College Algebra

<p><strong>P. Prerequisites: Fundamental Concepts of Algebra</strong></p> <p>P.1 Algebraic Expressions, Mathematical Models, and Real Numbers</p> <p>P.2 Basic Rules of Algebra</p> <p>P.3 Exponents and Scientific Notation</p> <p>P.4 Radicals and Rational Exponents</p> <p>P.5 Polynomials</p> <p>P.6 Factoring Polynomials</p> <p>P.7 Rational Expressions</p> <p><strong>1. Functions and Graphs</strong></p> <p>1.1 Graphs and Graphing Utilities</p> <p>1.2 Basics of Functions and Their Graphs</p> <p>1.3 More on Functions and Their Graphs</p> <p>1.4 Linear Functions and Slope</p> <p>1.5 More on Slope</p> <p>1.6 Transformations of Functions</p> <p>1.7 Combinations of Functions; Composite Functions</p> <p>1.8 Inverse Functions</p> <p>1.9 Distance and Midpoint Formulas; Circles</p> <p><strong>2. Equations and Inequalities</strong></p> <p>2.1 Linear Equations and Rational Equations</p> <p>2.2 Models and Applications</p> <p>2.3 Complex Numbers</p> <p>2.4 Quadratic Equations</p> <p>2.5 Other Types of Equations</p> <p>2.6 Linear Inequalities and Absolute Value Inequalities</p> <p><strong>3. Polynomial and Rational Functions</strong></p> <p>3.1 Quadratic Functions</p> <p>3.2 Polynomial Functions and Their Graphs</p> <p>3.3 Dividing Polynomials; Remainder and Factor Theorems</p> <p>3.4 Zeros of Polynomial Functions</p> <p>3.5 Rational Functions and Their Graphs</p> <p>3.6 Polynomial and Rational Inequalities</p> <p>3.7 Modeling Using Variation</p> <p><strong>4. Exponential and Logarithmic Functions</strong></p> <p>4.1 Exponential Functions</p> <p>4.2 Logarithmic Functions</p> <p>4.3 Properties of Logarithms</p> <p>4.4 Exponential and Logarithmic Equations</p> <p>4.5 Exponential Growth and Decay; Modeling Data</p> <p><strong>5. Systems of Equations and Inequalities</strong></p> <p>5.1 Systems of Linear Equations in Two Variables</p> <p>5.2 Systems of Linear Equations in Three Variables</p> <p>5.3 Partial Fractions</p> <p>5.4 Systems of Nonlinear Equations in Two Variables</p> <p>5.5 Systems of Inequalities</p> <p>5.6 Linear Programming</p> <p><strong>6. Matrices and Determinants</strong></p> <p>6.1 Matrix Solutions to Linear Systems</p> <p>6.2 Inconsistent and Dependent Systems and Their Applications</p> <p>6.3 Matrix Operations and Their Applications</p> <p>6.4 Multiplicative Inverses of Matrices and Matrix Equations</p> <p>6.5 Determinants and Cramer's Rule</p> <p><strong>7. Conic Sections</strong></p> <p>7.1 The Ellipse</p> <p>7.2 The Hyperbola</p> <p>7.3 The Parabola</p> <p><strong>8. Sequences, Induction, and Probability</strong></p> <p>8.1 Sequences and Summation Notation</p> <p>8.2 Arithmetic Sequences</p> <p>8.3 Geometric Sequences and Series</p> <p>8.4 Mathematical Induction</p> <p>8.5 The Binomial Theorem</p> <p>8.6 Counting Principles, Permutations, and Combinations</p> <p>8.7 Probability</p>