**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 2π

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**