Convenient Organization of Essential Material so You Can Look up Formulas Fast Containing a careful selection of standard and timely topics, the Pocket Book of Integrals and Mathematical Formulas, Fourth Edition presents many numerical and statistical tables, scores of worked examples, and the most useful mathematical formulas for engineering and scientific applications. This fourth edition of a bestseller provides even more comprehensive coverage with the inclusion of several additional topics, all while maintaining its accessible, clear style and handy size.
New to the Fourth Edition * An expanded chapter on series that covers many fascinating properties of the natural numbers that follow from number theory * New applications such as geostationary satellite orbits and drug kinetics * An expanded statistics section that discusses nonlinear regression as well as the normal approximation of the binomial distribution * Revised format of the table of integrals for easier use of the forms and functions Easy to Use on the Go The book addresses a range of areas, from elementary algebra, geometry, matrices, and trigonometry to calculus, vector analysis, differential equations, and statistics. Featuring a convenient, portable size, it is sure to remain in the pockets or on the desks of all who use mathematical formulas and tables of integrals and derivatives.
Table of Contents
Prefaces Elementary Algebra and Geometry Fundamental Properties (Real Numbers) Exponents Fractional Exponents Irrational Exponents Logarithms Factorials Binomial Theorem Factors and Expansion Progression Complex Numbers Polar Form Permutations Combinations Algebraic Equations Geometry Pythagorean Theorem Determinants, Matrices, and Linear Systems of Equations Determinants Evaluation by Cofactors Properties of Determinants Matrices Operations Properties Transpose Identity Matrix Adjoint Inverse Matrix Systems of Linear Equations Matrix Solution Trigonometry Triangles Trigonometric Functions of an Angle Trigonometric Identities Inverse Trigonometric Functions Analytic Geometry Rectangular Coordinates Distance between Two Points: Slope Equations of Straight Lines Distance from a Point to a Line Circle Parabola Ellipse Hyperbola (e 1) Change of Axes General Equation of Degree 2 Polar Coordinates Curves and Equations Exponential Function (Half-Life) Series, Number Facts, and Theory Bernoulli and Euler Numbers Series of Functions Error Function Fermat's Little Theorem Fermat's Last Theorem Beatty's Theorem An Interesting Prime Goldbach Conjecture Twin Primes Collatz Conjecture Differential Calculus Notation Slope of a Curve Angle of Intersection of Two Curves Radius of Curvature Relative Maxima and Minima Points of Inflection of a Curve Taylor's Formula Indeterminant Forms Numerical Methods Functions of Two Variables Partial Derivatives Integral Calculus Indefinite Integral Definite Integral Properties Common Applications of the Definite Integral Cylindrical and Spherical Coordinates Double Integration Surface Area and Volume by Double Integration Centroid Vector Analysis Vectors Vector Differentiation Divergence Theorem (Gauss) Stokes' Theorem Planar Motion in Polar Coordinates Geostationary Satellite Orbit Special Functions Hyperbolic Functions Gamma Function (Generalized Factorial Function) Laplace Transforms Z Transform Fourier Series Functions with Period Other Than 2pi Bessel Functions Legendre Polynomials Laguerre Polynomials Hermite Polynomials Orthogonality Differential Equations First-Order, First-Degree Equations Second-Order Linear Equations (with Constant Coefficients) Runge Kutta Method (of Order 4) Statistics Arithmetic Mean Median Mode Geometric Mean Harmonic Mean Variance Standard Deviation Coefficient of Variation Probability Binomial Distribution Mean of Binomially Distributed Variable Normal Distribution Poisson Distribution Empirical Distributions Estimation Hypotheses Testing t Distribution Hypothesis Testing with t and Normal Distributions Chi-Square Distribution Least Squares Regression Nonlinear Regression Analysis The F Distribution (Analysis of Variance) Summary of Probability Distributions Sample Size Determinations Financial Mathematics Simple Interest True Interest Formula (Loan Payments) Loan Payment Schedules Loan Balance Calculation Accelerated Loan Payment Lump Sum Payment Compound Interest Time to Double (Your Money) Present Value of a Single Future Payment Regular Saving to Accumulate a Specified Amount Monthly Payments to Achieve a Specified Amount Periodic Withdrawals from an Interest-Bearing Account Periodic Withdrawals That Maintain the Principal Time to Deplete an Interest-Bearing Account with Periodic Withdrawals Amounts to Withdraw for a Specified Number of Withdrawals I: Payments at the End of Each Year Amounts to Withdraw for a Specified Number of Withdrawals II: Payments at the Beginning of Each Year Present Value of Regular Payments Annuities The In-Out Formula Stocks and Stock Quotations Bonds Tax-Free Yield Stock Options (Puts and Calls) Market Averages Mutual and Quotations Dollar Cost Averaging Moving Average Table of Derivatives Table of Integrals: Indefinite and Definite Integrals Appendix Index