 6.1 Combinations of Logarithms and Polynomials; Chapter 7. Indefinite Integrals of Hyperbolic Functions; 7.1 Basic Results; 7.2 Integrands Involving Powers of sinh(bx) or cosh(bx); 7.3 Integrands Involving (a ± bx)m sinh(cx) or (a + bx)m cosh(cx); 7.4 Integrands Involving xm sinhnx or xm coshnx

7.5 Integrands Involving xm sinh-nx or xm cosh-nx7.6 Integrands Involving (1 ± cosh x)-m; 7.7 Integrands Involving sinh(ax)cosh-nx or cosh(ax)sinh-nx; 7.8 Integrands Involving sinh(ax + b) and cosh(cx + d); 7.9 Integrands Involving tanh kx and coth kx; 7.10 Integrands Involving (a + bx)m sinh kx or (a + bx)m cosh kx; Chapter 8. Indefinite Integrals Involving Inverse Hyperbolic Functions; 8.1 Basic Results; 8.2 Integrands Involving x-n arcsinh(x/a) or x-n arccosh(x/a); 8.3 Integrands Involving xn arctanh(x/a) or xn arccoth(x/a); 8.4 Integrands Involving x-n arctanh(x/a) or x-n arccoth(x/a)

Chapter 9. Indefinite Integrals of Trigonometric Functions

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 439-441) and index.

ISBN:

1-281-02049-4

9786611020491

0-08-052301-3

OCLC:

437182443