John Hornsby : 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 after twenty-five years of teaching at the high school and university levels and fifteen years of writing mathematics textbooks, all three of his goals have been realized; his love for teaching and for mathematics 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.
Marge Lial has always been 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, is now affiliated with American River College.
Marge is an avid reader and traveler. Her travel experiences often find their way into her books as applications, exercise sets, and feature sets. She is particularly interested in archeology. Trips to various digs and ruin sites have 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.
Gary Rockswold has been teaching mathematics for 33 years at all levels from seventh grade to graduate school, including junior high and high school students, talented youth, vocational, undergraduate, and graduate students, and adult education classes. He is currently employed at Minnesota State University, Mankato, where he is a full professor of mathematics. He graduated with majors in mathematics and physics from St. Olaf College in Northfield, Minnesota, where he was elected to Phi Beta Kappa. He received his Ph.D. in applied mathematics from Iowa State University. He has an interdisciplinary background and has also taught physical science, astronomy, and computer science. Outside of mathematics, he enjoys spending time with his lovely wife and two children.
Chapter 1 Linear Functions, Equations, and Inequalities
1.1 Real Numbers and the Rectangular Coordinate System
1.2 Introduction to Relations and Functions
Reviewing Basic Concepts
1.3 Linear Functions
1.4 Equations of Lines and Linear Models
Reviewing Basic Concepts
1.5 Linear Equations and Inequalities
1.6 Applications of Linear Functions
Reviewing Basic Concepts
Summary
Review Exercises
Test
Chapter 2 Analysis of Graphs of Functions
2.1 Graphs of Basic Functions and Relations; Symmetry
2.2 Vertical and Horizontal Shifts of Graphs
2.3 Stretching, Shrinking, and Reflecting Graphs
Reviewing Basic Concepts
2.4 Absolute Value Functions
2.5 Piecewise-Defined Functions
2.6 Operations and Composition
Reviewing Basic Concepts
Summary
Review Exercises
Test
Chapter 3 Polynomial Functions
3.1 Complex Numbers
3.2 Quadratic Functions and Graphs
3.3 Quadratic Equations and Inequalities
Reviewing Basic Concepts
3.4 Further Applications of Quadratic Functions and Models
3.5 Higher-Degree Polynomial Functions and Graphs
Reviewing Basic Concepts
3.6 Topics in the Theory of Polynomial Functions (I)
3.7 Topics in the Theory of Polynomial Functions (II)
3.8 Polynomial Equations and Inequalities; Further Applications and Models
Reviewing Basic Concepts
Summary
Review Exercises
Test
Chapter 4 Rational, Power, and Root Functions
4.1 Rational Functions and Graphs
4.2 More on Rational Functions and Graphs
4.3 Rational Equations, Inequalities, Models, and Applications
Reviewing Basic Concepts
4.4 Functions Defined by Powers and Roots
4.5 Equations, Inequalities, and Applications Involving Root Functions
Reviewing Basic Concepts
Summary
Review Exercises
Test
Chapter 5 Inverse, Exponential, and Logarithmic Functions
5.1 Inverse Functions
5.2 Exponential Functions
5.3 Logarithms and Their Properties
Reviewing Basic Concepts
5.4 Logarithmic Functions
5.5 Exponential and Logarithmic Equations and Inequalities
Reviewing Basic Concepts
5.6 Further Applications and Modeling with Exponential and Logarithmic Functions
Summary
Review Exercises
Test
Chapter 6 Analytic Geometry
6.1 Circles and Parabolas
6.2 Ellipses and Hyperbolas
Reviewing Basic Concepts
6.3 Summary of Conic Sections
6.4 Parametric Equations
Reviewing Basic Concepts
Summary
Review Exercises
Test
Chapter 7 Systems of Equations and Inequalities; Matrices
7.1 Systems of Equations
7.2 Solution of Linear Systems in Three Variables
7.3 Solution of Linear Systems by Row Transformations
Reviewing Basic Concepts
7.4 Matrix Properties and Operations
7.5 Determinants and Cramer’s Rule
7.6 Solution of Linear Systems by Matrix Inverses
Reviewing Basic Concepts
7.7 Systems of Inequalities and Linear Programming
7.8 Partial Fractions
Reviewing Basic Concepts
Summary
Review Exercises
Test
Chapter 8 The Unit Circle and the Functions of Trigonometry
8.1 Angles, Arcs, and Their Measures
8.2 The Unit Circle and Its Functions
Reviewing Basic Concepts
8.3 Graphs of the Sine and Cosine Functions
Periodic Functions
8.4 Graphs of the Other Circular Functions
8.5 Functions of Angles and Fundamental Identities
8.6 Evaluating Trigonometric Functions
Definitions of the Trigonometric Functions
8.7 Applications of Right Triangles
8.8 Harmonic Motion
Reviewing Basic Concepts
Summary
Review Exercises
Test
Chapter 9 Trigonometric Identities and Equations
9.1 Trigonometric Identities
9.2 Sum and Difference Identities
Reviewing Basic Concepts
9.3 Further Identities
9.4 The Inverse Circular Functions
Reviewing Basic Concepts
9.5 Trigonometric Equations and Inequalities (I)
9.6 Trigonometric Equations and Inequalities (II)
Summary
Review Exercises
Test
Chapter 10 Applications of Trigonometry and Vectors
10.1 The Law of Sines
10.2 The Law of Cosines and Area Formulas
10.3 Vectors and Their Applications
Reviewing Basic Concepts
10.4 Trigonometric (Polar) Form of Complex Numbers
10.5 Powers and Roots of Complex Numbers
Reviewing Basic Concepts
10.6 Polar Equations and Graphs
10.7 More Parametric Equations
Reviewing Basic Concepts
Summary
Review Exercises
Test
Chapter 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 Counting Theory
11.7 Probability
Chapter 12 Limits, Derivatives, and Definite Integrals
12.1 An Introduction to Limits
12.2 Techniques for Calculating Limits
12.3 One-Sided Limits; Limits Involving Infinity
12.4 Tangent Lines and Derivatives
12.5 Area and the Definite Integral
Chapter R Reference: Basic Algebraic Concepts
R.1 Review of Exponents and Polynomials
R.2 Review of Factoring
R.3 Review of Rational Expressions
R.4 Review of Negative and Rational Exponents
R.5 Review of Radicals
Chapter R Test
Appendix Geometry Formulas
Answers to Selected Exercises
Index