Algebra for College Students

(Each Chapter ends with a Group Activity, Summary, Review Exercises, a Chapter Test and, with the exception of Chapter 1, a Cumulative Review.)

1. Review of the Real Number System.


Basic Concepts.



Operations on Real Numbers.



Exponents, Roots, and Order of Operations.



Properties of Real Numbers.



2. Linear Equations, Inequalities, and Applications.


Linear Equations in One Variable.



Formulas.



Applications of Linear Equations.



Further Applications of Linear Equations.



Summary Exercises on Solving Applied Problems.



Linear Inequalities in One Variable.



Set Operations and Compound Inequalities.



Absolute Value Equations and Inequalities.



Summary Exercises on Solving Linear and Absolute Value Equations and Inequalities.



3. Graphs, Linear Equations, and Functions.


The Rectangular Coordinate System.



The Slope of a Line.



Linear Equations in Two Variables.



Linear Inequalities in Two Variables.



Introduction to Functions.



Variation.



4. Systems of Linear Equations.


Systems of Linear Equations in Two Variables.



Systems of Linear Equations in Three Variables.



Applications of Systems of Linear Equations.



Solving Systems of Linear Equations by Matrix Methods.



Determinants and Cramer's Rule.



5. Exponents, Polynomials, and Polynomial Functions.


Integer Exponents and Scientific Notation.



Adding and Subtracting Polynomials.



Polynomial Functions.



Multiplying Polynomials.



Dividing Polynomials.



6. Factoring.


Greatest Common Factors; Factoring by Grouping.



Factoring Trinomials.



Special Factoring.



A General Approach to Factoring.



Solving Equations by Factoring.



7. Rational Expressions and Functions.


Rational Expressions and Functions; Multiplying and Dividing.



Adding and Subtracting Rational Expressions.



Complex Fractions.



Equations with Rational Expressions and Graphs.



Summary Exercises on Operations and Equations with Rational Expressions.



Applications of Rational Expressions.



8, Roots, Radicals, and Root Functions.


Radical Expressions and Graphs.



Rational Exponents.



Simplifying Radical Expressions.



Adding and Subtracting Radical Expressions.



Multiplying and Dividing Radical Expressions.



Summary Exercises on Operations with Radicals.



Solving Equations with Radicals.



Complex Numbers.



9. Quadratic Equations and Inequalities.


The Square Root Property and Completing the Square.



The Quadratic Formula.



Equations Quadratic in Form.



Summary Exercises on Solving Quadratic Equations.



Formulas and Further Applications.



Quadratic and Rational Inequalities.



10. Additional Functions and Relations.


Operations and Composition.



Graphs of Quadratic Functions.



More about Parabolas; Applications.



Symmetry; Increasing and Decreasing Functions.



Piecewise Linear Functions.



11. Inverse, Exponential, and Logarithmic Functions.


Inverse Functions.



Exponential Functions.



Logarithmic Functions.



Properties of Logarithms.



Common and Natural Logarithms.



Exponential and Logarithmic Equations; Further Applications.



12. More on Polynomial and Rational Functions.


Synthetic Division.



Zeros of Polynomial Functions.



Graphs and Applications of Polynomial Functions.



Summary Exercises on Polynomial Functions and Graphs.



Graphs and Applications of Rational Functions.



13. Conic Sections.


The Circle and the Ellipse.



The Hyperbola; Conic Sections.



Nonlinear Systems.



Second-Degree Inequalities, Systems of Inequalities, and Linear Programming.



14. Further Topics in Algebra.


Sequences and Series.



Arithmetic Sequences.



Geometric Sequences.



The Binomial Theorem.



Mathematical Induction.



Counting Theory.



Basics of Probability.



Appendix A An Introduction to Calculators.


Appendix B Properties of Matrices.


Appendix C Matrix Inverses.


Answers to Selected Exercises.


Glossary.


Index.


Videotape and CD Index.