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Marvin Bittinger has been teaching math at the university level for more than thirty-eight years. Since 1968, he has been employed at Indiana University Purdue University Indianapolis, and is now professor emeritus of mathematics education. Professor Bittinger has authored over 190 publications on topics ranging from basic mathematics to algebra and trigonometry to applied calculus. He received his BA in mathematics from Manchester College and his PhD in mathematics education from Purdue University. Special honors include Distinguished Visiting Professor at the United States Air Force Academy and his election to the Manchester College Board of Trustees from 1992 to 1999. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently giving a lecture entitled "Baseball and Mathematics." His hobbies include hiking in Utah, baseball, golf, and bowling. In addition, he also has an interest in philosophy and theology, in particular, apologetics. Professor Bittinger currently lives in Carmel, Indiana with his wife Elaine. He has two grown and married sons, Lowell and Chris, and four granddaughters.
David Ellenbogen has taught math at the college level for nearly 30 years, spending most of that time in the Massachusetts and Vermont community college systems, where he has served on both curriculum and developmental math committees. He has taught at St. Michael's College and The University of Vermont. Professor Ellenbogen has been active in the American Mathematical Association of Two Year Colleges (AMATYC) since 1985, having served on its Developmental Mathematics Committee and as a delegate. He has been a member of the Mathematical Association of America (MAA) since 1979. He has authored dozens of texts on topics ranging from prealgebra to calculus and has delivered lectures on the use of language in mathematics. Professor Ellenbogen received his bachelor's degree in mathematics from Bates College and his master’s degree in community college mathematics education from The University of Massachusetts—Amherst. In his spare time, he enjoys playing piano, biking, hiking, skiing and volunteer work. He currently serves on the boards of the Vermont Sierra Club and the Vermont Bicycle Pedestrian Coalition. He has two sons, Monroe and Zachary.
Barbara Johnson has a B.S. in mathematics from Bob Jones University and a M.S. in math from Clemson University. She has taught high school and college math for 25 years, and enjoys the challenge of helping each student grow in appreciation for and understanding of mathematics. As a Purdue Master Gardener, she also enjoys helping others learn gardening skills. Believing that the best teacher is always learning, she recently earned a black belt in karate.
Preface
1. Basics of Algebra and Graphing
1.1 Some Basics of Algebra
1.2 Operations with Real Numbers
1.3 Equivalent Algebraic Expressions
1.4 Exponential Notation and Scientific Notation
Mid-Chapter Review
1.5 Graphs
1.6 Solving Equations and Formulas
1.7 Introduction to Problem Solving and Models
Summary and Review
Test
2. Functions, Linear Equations, and Models
2.1 Functions
2.2 Linear Functions: Slope, Graphs, and Models
2.3 Another Look at Linear Graphs
2.4 Introduction to Curve Fitting: Point-Slope Form
Mid-Chapter Review
2.5 The Algebra of Functions
Summary and Review
Test
3. Systems of Linear Equations and Problem Solving
3.1 Systems of Equations in Two Variables
3.2 Solving by Substitution or Elimination
3.3 Solving Applications: Systems of Two Equations
Mid-Chapter Review
3.4 Systems of Equations in Three Variables
3.5 Solving Applications: Systems of Three Equations
3.6 Elimination Using Matrices
3.7 Determinants and Cramer's Rule
3.8 Business and Economics Applications
Summary and Review
Test
Cumulative Review: Chapters 1—3
4. Inequalities
4.1 Inequalities and Applications
4.2 Solving Equations and Inequalities by Graphing
4.3 Intersections, Unions, and Compound Inequalities
4.4 Absolute-Value Equations and Inequalities
Mid-Chapter Review
4.5 Inequalities in Two Variables
Summary and Review
Test
5. Polynomials and Polynomial Functions
5.1 Introduction to Polynomials and Polynomial Functions
5.2 Multiplication of Polynomials
5.3 Polynomial Equations and Factoring
5.4 Trinomials of the Type x ^{2} + bx + c
5.5 Trinomials of the Type ax ^{2} + bx + c
5.6 Perfect-Square Trinomials and Differences of Squares
5.7 Sums or Differences of Cubes
Mid-Chapter Review
5.8 Applications of Polynomial Equations
Summary and Review
Test
6. Rational Expressions, Equations, and Functions
6.1 Rational Expressions and Functions: Multiplying and Dividing
6.2 Rational Expressions and Functions: Adding and Subtracting
6.3 Complex Rational Expressions
Mid-Chapter Review
6.4 Rational Equations
6.5 Applications Using Rational Equations
6.6 Division of Polynomials
6.7 Synthetic Division
6.8 Formulas, Applications, and Variation
Summary and Review
Test
Cumulative Review: Chapters 1—6
7. Exponents and Radical Functions
7.1 Radical Expressions, Functions, and Models
7.2 Rational Numbers as Exponents
7.3 Multiplying Radical Expressions
7.4 Dividing Radical Expressions
7.5 Expressions Containing Several Radical Terms
Mid-Chapter Review
7.6 Solving Radical Equations
7.7 The Distance Formula, the Midpoint Formula, and Other Applications
7.8 The Complex Numbers
Summary and Review
Test
8. Quadratic Functions and Equations
8.1 Quadratic Equations
8.2 The Quadratic Formula
8.3 Studying Solutions of Quadratic Equations
8.4 Studying Solutions of Quadratic Equations
8.5 Equations Reducible to Quadratic
Mid-Chapter Review
8.6 Quadratic Functions and Their Graphs
8.7 More About Graphing Quadratic Functions
8.8 Problem Solving and Quadratic Functions
8.9 Polynomial Inequalities and Rational Inequalities
Summary and Review
Test
9. Exponential Functions and Logarithmic Functions
9.1 Composite Functions and Inverse Functions
9.2 Exponential Functions
9.3 Logarithmic Functions
9.4 Properties of Logarithmic Functions
Mid-Chapter Review
9.5 Natural Logarithms and Changing Bases
9.6 Solving Exponential and Logarithmic Equations
9.7 Applications of Exponential and Logarithmic Functions
Summary and Review
Test
Cumulative Review: Chapters 1—9
10. Conic Sections
10.1 Conic Sections: Parabolas and Circles
10.2 Conic Sections: Ellipses
10.3 Conic Sections: Hyperbolas
Mid-Chapter Review
10.4 Nonlinear Systems of Equations
Summary and Review
Test
11. Sequences, Series, and the Binomial Theorem
11.1 Sequences and Series
11.2 Arithmetic Sequences and Series
11.3 Geometric Sequences and Series
Mid-Chapter Review
11.4 The Binomial Theorem
Summary and Review
Test
Cumulative Review: Chapters 1-11
Answers
Glossary
Photo Credits
Index
Index of Applications