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Table of Contents

Chapter 0: Prerequisites

0.1The Coordinate Plane: Lines and Circles

0.2Linear Inequalities

0.3Nonlinear Inequalities

Unit 1: Polynomial and Rational Functions

Chapter 1: Polynomial Functions

1.1Function Essentials

1.2Rates of Change

1.3Rates of Change: Linear and Quadratic Functions

1.4Rates of Change: Polynomial Functions

1.5Polynomial Functions: Characteristics Related to Zeros

1.6Polynomial Functions: End Behavior

Chapter 2: Rational Functions

2.1Rational Functions: End Behavior

2.2Rational Functions: Zeros

2.3Rational Functions: Vertical Asymptotes

2.4Rational Functions: Holes

2.5Equivalent Representations of Polynomials and Rational Expressions

Chapter 3: Transformations and Modeling

3.1Transformations of Functions

3.2Function Models: Selection, Assumptions, Limitations

3.3Function Models: Applications

Unit 2: Exponential and Logarithmic Functions

Chapter 4: Exponential Functions

4.1Rates of Change: Arithmetic and Geometric Sequences, Linear and Exponential Functions

4.2Exponential Functions: Characteristics and Properties

4.3Exponential Function Models

4.4Composition of Functions

Chapter 5: Logarithmic Functions

5.1Inverse Functions

5.2Logarithmic Functions: Characteristics and Properties

5.3Exponential and Logarithmic Equations and Inequalities

5.4Function Models: Logarithmic

5.5Semi-Log Plots

Unit 3: Trigonometric and Polar Functions

Chapter 6: Trigonometry Part 1

6.1Periodic Phenomena

6.2Sine, Cosine, and Tangent Functions

6.3Sine and Cosine Graphs

6.4The Sine and Cosine Functions: Transformations

6.5Sinusoidal Function Models

6.6The Tangent Function

Chapter 7: Trigonometry Part 2

7.1Inverse Trigonometric Functions

7.2Trigonometric Equations and Inequalities

7.3The Secant, Cosecant, and Cotangent Functions

7.4Trigonometric Identities and Simplifications

7.5Verifying Trigonometric Identities

Chapter 8: Polar Functions

8.1The Polar Coordinate System

8.2Polar Function Graphs

8.3Rates of Change in Polar Functions

Unit 4: Functions Involving Parameters, Vectors, and Matrices

Chapter 9: Parametric Equations and Functions Defined Implicitly

9.1Parametric Equations: Definitions and Graphs

9.2Parametric Equations: Modeling Motion

9.3Parametric Equations: Rates of Change

9.4Parametric Equations: Circles and Lines

9.5Functions Defined Implicitly

9.6Conic Sections

9.7Rewriting Equations in Parametric Form

Chapter 10: Vectors and Matrices

10.1Vectors

10.2Vector-Valued Functions

10.3Matrices

10.4The Determinant and the Inverse of a Matrix

10.5Linear Transformations

10.6Representation of Functions using Matrices

10.7Matrix Models

Appendix

A.1Law of Sines

A.2Law of Cosines

Authors

Stephen Kokoska

Steve Kokoska received his undergraduate degree from Boston College, and his M.S and Ph.D. from the University of New Hampshire. His initial research interests included the statistical analysis of cancer chemoprevention experiments. He has published a number of research papers in mathematics journals, including: Biometrics, Anticancer Research, and Computer Methods and Programs in Biomedicine. He has also presented results at national conferences, written several books, and been awarded grants from the National Science Foundation, the Center for Rural Pennsylvania, and the Ben Franklin Program.

Steve is a long-time consultant for the College Board and conducted workshops in Brazil, the Dominican Republic, and China. He was the AP Calculus Chief Reader for four years, and has been involved with calculus reform and the use of technology in the classroom. He has been teaching at Bloomsburg University for 25years and recently served as Director of the Honors Program.

Steve has been teaching introductory statistics classes throughout his academic career, and there is no doubt that this is his favorite course. This class (and text) provides students with basic, life-long, quantitative skills that they will use in almost any job and teaches them how to think and reason logically. Steve believes very strongly in data-driven decisions and conceptual understanding through problem solving.

Bruce Crauder

Bruce Crauder received his B.A. from Haverford College and his M.S. and Ph.D. from Columbia University. After post-doctoral positions at the Institute for Advanced Study, the University of Utah, and the University of Pennsylvania, Crauder came to Oklahoma State University, where he is now Professor of Mathematics and Associate Dean. Crauder’s research in algebraic geometry has resulted in 10 refereed articles in as many years in his specialty, three-dimensional birational geometry.

Benny Evans

Benny Evans received his Ph.D. in mathematics from the University of Michigan. He is currently Professor of Mathematics at Oklahoma State University, where he has served as undergraduate director, associate head, and department head. He has held visiting appointments at the Institute for Advanced Study, Rice University, and Texas A&M. His research interests are topology and mathematics education.

Alan Noell

Alan Noell has a B.A. degree in Mathematics from Texas A&M University, and M.A. and Ph.D. degrees in Mathematics from Princeton University. After a postdoctoral position at CalTech, in 1985 he joined the faculty at Oklahoma State University, where he is now Professor of Mathematics. His research interests are in the area of several complex variables. He has also enjoyed working in the area of curriculum development. His work has been supported by the National Science Foundation and other sources.

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