R. Basic Concepts of Algebra. The Real-Number System.
Integer Exponents, Scientific Notation, and Order of Operations.
Addition, Subtraction, and Multiplication of Polynomials.
Factoring.
Rational Expressions.
Radical Notation and Rational Exponents.
1. Graphs, Functions, and Models. Introduction to Graphing.
Functions and Graphs.
Linear Functions, Slope, and Applications.
Equations of Lines and Modeling.
More on Functions.
The Algebra of Functions.
Symmetry and Transformations.
2. Functions, Equations, and Inequalities. Linear Equations, Functions, and Models.
The Complex Numbers.
Quadratic Equations, Functions, and Models.
Analyzing Graphs of Quadratic Functions.
More Equation Solving.
Solving Linear Inequalities.
3. Polynomial and Rational Functions. Polynomial Functions and Models.
Polynomial Division; The Remainder and Factor Theorems.
Theorems about Zeros of Polynomial Functions.
Rational Functions.
Polynomial and Rational Inequalities.
Variation and Applications.
4. Exponential and Logarithmic Functions. Inverse Functions.
Exponential Functions and Graphs.
Logarithmic Functions and Graphs.
Properties of Logarithmic Functions.
Solving Exponential and Logarithmic Equations.
Applications and Models: Growth and Decay.
5. Systems of Equations and Matrices. Systems of Equations in Two Variables.
Systems of Equations in Three Variables.
Matrices and Systems of Equations.
Matrix Operations.
Inverses of Matrices.
Determinants and Cramer's Rule.
Systems of Inequalities and Linear Programming.
Partial Fractions.
6. Conic Sections. The Parabola.
The Circle and the Ellipse.
The Hyperbola.
Nonlinear Systems of Equations.
7. Sequences, Series, and Combinatorics. Sequences and Series.
Arithmetic Sequences and Series.
Geometric Sequences and Series.
Mathematical Induction.
Combinatorics: Permutations.
Combinatorics: Combinations.
The Binomial Theorem.
Probability.
Answers. Photo Credits. Index. AIndex of Applications. 