Description
Book SynopsisMarge Lial (late) was always interested in math; it was her favorite subject in the first grade! Marge's intense desire to educate both her students and herself has inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was affiliated with American River College. An avid reader and traveler, her travel experiences often found their way into her books as applications, exercise sets, and feature sets. Her interest in archeology led to trips to various digs and ruin sites, producing some fascinating problems for her textbooks involving such topics as the building of Mayan pyramids and the acoustics of ancient ball courts in the Yucatan.
When John Hornsby enrolled as an undergraduate at Louisiana State University, he was uncertain whether he wanted to study mathematics education or journalism. His ultimate decision was to become a teacher, but af
Table of Contents
R. Review of Basic Concepts
- R.1. Fractions, Decimals, and Percents
- R.2. Sets and Real Numbers
- R.3. Real Number Operations and Properties
- R.4. Integer and Rational Exponents
- R.5. Polynomials
- R.6. Factoring Polynomials
- R.7. Rational Expressions
- R.8. Radical Expressions
1. Equations and Inequalities
- 1.1. Linear Equations
- 1.2. Applications and Modeling with Linear Equations
- 1.3. Complex Numbers
- 1.4. Quadratic Equations
- 1.5. Applications and Modeling with Quadratic Equations
- 1.6. Other Types of Equations and Applications
- 1.7. Inequalities
- 1.8. Absolute Value Equations and Inequalities
2. Graphs and Functions
- 2.1. Rectangular Coordinates and Graphs
- 2.2. Circles
- 2.3. Functions
- 2.4. Linear Functions
- 2.5. Equations of Lines and Linear Models
- 2.6. Graphs of Basic Functions
- 2.7. Graphing Techniques
- 2.8. Function Operations and Composition
3. Polynomial and Rational Functions
- 3.1. Quadratic Functions and Models
- 3.2. Synthetic Division
- 3.3. Zeros of Polynomial Functions
- 3.4. Polynomial Functions: Graphs, Applications, and Models
- 3.5. Rational Functions: Graphs, Applications, and Models
- 3.6. Polynomial and Rational Inequalities
- 3.7. Variation
4. Inverse, Exponential, and Logarithmic Functions
- 4.1. Inverse Functions
- 4.2. Exponential Functions
- 4.3. Logarithmic Functions
- 4.4. Evaluating Logarithms and the Change-of-Base Theorem
- 4.5. Exponential and Logarithmic Equations
- 4.6. Applications of Models of Exponential Growth and Decay
5. Trigonometric Functions
- 5.1. Angles
- 5.2. Trigonometric Functions
- 5.3. Trigonometric Function Values and Angle Measures
- 5.4. Solutions and Applications of Right Triangles
6. The Circular Functions and Their Graphs
- 6.1. Radian Measure
- 6.2. The Unit Circle and Circular Functions
- 6.3. Graphs of the Sine and Cosine Functions
- 6.4. Translations of the Graphs of the Sine and Cosine Functions
- 6.5. Graphs of the Tangent and Cotangent Functions
- 6.6. Graphs of the Secant and Cosecant Functions
- 6.7. Harmonic Motion
7. Trigonometric Identities and Equations
- 7.1. Fundamental Identities
- 7.2. Verifying Trigonometric Identities
- 7.3. Sum and Difference Identities
- 7.4. Double-Angle and Half-Angle Identities
- 7.5. Inverse Circular Functions
- 7.6. Trigonometric Equations
- 7.7. Equations Involving Inverse Trigonometric Functions
8. Applications of Trigonometry
- 8.1. The Law of Sines
- 8.2. The Law of Cosines
- 8.3. Geometrically Defined Vectors and Applications
- 8.4. Algebraically Defined Vectors and the Dot Product
- 8.5. Trigonometric (Polar) Form of Complex Numbers; Products and Quotients
- 8.6. De Moivre's Theorem; Powers and Roots of Complex Numbers
- 8.7. Polar Equations and Graphs
- 8.8. Parametric Equations, Graphs, and Applications
9. Systems and Matrices
- 9.1. Systems of Linear Equations
- 9.2. Matrix Solution of Linear Systems
- 9.3. Determinant Solution of Linear Systems
- 9.4. Partial Fractions
- 9.5. Nonlinear Systems of Equations
- 9.6. Systems of Inequalities and Linear Programming
- 9.7. Properties of Matrices
- 9.8. Matrix Inverses
10. Analytic Geometry
- 10.1. Parabolas
- 10.2. Ellipses
- 10.3. Hyperbolas
- 10.4. Summary of the Conic Sections
11. Further Topics in Algebra
- 11.1. Sequences and Series
- 11.2. Arithmetic Sequences and Series
- 11.3. Geometric Sequences and Series
- 11.4. The Binomial Theorem
- 11.5. Mathematical Induction
- 11.6. Basics of Probability
- Appendix A Polar Form of Conic Sections
- Appendix B Rotation of Axes
- Appendix C Geometry Formulas
