College Algebra - 3rd edition

Dugopolski, Mark : Southeastern Louisiana University

P. Prerequisites.

Real Numbers and Their Properties.
Integral Exponents and Scientific Notation.
Rational Exponents and Radicals.
Polynomials.
Factoring Polynomials.
Rational Expressions.

1. Equations, Inequalities, and Modeling.

Equations in One Variable.
Constructing Models to Solve Problems.
Equations and Graphs in Two Variables.
Linear Equations in Two Variables.
Scatter Diagrams and Curve Fitting.
Quadratic Equations.
Linear and Absolute Value Inequalities.

2. Functions and Graphs.

Functions.
Graphs of Relations and Functions.
Families of Functions, Transformations, and Symmetry.
Operations with Functions.
Inverse Functions.
Constructing Functions with Variation.

3. Polynomial and Rational Functions.

Quadratic Functions and Inequalities.
Complex Numbers.
Zeros of Polynomial Functions.
The Theory of Equations.
Miscellaneous Equations.
Graphs of Polynomial Functions.
Rational Functions and Inequalities.

4. Exponential and Logarithmic Functions.

Exponential Functions and Their Applications.
Logarithmic Functions and Their Applications.
Rules of Logarithms.
More Equations and Applications.

5. Systems of Equations and Inequalities.

Systems of Linear Equations in Two Variables.
Systems of Linear Equations in Three Variables.
Nonlinear Systems of Equations.
Partial Fractions.
Inequalities and Systems of Inequalities in Two Variables.
The Linear Programming Model.

6. Matrices and Determinants.

Solving Linear Systems Using Matrices.
Operations with Matrices.
Multiplication of Matrices.
Inverses of Matrices.
Solution of Linear Systems in Two Variables Using Determinants.
Solution of Linear Systems in Three Variables Using Determinants.

7. The Conic Sections.

The Parabola.
The Ellipse and the Circle.
The Hyperbola.

8. Sequences, Series, and Probability.

Sequences.
Series.
Geometric Sequences and Series.
Counting and Permutations.
Combinations, Labeling, and the Binomial Theorem.
Probability.
Mathematical Induction.