Precalculus

Marge Lial (late) was always interested in math; it was her favorite subject in the first grade! Her desire to educate both her students and herself inspired the writing of numerous best-selling textbooks. Marge, who received Bachelor's and Master's degrees from California State University at Sacramento, was most recently affiliated with American River College. An avid reader and traveler, Marge’s travel experiences often find their way into her books as applications, exercise sets, and feature sets. She was particularly interested in archeology. Trips to various digs and ruin sites produced 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, and now after more than twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, both of his goals have been realized. His love for both teaching andmathematics is evident in his passion for working with students and fellow teachers as well. His specific professional interests are recreational mathematics, mathematics history, and incorporating graphing calculators into the curriculum. John's personal life is busy, as he devotes time to his family (wife Gwen, and sons Chris, Jack, and Josh). He has been a rabid baseball fan all of his life. John's other hobbies include numismatics (the study of coins) and record collecting. He loves the music of the 1960s and has an extensive collection of the recorded works of Frankie Valli and the Four Seasons.  David Schneider has taught mathematics at universities for more than 34 years and has authored 36 books. He has an undergraduate degree in mathematics from Oberlin College and a PhD in mathematics from MIT. During most of his professional career, he was on the faculty of the University of Maryland—College Park. His hobbies include travel, dancing, bicycling, and hiking.  Callie Daniels has always had a passion for learning mathematics and brings that passion into the classroom with her students. She attended the University of the Ozarks on an athletic scholarship, playing both basketball and tennis. While there, she earned a Bachelor’s degree in Secondary Mathematics Education as well as the NAIA Academic All-American Award. She has two Master’s degrees: one in Applied Mathematics and Statistics from the University of Missouri—Rolla, the second in Adult Education from the University of Missouri—St. Louis. Her hobbies include watching her sons play sports, riding horses, fishing, shooting photographs, and playing guitar. Her professional interests include improving success in the community college mathematics sequence, using technology to enhance students’ understanding of mathematics, and creating materials that support classroom teaching and student understanding.

• R. Review of Basic ConceptsR-1 SetsR-2 Real Numbers and Their PropertiesR-3 PolynomialsR-4 Factoring PolynomialsR-5 Rational ExpressionsR-6 Rational ExponentsR-7 Radical Expressions  1. Equations and Inequalities1-1 Linear Equations1-2 Applications and Modeling with Linear Equations1-3 Complex Numbers1-4 Quadratic Equations1-5 Applications and Modeling with Quadratic Equations1-6 Other Types of Equations and Applications1-7 Inequalities1-8 Absolute Value Equations and Inequalities  2. Graphs and Functions2-1 Rectangular Coordinates and Graphs2-2 Circles2-3 Functions2-4 Linear Functions2-5 Equations of Lines and Linear Models2-6 Graphs of Basic Functions2-7 Graphing Techniques2-8 Function Operations and Composition  3. Polynomial and Rational Functions3-1 Quadratic Functions and Models3-2 Synthetic Division3-3 Zeros of Polynomial Functions3-4 Polynomial Functions: Graphs, Applications, and Models3-5 Rational Functions: Graphs, Applications, and Models3-6 Variation  4. Inverse, Exponential, and Logarithmic Functions4-1 Inverse Functions4-2 Exponential Functions4-3 Logarithmic Functions4-4 Evaluating Logarithms and the Change-of-Base Theorem4-5 Exponential and Logarithmic Equations4-6 Applications of Models of Exponential Growth and Decay  5. Trigonometric Functions5-1 Angles5-2 Trigonometric Functions5-3 Trigonometric Function Values and Angle Measures5-4 Solutions and Applications of Right Triangles  6. The Circular Functions and Their Graphs6-1 Radian Measure6-2 The Unit Circle and Circular Functions6-3 Graphs of the Sine and Cosine Functions6-4 Translations of the Graphs of the Sine and Cosine Functions6-5 Graphs of the Tangent and Cotangent Functions6-6 Graphs of the Secant and Cosecant Functions6-7 Harmonic Motion  7. Trigonometric Identities and Equations7-1 Fundamental Identities7-2 Verifying Trigonometric Identities7-3 Sum and Difference Identities7-4 Double-Angle and Half-Angle Identities7-5 Inverse Circular Functions7-6 Trigonometric Equations7-7 Equations Involving Inverse Trigonometric Functions  8. Applications of Trigonometry8-1 The Law of Sines8-2 The Law of Cosines8-3 Geometrically Defined Vectors and Applications8-4 Algebraically Defined Vectors and the Dot Product8-5 Trigonometric (Polar) Form of Complex Numbers; Products and Quotients8-6 De Moivre’s Theorem; Powers and Roots of Complex Numbers8-7 Polar Equations and Graphs8-8 Parametric Equations, Graphs, and Applications  9. Systems and Matrices9-1 Systems of Linear Equations9-2 Matrix Solution of Linear Systems9-3 Determinant Solution of Linear Systems9-4 Partial Fractions9-5 Nonlinear Systems of Equations9-6 Systems of Inequalities and Linear Programming9-7 Properties of Matrices9-8 Matrix Inverses  10. Analytic Geometry10-1 Parabolas10-2 Ellipses10-3 Hyperbolas10-4 Summary of the Conic Sections  11. Further Topics in Algebra11-1 Sequences and Series11-2 Arithmetic Sequences and Series11-3 Geometric Sequences and Series11-4 The Binomial Theorem11-5 Mathematical Induction11-6 Counting Theory11-7 Basics of Probability  Appendices