Algebra For College Students

1. BASIC CONCEPTS AND PROPERTIES. Sets, Real Numbers, and Numerical Expressions. Operations with Real Numbers. Properties of Real Numbers and the Use of Exponents. Algebraic Expressions. Summary. Review Problem Set. Test. 2. EQUATIONS, INEQUALITIES, AND PROBLEM SOLVING. Solving First-Degree Equations. Equations Involving Fractional Forms. Equations Involving Decimals and Problem Solving. Formulas. Inequalities. More on Inequalities and Problem Solving. Equations and Inequalities Involving Absolute Value. Summary. Review Problem Set. Test. 3. POLYNOMIALS. Polynomials: Sums and Differences. Products and Quotients of Monomials. Multiplying Polynomials. Factoring: Use of the Distributive Property. Factoring: Difference of Two Squares and Sum or Difference of Two Cubes. Factoring Trinomials. Equations and Problem Solving. Summary. Review Problem Set. Test. Cumulative Review Problem Set (Chapters 1-3). 4. RATIONAL EXPRESSIONS. Simplifying Rational Expressions. Multiplying and Dividing Rational Expressions. Adding and Subtracting Rational Expressions. More on Rational Expressions and Complex Fractions. Dividing Polynomials. Fractional Equations. More Fractional Equations and Applications. Summary. Review Problem Set. Test. 5. EXPONENTS AND RADICALS. Using Integers as Exponents. Roots and Radicals. Combining Radicals and Simplifying Radicals That Contain Variables. Products and Quotients Involving Radicals. Equations Involving Radicals. Merging Exponents and Roots. Scientific Notation. Summary. Review Problems Set. Test. 6. QUADRATIC EQUATIONS AND INEQUALITIES. Complex Numbers. Quadratic Equations. Completing the Square. Quadratic Formula. More Quadratic Equations and Applications. Quadratic and Other Nonlinear Inequalities. Summary. Review Problem Set. Test. Cumulative Review Problem Set (Chapters 1-6). 7. LINEAR EQUATIONS AND INEQUALITIES IN TWO VARIABLES. Rectangular Coordinate System and Linear Equations. Graphing Nonlinear Equations Linear Inequalities in Two Variables. Distance and Slope. Determining the Equation of a Line. Summary. Review Problem Set. Test. 8. FUNCTIONS. Concept of a Function. Linear Functions and Applications. Quadratic Functions. More Quadratic Functions and Applications. Transformations of Some Basic Curves. Combining Functions. Direct and Inverse Variation. Summary. Review Problem Set. Test. 9. POLYNOMIAL AND RATIONAL FUNCTIONS. Synthetic Division. Remainder and Factor Theorems. Polynomial Equations. Graphing Polynomial Functions. Graphing Rational Functions. More on Graphing Rational Functions. Summary. Review Problem Set. Test. 10. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponents and Exponential Functions. Applications of Exponential Functions. Inverse Functions. Logarithms. Logarithmic Functions. Exponential Equations, Logarithmic Equations, and Problem Solving. Summary. Review Problem Set. Test. Cumulative Review Problem Set (Chapter 1-10). 11. SYSTEMS OF EQUATIONS. Systems of Two Linear Equations in Two Variables. Systems of Three Linear Equations in Three Variables. Matrix Approach to Solving Linear Systems. Determinants. Cramer"s Rule. Partial Fractions. Summary. Review Problem Set. Test. 12. ALGEBRA OF MATRICES. Algebra of 2 X 2 Matrices. Multiplicative Inverses. m x n Matrices. Systems of Linear Inequalities: Linear Programming. Summary. Review Problem Set. Test. 13. CONIC SECTIONS. Circles. Parabolas. Ellipses. Hyperbolas. System Involving Nonlinear Equations. Summary. Review Problem Set. Test. 14. SEQUENCES AND MATHEMATICAL INDUCTION. Arithmetic Sequences. Geometric Sequences. Another Look at Problem Solving. Mathematical Induction. Summary. Review Problem Set. Test. 15. COUNTING TECHNIQUES, PROBABILITY, AND THE BINOMIAL THEOREM. Fundamental Principle of Counting. Permutations and Combinations. Probability. Some Properties of Probability: Expected Values. Conditional Probability: Dependent and Independent Events. Binomial Theorem. Summary. Review Problem Set. Test. Appendix A: Common Logarithms. Appendix B: Natural Logarithms. Answers. Index.