Class Outline

1. Fundamentals 7. Analytic Trigonometry
1.1 Real Numbers 7.1 Trigonometric Identities 
1.2 Exponents and Radicals 7.2 Addition and Subtraction Formulas
1.3 Algebraic Expressions 7.3 Double-Angle, Half-Angle, and Sum-Product Formulas
1.4 Rational Expressions 7.4 Inverse Trigonometric Functions
1.5 Equations 7.5 Trigonometric Equations
1.6 Modeling with Equations 8. Polar Coordinates and Vectors
1.7 Inequlities 8.1 Polar Coordinates
1.8 Coordinate Geometry 8.2 Graphs of Polar Equations
1.9 Graphing Calculators; Solving and Inequalities Graphically 8.3 Polar Form of Complex Numbers; DeMoivre's Theorem
1.10 Lines 8.4 Vectors
1.11 Modeling Variation 8.5 The Dot Product
2. Functions 9. Systems of Equations and Inequalities
2.1 What is a functions 9.1 Systems of Equations
2.2 Graphs of functions 9.2 Systems of Linear Equations in Two Variables
2.3 Incresing and Decreasing Functions; Average Rate of Change 9.3 Systems of Linear Equations in Several Variables
2.4 Transformation of Functions 9.4 System of Linear Equations: Matrices
2.5 Quadratic Functions; Maxima and Minima 9.5 The Algebra of Matrices
2.6 Modeling With Functions 9.6 Inverses of Matrices and Matrix Equation
2.7 Combining Functions 9.7 Determinates and Crammers Rule
2.8 One-to-one Functions and Their Inverses 9.8 Partial Fractions
3. Polynomial and Rational Functions 9.9 Systems of Inequalities
3.1 Polynomial Functions and Their Graphs 10. Analytic Geometry
3.2 Dividing Polynomials 10.1 Parabolas
3.3 Real Zeros of Polynomials 10.2 Ellipses
3.4 Complex Numbers 10.3 Hyperbolas
3.5 Complex Zeros and the Fundamental Theorem of Algebra 10.4 Shifted Conics
3.6 Rational Functions 10.5 Rotation of Axes
4. Exponential and Logarithmic Functions 10.6 Polar Equations of Conics
4.1 Exponential Functions 10.7 Plane Curves and Parametric Equations
4.2 Logarithmic Functions 11. Sequences and Series
4.3 Laws of Logarithmic 11.1 Sequences and Summation Notation
4.4 Exponential and Logarithmic Equations 11.2 Arithmetic Sequences
4.5 Modeling with Exponential and Logarithmic Functions 11.3 Geometric Sequences 
5. Trigonometric Functions of Real Numbers 11.4 Mathematics of Finance
5.1 The Unite Circle  11.5 Mathematical Induction
5.2 Trigonometric Functions of Real Numbers  11.6 The Binomial Theorem
5.3 Trigonometric Graphs 12. Limits: A Preview of Calculus
5.4 More Trigonometric Graphs 12.1 Finding Limits Numerically and Graphically
5.5 Modeling Harmonic Motion 12.2 Finding Limits Algebraically
6. Trigonometric Functions of Angles 12.3 Tangent Lines and Derivatives
6.1 Angle Measure 12.4 Limits at Infinity: Limits of Sequences
6.2 Trigonometry of right Triangles  12.5 Areas 
6.3 Trigonometric Functions of Angles  
6.4 The Law of Sines  
6.5 The Law of Cosines