A Review of Basic Concepts and Skills | |
The Language, Notation, and Numbers of Mathematics | |
Algebraic Expressions and the Properties of Real Numbers | |
Exponents, Scientific Notation, and a Review of Polynomials | |
Factoring Polynomials | |
Rational Expressions | |
Radicals and Rational Exponents | |
Equations and Inequalities | |
Linear Equations, Formulas, and Problem Solving | |
Linear Inequalities in One Variable | |
Absolute Value Equations and Inequalities | |
Complex Numbers | |
Solving Quadratic Equations | |
Solving Other Types of Equation | |
Relations, Functions and Graphs | |
Rectangular Coordinates; Graphing Circles and Relations | |
Graphs of Linear Equations | |
Linear Equations and Rates of Change | |
Functions, Notation, and Graphs of Functions | |
Analyzing the Graph of a Function | |
Toolbox Functions and Transformations | |
Piecewise-Defined Functions | |
The Algebra and Composition of Functions | |
Polynomial and Rational Functions | |
Quadratic Functions and Applications | |
Synthetic Division; The Remainder and Factor Theorems | |
The Zeroes of Polynomial Functions | |
Graphing Polynomial Functions | |
Graphing Rational Functions | |
Additional Insights into Rational Functions | |
Polynomial and Rational Inequalities | |
Variation: Function Models in Action | |
Exponential and Logarithmic Functions | |
One-to-One and Inverse Functions | |
Exponential Functions | |
Logarithms and Logarithmic Functions | |
Properties of Logarithms; Solving Exponential and Logarithmic Equations | |
Applications from Business, Finance, and Science | |
Systems of Equations and Inequalities | |
Linear Systems in Two Variables with Applications | |
Linear Systems in Three Variables with Applications | |
Nonlinear Systems of Equations and Inequalities | |
Systems of Inequalities and Linear Programming | |
Matrices and Matrix Applications | |
Solving Systems Using Matrices and Row Operations | |
The Algebra of Matrices | |
Solving Linear Systems Using Matrix Equations | |
Applications of Matrices and Determinants: | |
Analytical Geometry and Conic Sections | |
Introduction to Analytic Geometry | |
The Circle and the Ellipse | |
The Hyperbola | |
The Analytic Parabola | |
Additional Topics in Algebra | |
Sequences and Series | |
Arithmetic Sequences | |
Geometric Sequences | |
Mathematical Induction | |
Counting Techniques | |
Introduction to Probability | |
The Binomial Theorem | |
Appendices | |
More on Synthetic Division | |
More on Matrices | |
Deriving the Equation of a Conic | |
Proof Positive - A Selection of Proofs from College Algebra | |
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