## Table of Contents

1. FUNDAMENTALS OF ALGEBRA.

1.1 Real Numbers; 1.2 Polynomials; 1.3 Factoring Polynomials; 1.4 Rational Expressions; 1.5 Integral Exponents; 1.6 Solving Equations; 1.7 Rational Exponents and Radicals; 1.8 Quadratic Equations; 1.9 Inequalities and Absolute Value.

2. FUNCTIONS AND THEIR GRAPHS.

2.1 The Cartesian Coordinate System and Straight Lines; 2.2 Equations of Lines; 2.3 Functions and Their Graphs; 2.4 The Algebra of Functions; 2.5 Linear Functions; 2.6 Quadratic Functions; 2.7 Functions and Mathematical Models; 2.8 The Method of Least Squares (Optional).

3. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.

3.1 Exponential Functions; 3.2 Logarithmic Functions; 3.3 Exponential Functions as Mathematical Models.

4. MATHEMATICS OF FINANCE.

4.1 Compound Interest; 4.2 Annuities; 4.3 Amortization and Sinking Funds; 4.4 Arithmetic and Geometric Progressions.

5. SYSTEMS OF LINEAR EQUATIONS AND MATRICES.

5.1 Systems of Linear Equations: An Introduction; 5.2 Systems of Linear Equations: Unique Solutions; 5.3 Systems of Linear Equations: Underdetermined.and Overdetermined Systems; 5.4 Matrices; 5.5 Multiplication of Matrices; 5.6 The Inverse of a Square Matrix.

6. LINEAR PROGRAMMING.

6.1 Graphing Systems of Linear Inequalities in Two Variables; 6.2 Linear Programming Problems; 6.3 Graphical Solution of Linear Programming Problems; 6.4 The Simplex Method: Standard Maximization Problems; 6.5 The Simplex Method: Standard Minimization Problems.

7. SETS AND PROBABILITY.

7.1 Sets and Set Operations; 7.2 The Number of Elements in a Finite Set; 7.3 The Multiplication Principle; 7.4 Permutations and Combinations; 7.5 Experiments, Sample Spaces, and Events; 7.6 Definition of Probability; 7.7 Rules of Probability.

8. ADDITIONAL TOPICS IN PROBABILITY.

8.1 Use of Counting Techniques in Probability; 8.2 Conditional Probability and Independent Events; 8.3 Bayes' Theorem; 8.4 Distributions of Random Variables; 8.5 Expected Value; 8.6 Variance and Standard Deviation.

9. THE DERIVATIVE.

9.1 Limits; 9.2 One-Sided Limits and Continuity; 9.3 The Derivative; 9.4 Basic Rules of Differentiation; 9.5 The Product and Quotient Rules; Higher Order Derivatives; 9.6 The Chain Rule; 9.7 Differentiation of Exponential and Logarithmic Functions; 9.8 Marginal Functions in Economics.

10. APPLICATIONS OF THE DERIVATIVE.

10.1 Applications of the First Derivative; 10.2 Applications of the Second Derivative; 10.3 Curve Sketching; 10.4 Optimization I; 10.5 Optimization II.

11. INTEGRATION.

11.1 Antiderivatives and the Rules of Integration; 11.2 Integration by Substitution; 11.3 Area and the Definite Integral; 11.4 The Fundamental Theorem of Calculus; 11.5 Evaluating Definite Integrals; 11.6 Area between Two Curves; 11.7 Applications of the Definite Integral to Business and Economics.

12. CALCULUS OF SEVERAL VARIABLES.

12.1 Functions of Several Variables; 12.2 Partial Derivatives; 12.3 Maxima and Minima of Functions of Several Variables.