Precalculus Book

1. ALGEBRA BACKGROUND FOR PRECALCULUS. Sets of Real Numbers. Absolute Value. Polynomials and Factoring. Quadratic Equations. 2. COORDINATES, GRAPHS, AND INEQUALITIES. Rectangular Coordinates. Graphs and Equations, A Second Look. Equations of Lines. Symmetry and Graphs. Inequalities. More on Inequalities. 3. FUNCTIONS. The Definition of a Function. The Graph of a Function. Techniques in Graphing. Methods of Combining Functions. Iteration. Inverse Functions. 4. POLYNOMIAL AND RATIONAL FUNCTIONS. Applications to Iterations and Optimization. Linear Functions. Quadratic Functions. More on Iteration. Quadratics and Population Growth. Applied Functions: Setting Up Equations. Maximum and Minimum Problems. Polynomial Functions. Rational Functions. 5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. The Exponential Function y = e to the x Power. Logarithmic Functions. Properties of Logarithms. Equations and Inequalities with Logs and Exponents. Compound Interest. Exponential Growth and Decay. 6. THE TRIGONOMETRIC FUNCTIONS. Radian Measure. Trigonometric Functions of Angles. Evaluating the Trigonometric Functions. Algebra and the Trigonometric Functions. Right-Triangle Trigonometry. 7. GRAPHS OF THE TRIGONOMETRIC FUNCTIONS. Trigonometric Functions of Real Numbers. Graphs of the Sine and the Cosine Functions. Graphs of y = A sin(Bx-C) and y = A cos(Bx - C). Simple Harmonic Motion. Graphs of the Tangent and the Reciprocal Functions. 8. ANALYTICAL TRIGONOMETRY. The Addition Formulas. The Double-Angle Formulas. The Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations. The Inverse Trigonometric Functions. 9. ADDITIONAL TOPICS IN TRIGONOMETRY. Right-Triangle Applications. The Law of Sines and the Law of Cosines. Vectors in the Plane, a Geometric Approach. Vectors in the Plane, an Algebraic Approach. Parametric Equations. Introduction to Polar Coordinates. Curves in Polar Coordinates. 10. SYSTEMS OF EQUATIONS. Systems of Two Linear Equations in Two Unknowns. Gaussian Elimination. Matrices. The Inverse of a Square Matrix. Determinants and Cramer's Rule. Nonlinear Systems of Equations. Systems of Inequalities. 11. ANALYTIC GEOMETRY. The Basic Equations. The Parabola. Tangents to Parabolas (Optional). The Ellipse. The Hyperbola. The Focus-Directrix Property of Conics. The Conics in Polar Coordinates. Rotation of Axes. 12. ROOTS OF POLYNOMIAL EQUATIONS. The Complex Number System. Division of Polynomials. Roots of Polynomial Equations: The Remainder Theorem and the Factor Theorem. The Fundamental Theorem of Algebra. Rational and Irrational Roots. Conjugate Roots and Descartes'' Rule of Signs. Introduction to Partial Fractions. More About Partial Fractions. 13. ADDITIONAL TOPICS. Mathematical Induction. The Binomial Theorem. Introduction to Sequences and Series. Arithmetic Sequences and Series. Geometric Sequences and Series. DeMoivre's Theorem. Appendix A.1: Using a Graphing Utility. Appendix A.2: Significant Digits and Calculators. Tables. Answers to Selected Exercises. Index.