Table of Contents
(Each chapter ends with a Summary, Review Exercises, Test, and an Internet Project.)
1. Algebraic Expressions.
Real Numbers and Their Properties.
Order and Absolute Value.
Polynomials; The Binomial Theorem.
Factoring Polynomials.
Rational Expressions.
Rational Exponents.
Radical Expressions.
2. Equations and Inequalities.
Linear Equations.
Linear Applications and Modeling.
Complex Numbers.
Quadratic Equations.
Quadratic Applications and Modeling.
Other Types of Equations.
Inequalities.
Absolute Value Equations and Inequalities.
3. Relations, Functions, and Graphs.
Relations and the Rectangular Coordinate System; Circles.
Functions.
Linear Functions.
Equations of Lines; Curve Fitting.
Graphs of Relations and Functions.
General Graphing Techniques.
Operations and Composition.
4. Polynomial and Rational Functions.
Quadratic Functions; Curve Fitting.
Synthetic Division.
Zeros of Polynomial Functions.
Polynomials Functions: Graphs, Applications, and Models.
Rational Functions: Graphs, Applications, and Models.
Variation.
5. Exponential and Logarithmic Functions.
Inverse Functions.
Exponential Functions.
Logarithmic Functions.
Evaluating Logarithms and the Change-of-Base Theorem.
Exponential and Logarithmic Equations.
Applications and Models of Exponential Growth and Decay.
6. Systems of Equations and Inequalities.
Linear Systems of Equations.
Matrix Solution of Linear Systems.
Determinant Solution of Linear Systems.
Partial Fractions.
Nonlinear Systems.
Systems of Inequalities and Linear Programming.
Properties of Matrices.
Matrix Inverses.
7. Analytic Geometry.
Parabolas.
Ellipses.
Hyperbolas.
Summary of the Conic Sections.
8. Further Topics in Algebra.
Sequences and Series.
Arithmetic Sequences and Series.
Geometric Sequences and Series.
The Binomial Theorem Revisited.
Mathematical Induction.
Counting Theory.
Basics of Probability.
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