College algebra

Synopsis

P. PREREQUISITES. Chapter Overview. Modeling the Real World. Real Numbers. Integer Exponents. Rational Exponents and Radicals. Algebraic Expressions. Discovery Project: Visualizing a Formula. Factoring Algebraic Expressions. Rational Expressions. Focus on Problem Solving: General Principles. 1. EQUATIONS AND INEQUALITIES. Chapter Overview. Equations. Modeling with Linear Equations. Discovery Project: Equations Through the Ages. Quadratic Equations. Complex Numbers. Other Types of Equations. Inequalities. Absolute Value Equations and Inequalities. Focus on Modeling: Making the Best Decisions. 2. COORDINATES AND GRAPHS. Chapter Overview. The Coordinate Plane. Discovery Project: Visualizing Data. Graphs of Equations in Two Variables. Graphing Calculators: Solving Equations Graphically. Lines. Modeling: Variation. Focus on Modeling: Fitting Lines to Data. 3. FUNCTIONS. Chapter Overview. What is a Function'. Graphs of Functions. Increasing and Decreasing Functions: Average Rate of Change. Transformations of Functions. Quadratic Functions; Maxima and Minima. Combining Functions. Discovery Project: Iteration and Chaos. One-to-One Functions and Their Inverses. Focus on Modeling: Modeling with Functions. 4. POLYNOMIAL AND RATIONAL FUNCTIONS. Chapter Overview. Polynomial Functions and Their Graphs. Dividing Polynomials. Real Zeros of Polynomials. Discovery Project: Zeroing in on a Zero. Complex Zeros and the Fundamental Theorem of Algebra. Rational Functions. Focus on Modeling: Fitting Polynomials to Data. 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Chapter Overview. Exponential Functions. Discovery Project: Exponential Explosion. Logarithmic Functions. Laws of Logarithms. Exponential and Logarithmic Equations. Modeling with Exponential and Logarithmic Functions. Focus on Modeling: Fitting Exponential and Power Curves to Data. 6. SYSTEMS OF EQUATIONS AND INEQUALITIES. Chapter Overview. Systems of Equations. Systems of Linear Equations in Two Variables. Systems of Linear Equations in Several Variables. Discovery Project: Exact Fit Versus Best Fit. Systems of Inequalities. Partial Fractions. Focus on Modeling: Linear Programming. 7. MATRICES AND DETERMINANTS. Chapter Overview. Matrix Representation of Linear Systems. The Algebra of Matrices. Discovery Project: Will the Specie Survive'. Inverses of Matrices and Matrix Equations. Determinants and Cramer's Rule. Focus on Modeling: Computer Graphics. 8. CONIC SECTIONS. Chapter Overview. Parabolas. Laboratory Project: Rolling Down a Ramp. Ellipses. Hyperbolas. Shifted Conics. Focus on Modeling: Conics in Architecture. 9. SEQUENCES AND SERIES. Chapter Overview. Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Discovery Project: Finding Patterns. Mathematics of Finance: Annuities. Mathematical Induction. The Binomial Theorem. Focus on Modeling: Modeling with Recursive Sequences. 10. COUNTING AND PROBABILITY. Chapter Overview. Counting Principles. Permutations and Combinations. Probability. Laboratory Project: Small Samples, Big Results. Binomial Probability. Expected Value. Focus on Modeling: The Monte Carlo Method.