Synopses & Reviews
In this new edition of Precalculus, Seventh Edition, the authors encourage graphical, numerical, and algebraic modeling of functions as well as a focus on problem solving, conceptual understanding, and facility with technology. They responded to many helpful suggestions provided by students and teachers in order to create a book that is designed for instructors and written for students. As a result, we believe that the changes made in this edition make this the most effective precalculus text available today.
About the Author
Frank Demana received his master’s degree in mathematics and his Ph.D. from Michigan State University. Currently, he is Professor Emeritus of Mathematics at The Ohio State University. As an active supporter of the use of technology to teach and learn mathematics, he is cofounder of the national Teachers Teaching with Technology (T^{3}) professional development program. He has been the director and co-director of more than $10 million of National Science Foundation (NSF) and foundational grant activities. He is currently a co-PI on a $3 million dollar grant from the Department of Education Mathematics and Science Educational Research grant awarded to The Ohio State University. Along with frequent presentations at professional meetings, he has published a variety of articles in the areas of computer and calculator-enhanced mathematics instruction. Dr. Demana is also cofounder (with Bert Waits) of the annual International Conference on Technology in Collegiate Mathematics (ICTCM). He is co-recipient of the 1997 Glenn Gilbert National Leadership Award presented by the National Council of Supervisors of Mathematics, and recipient of the 1998 Christoggerson-Fawcett Mathematics Education Award presented by the Ohio Council of Teachers of Mathematics. Dr. Demana has coauthored Calculus: Graphical, Numerical, Algebraic; Essential Algebra: A Calculator Approach; Transition to College Mathematics; College Algebra and Trigonometry: A Graphing Approach; College Algebra: A Graphing Approach; Precalculus: Functions and Graphs; and Intermediate Algebra: A Graphing Approach.
Bert Waits received his Ph.D. from The Ohio State University and is currently Professor Emeritus of Mathematics there. Dr. Waits is cofounder of the national Teachers Teaching with Technology (T^{3}) professional development program, and has been co-director or principal investigator on several large NSF projects. Dr. Waits has published articles in more than 50 nationally recognized professional journals. He frequently gives invited lectures, workshops, and minicourses at national meetings of the MAA and teh National Council of Teachers of Mathematics (NCTM) on how to use computer technology to enhance the teaching and learning of mathematics. He has given invited presentations at the International Congress on Mathematical Education (ICME 6, 7, and 8) in Budapest (1988), Quebec (1992) and Seville (1996). Dr. Waits is co-recipient of the 1997 Glenn Gilbert National Leadership Award presented by the National Council of Supervisors of Mathematics, and is the co-founder (with Frank Demana) of the ICTCM. Dr. Waits has coauthored Calculus: Graphical, Numerical, Algebraic; College Algebra and Trigonometry: A Graphing Approach; College Algebra: A Graphing Approach; Precalculus: Functions and Graphs; and Intermediate Algebra: A Graphing Approach.
Greg Foley received B.A. and M.A. degrees in mathematics and a Ph.D. in mathematics education from The University of Texas at Austin. He is Director of the Liberal Arts and Science Academy of Austin, the advanced academic magnet high school program of the Austin Independent School District in Texas. Dr. Foley has taught elementary arithmetic through graduate-level mathematics, as well as upper division and graduate-level mathematics education classes. From 1977 until 2004, he held full-time faculty positions at North Harris County College, Austin Community College, The Ohio State University, Sam Houston State University, and Appalachian State University, where he was Distinguished Professor of Mathematics Education in the Department of Mathematical Sciences and directed the Mathematics Education Leadership Training (MELT) program. Dr. Foley has presented over 200 lectures, workshops, and institutes throughout the United States and internationally, has directed a variety of funded projects, and has published articles in several professional journals. Active in various learned societies, he is a member of the Committee on the Mathematical Education of Teachers of the Mathematical Association of America (MAA). In 1998, Dr. Foley received the biennial American Mathematical Association of Two-Year Colleges (AMATYC) Award for Mathematics Excellence, and in 2005, he received the annual Teachers Teaching with Technology (T^{3}) Leadership Award.
Dan Kennedy received his undergraduate degree from the College of the Holy Cross and his master’s and Ph.D. in mathematics from the University of North Carolina at Chapel Hill. Since 1973, he has taught mathematics at the Baylor School in Chattanooga, Tennessee, where he holds the Cartter Lupton Distinguished Professorship. Dr. Kennedy became an Advanced Placement Calculus reader in 1978, which led to an increasing level of involvement with the program as workshop consultant, table leader, and exam leader. He joined the Advanced Placement Calculus Test Development Committee in 1986, then in 1990, became the first high school teacher in 35 years to chair that committee. It was during his tenure as chair that the program moved to require graphing calculators and laid the early groundwork for the recent major reform of the Advanced Placement Calculus curriculum. The author of the 1997 Teacher’s Guide--APÒ Calculus, Dr. Kennedy has conducted more than 50 workshops and institutes for high school calculus teachers. His articles on mathematics teacher have appeared in the Mathematics Teacher and the American Mathematical Monthly, and he is a frequent speaker on education reform at professional and civic meetings. Dr. Kennedy was name a Tandy Technology Scholar in 1992 and was a Presidential Award winner in 1995. Dr. Kennedy has coauthored Calculus: Graphical, Numerical, Algebraic; Prentice Hall Algebra 1; Prentice Hall Geometry; and Prentice Hall Algebra 2.
Table of Contents
Chapter P Prerequisites
P.1 Real Numbers
P.2 Cartesian Coordinate System
P.3 Linear Equations and Inequalities
P.4 Lines in the Plane
P.5 Solving Equations Graphically, Numerically, and Algebraically
P.6 Complex Numbers
P. 7 Solving Inequalities Algebraically and Graphically
Chapter 1 Functions and Graphs
1.1 Modeling and Equation Solving
1.2 Functions and Their Properties
1.3 Twelve Basic Functions
1.4 Building Functions from Functions
1.5 Parametric Relations and Inverses
1.6 Graphical Transformations
1.7 Modeling With Functions
Chapter 2 Polynomial, Power, and Rational Functions
2.1 Linear and Quadratic Functions with Modeling
2.2 Power Functions with Modeling
2.3 Polynomial Functions of Higher Degree with Modeling
2.4 Real Zeros of Polynomial Functions
2.5 Complex Zeros and the Fundamental Theorem of Algebra
2.6 Graphs of Rational Functions
2.7 Solving Equations in One Variable
2.8 Solving Inequalities in One Variable
Chapter 3 Exponential, Logistic, and Logarithmic Functions
3.1 Exponential and Logistic Functions
3.2 Exponential and Logistic Modeling
3.3 Logarithmic Functions and Their Graphs
3.4 Properties of Logarithmic Functions
3.5 Equation Solving and Modeling
3.6 Mathematics of Finance
Chapter 4 Trigonometric Functions
4.1 Angles and Their Measures
4.2 Trigonometric Functions of Acute Angles
4.3 Trigonometry Extended: The Circular Functions
4.4 Graphs of Sine and Cosine: Sinusoids
4.5 Graphs of Tangent, Cotangent, Secant, and Cosecant
4.6 Graphs of Composite Trigonometric Functions
4.7 Inverse Trigonometric Functions
4.8 Solving Problems with Trigonometry
Chapter 5 Analytic Trigonometry
5.1 Fundamental Identities
5.2 Proving Trigonometric Identities
5.3 Sum and Difference Identities
5.4 Multiple-Angle Identities
5.5 The Law of Sines
5.6 The Law of Cosines
Chapter 6 Applications of Trigonometry
6.1 Vectors in the Plane
6.2 Dot Product of Vectors
6.3 Parametric Equations and Motion
6.4 Polar Coordinates
6.5 Graphs of Polar Equations
6.6 De Moivre’s Theorem and nth Roots
Chapter 7 Systems and Matrices
7.1 Solving Systems of Two Equations
7.2 Matrix Algebra
7.3 Multivariate Linear Systems and Row Operations
7.4 Partial Fractions
7.5 Systems of Inequalities in Two Variables
Chapter 8 Analytic Geometry in Two and Three Dimensions
8.1 Conic Sections and Parabolas
8.2 Ellipses
8.3 Hyperbolas
8.4 Translation and Rotation of Axes
8.5 Polar Equations of Conics
8.6 Three-Dimensional Cartesian Coordinate System
Chapter 9 Discrete Mathematics
9.1 Basic Combinatorics
9.2 The Binomial Theorem
9.3 Probability
9.4 Sequences
9.5 Series
9.6 Mathematical Induction
9.7 Statistics and Data (Graphical)
9.8 Statistics and Data (Algebraic)
Chapter 10 An Introduction to Calculus: Limits, Derivatives, and Integrals
10.1 Limits and Motion: The Tangent Problem
10.2 Limits and Motion: The Area Problem
10.3 More on Limits
10.4 Numerical Derivatives and Integrals
Appendix A Algebra Review
Appendix B Key Formulas
Appendix C Logic