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Contents | |
0. A REVIEW OF BASIC ALGEBRA | |
Sets of Real Numbers | |
Integer Exponents and Scientific Notation | |
Rational Exponents and Radicals | |
Polynomials | |
Factoring Polynomials | |
Algebraic Fractions | |
1. EQUATIONS AND INEQUALITIES | |
Equations | |
Applications of Linear Equations | |
Quadratic Equations | |
Applications of Quadratic Equations | |
Complex Numbers | |
Polyomial and Radical Equations | |
Inequalities | |
Absolute Value | |
2. THE RECTANGULAR COORDINATE SYSTEM AND GRAPHS OF EQUATIONS | |
The Rectangular Coordinate System | |
The Slope of a Nonvertical Line | |
Writing Equations of Lines | |
Graphs of Equations | |
Proportion and Variation | |
3. FUNCTIONS | |
Functions and Function Notation | |
Quadratic Functions | |
Polynomial and Other Functions | |
Translating and Stretching Graphs | |
Rational Functions | |
Operations on Functions | |
Inverse Functions | |
4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS | |
Exponential Functions and Their Graphs | |
Applications of Exponential Functions | |
Logarithmic Functions and Their Graphs | |
Applications of Logarithmic Functions | |
Properties of Logarithms | |
Exponential and Logarithmic Equations | |
5. SOLVING POLYNOMIAL EQUATIONS | |
The Remainder and Factor Theorems; Synthetic Division | |
Descartes' Rule of Signs and Bounds on Roots | |
Rational Roots of Polynomial Equations | |
Irrational Roots of Polynomial Equations | |
6. LINEAR SYSTEMS | |
Systems of Linear Equations | |
Gaussian Eliminations and Matrix Methods | |
Matrix Algebra | |
Matrix Inversion | |
Determinants | |
Partial Fractions | |
Graphs of Linear Inequalities | |
Linear Programming | |
7. CONIC SECTIONS AND QUADRATIC SYSTEMS | |
The Circle and the Parabola | |
The Ellipse | |
The Hyperbola | |
Solving Simultaneous Second-Degree Equations | |
8. NATURAL NUMBER FUNCTIONS AND PROBABILITY | |
The Binomial Theorem | |
Sequences, Series, and Summation Notation | |
Arithmetic Sequences | |
Geometric Sequences | |
Mathematical Induction | |
Permutations and Combinations | |
Probability | |
Computation of Compound Probabilities | |
Odds and Mathematical Expectation | |
9. THE MATHEMATICS OF FINANCE | |
Compound Interest | |
Annuities and Future Value | |
Present Value of an Annuity; Amortization | |
Appendix 1: A Proof of the Binomial Theorem | |
Appendix 2: Tables | |
Table A | |
Powers and Roots | |
Table B | |
Base-10 Logarithms | |
Table C | |
Base-e Logarithms | |
Appendix 3: Answers to Selected Exercises | |
Index | |
Index of Applications |