Handbook of Mathematical Formulas and IntegralsThe extensive additions, and the inclusion of a new chapter, has made this classic work by Jeffrey, now joined by co-author Dr. H.H. Dai, an even more essential reference for researchers and students in applied mathematics, engineering, and physics. It provides quick access to important formulas, relationships between functions, and mathematical techniques that range from matrix theory and integrals of commonly occurring functions to vector calculus, ordinary and partial differential equations, special functions, Fourier series, orthogonal polynomials, and Laplace and Fourier transforms. During the preparation of this edition full advantage was taken of the recently updated seventh edition of Gradshteyn and Ryzhik's Table of Integrals, Series, and Products and other important reference works. Suggestions from users of the third edition of the Handbook have resulted in the expansion of many sections, and because of the relevance to boundary value problems for the Laplace equation in the plane, a new chapter on conformal mapping, has been added, complete with an atlas of useful mappings. - Comprehensive coverage in reference form of the branches of mathematics used in science and engineering - Organized to make results involving integrals and functions easy to locate - Results illustrated by worked examples |
Contents
| 1 | |
Chapter 1 Numerical Algebraic and Analytical Results for Series and Calculus | 27 |
Chapter 2 Functions and Identities | 109 |
Chapter 3 Derivatives of Elementary Functions | 149 |
Chapter 4 Indefinite Integrals of Algebraic Functions | 153 |
Chapter 5 Indefinite Integrals of Exponential Functions | 175 |
Chapter 6 Indefinite Integrals of Logarithmic Functions | 181 |
Chapter 7 Indefinite Integrals of Hyperbolic Functions | 189 |
Chapter 17 Bessel Functions | 289 |
Chapter 18 Orthogonal Polynomials | 309 |
Chapter 19 Laplace Transformation | 337 |
Chapter 20 Fourier Transforms | 353 |
Chapter 21 Numerical Integration | 363 |
Chapter 22 Solutions of Standard Ordinary Differential Equations | 371 |
Chapter 23 Vector Analysis | 415 |
Chapter 24 Systems of Orthogonal Coordinates | 433 |
Chapter 8 Indefinite Integrals Involving Inverse Hyperbolic Functions | 201 |
Chapter 9 Indefinite Integrals of Trigonometric Functions | 207 |
Chapter 10 Indefinite Integrals of Inverse Trigonometric Functions | 225 |
Chapter 11 The Gamma Beta Pi and Psi Functions and the Incomplete Gamma Functions | 231 |
Chapter 12 Elliptic Integrals and Functions | 241 |
Chapter 13 Probability Distributions and Integrals and the Error Function | 253 |
Chapter 14 Fresnel Integrals Sine and Cosine Integrals | 261 |
Chapter 15 Definite Integrals | 265 |
Chapter 16 Different Forms of Fourier Series | 275 |
Chapter 25 Partial Differential Equations and Special Functions | 447 |
Chapter 26 Qualitative Properties of the Heat and Laplace Equation | 473 |
Chapter 27 Solutions of Elliptic Parabolic and Hyperbolic Equations | 475 |
Chapter 28 The zTransform | 493 |
Chapter 29 Numerical Approximation | 499 |
Chapter 30 Conformal Mapping and Boundary Value Problems | 509 |
| 525 | |
| 529 | |
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Common terms and phrases
approximation arccos arccosh arcsin arctan asymptotic ax dx Bessel function boundary conditions boundary value problem bx dx bx)² coefficients complex numbers convergence cos² cosh cosine cosx coth curve defined definite integral denoted derivative differential equation Dirichlet dx dx elliptic integral Euler f(xo Figure finite Fourier series Fourier transform function f(x homogeneous Im{a improper integral initial conditions initial value problem Integrands Involving interval inverse Laplace equation Laplace transform Legendre linear linearly independent mapping matrix method notation odd function Pn(x polar coordinates polynomials power series radius Re{a Re{s reduction formula result roots satisfies scalar sin(x sin² sinh sinx solution spherical tanh theorem trigonometric variable vector x² dx z-plane z-transform zero θυ π π ди Эх