Table of Contents

Preface to the Fifth Edition

Preface to the Fourth Edition

Preface to the Third Edition

Preface to the Second Edition

Preface to the First Edition

Author

Greek Letters

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

Application of Derivatives Related Rate Problems Rectilinear Motion Applied Problem in Maximum and Minimum 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 Applications of Integration Indefinite Integral The Definite Integral 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 2 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

About the Author

Ronald J. Tallarida holds a BS and MS in physics/mathematics and a Ph.D in pharmacology. His primary appointment is professor of pharmacology at Temple University School of Medicine, Philadelphia, Pennsylvania, USA. For more than 30 years, he also served as adjunct professor of biomedical engineering at Drexel University, Philadelphia, Pennsylvania, USA, where he received the Lindback Award for distinguished teaching of mathematics. He has published more than 290 works, been the recipient of NIH research grants, and served as consultant to industry and government agencies. His research interests include the mathematical modeling of biological systems, feedback control, and the action of drugs and drug combinations.