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 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