About the Book
This text was written with the goal of having students succeed in this course, and gain a foundation to succeed in further mathematics courses. To that end, the authors have written a text with a theme (showing the connections between the zeros, x-intercepts, and solutions), with a series of side-by-side features (designed to show examples being solved algebraically and graphically), and with the knowledge that many students are using graphing technology to help them learn the key concepts in this course (and so the book automatically comes bundled with a free graphing calculator manual). Thus, the approach of this text is more interactive than most texts and the authors feel that, accordingly, more students will succeed in this course.
Table of Contents:
Introduction to Graphs and the Graphing Calculator.
R. Basic Concepts of Algebra.
The Real-Number System.
Integer Exponents, Scientific Notation, and Order of Operations.
Addition, Subtraction, and Multiplication of Polynomials.
Factoring.
Rational Expressions.
Radical Notation and Rational Exponents.
The Basics of Equation Solving.
1. Graphs, Functions, and Models.
Functions, Graphs, and Graphers.
Linear Functions, Slope, and Applications.
Modeling: Data Analysis, Curve Fitting, and Linear Regression.
More on Functions.
Symmetry and Transformations.
Variation and Applications.
Distance, Midpoints, and Circles.
2. Functions and Equations: Zeros and Solutions.
Zeros of Linear Functions and Models.
The Complex Numbers.
Zeros of Quadratic Functions and Models.
Analyzing Graphs of Quadratic Functions.
Modeling: Data Analysis, Curve Fitting, and Quadratic Regression.
Zeros and More Equation Solving.
Solving Inequalities.
3. Polynomial and Rational Functions.
Polynomial Functions and Modeling.
Polynomial Division; The Remainder and Factor Theorems.
Theorems about Zeros of Polynomial Functions.
Rational Functions.
Polynomial and Rational Inequalities.
4. Exponential and Logarithmic Functions.
Composite and Inverse Functions.
Exponential Functions and Graphs.
Logarithmic Functions and Graphs.
Properties of Logarithmic Functions.
Solving Exponential and Logarithmic Equations.
Applications and Models: Growth and Decay.
5. The Trigonometric or Circular Functions.
The Unit Circle.
Circular Functions: Graphs and Properties.
Angles and Rotations.
Trigonometric Functions Involving Angles and Rotations.
Right Triangle Trigonometry.
Graphs of Transformed Sine and Cosine Functions.
6. Trigonometric Identities, Inverse Functions, and Equations.
Identities: Pythagorean and Sum and Difference.
Identities: Cofunction, Double-Angle, and Half-Angle.
Proving Trigonometric Identities.
Inverses of the Trigonometric Functions.
Solving Trigonometric Equations.
7. Applications of Trigonometry.
Applications of Right Triangles.
The Law of Sines.
The Law of Cosines.
Complex Numbers: Trigonometric Form.
Vectors and Applications.
Vector Operations.
8. Systems of Equations and Matrices.
Systems of Equations in Two Variables.
Systems of Equations in Three Variables.
Matrices and Systems of Equations.
Matrix Operations.
Inverses of Matrices.
Systems of Inequalities and Linear Programming.
Partial Fractions.
9. Analytic Geometry Topics.
The Parabola.
The Circle and the Ellipse.
The Hyperbola.
Nonlinear Systems of Equations.
Rotation of Axes.
Polar Coordinates and Graphs.
Polar Equations of Conics.
Parametric Equations and Graphs.
10. Sequences, Series, and Combinatorics.
Sequences and Series.
Arithmetic Sequences and Series.
Geometric Sequences and Series.
Mathematical Induction.
Combinatorics: Permutations.
Combinatorics: Combinations.
The Binomial Theorem.
Probability.
Appendixes.
A. Descartes' Rule of Signs.
B. Determinants and Cramer's Rule.
About the Author :
Marvin Bittinger For over thirty years Professor Marvin L. Bittinger has been teaching math at the university level. Since 1968 he has been employed as a professor of mathematics education at Indiana University - Purdue University at Indianapolis. Professor Bittinger has authored 159 publications on topics ranging from Basic Mathematics to Algebra and Trigonometry to Brief Calculus. He received his BA in Mathematics from Manchester College in 1963 and his PhD in Mathematics Education from Purdue University in 1968. Special honors include being Distinguished Visiting Professor at the United States Air Force Academy and being elected to the Manchester College Board of Trustees from 1992 to 1999. His hobbies include hiking, baseball, golf, and bowling and he enjoys membership in the Professional Bowler's Association and the Society for the Advancement of Baseball Research.
Professor Bittinger has also had the privilege of speaking at a recent mathematics convention giving a lecture entitled, Baseball and Mathematics. 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 three grandchildren.
Judy Beecher has an undergraduate degree in mathematics fromIndiana University and a graduate degree in mathematics fromPurdue University. She has taught at both the high school andcollege levels with many years of developmental math and precalculusteaching experience at Indiana University Purdue University Indianapolis. Inaddition to her career in textbook publishing,she spends time reading, traveling, attending the theater, and promotingcharity projects for a children's camp.
David Ellenbogen has been teaching community college mathematics for over twenty years. Born in Weehawken New Jersey, David graduated with honors from Bates College. After teaching high school mathematics for two years, David earned a masters degree from the University of Massachusetts. He has taught at Greenfield Community College and Cape Cod Community College in Massachusetts, as well as, at Saint Michaels College, and The University of Vermont. For the past seven years David has been a part time lecturer for the Community College of Vermont where he has served on their statewide math curriculum committee. Currently residing in Colchester, Vermont, David enjoys playing the piano, downhill skiing, basketball, bicycling, hiking, and coaching. He has two sons and a wolf/husky hybrid.
Judy Penna received her undergraduate degree from Kansas State University in mathematics and her graduate degree from the University of Illinois in mathematics. Since then, she has taught at Indiana University Purdue University Indianapolis and at Butler University, and continues to focus on writing quality textbooks for undergraduates students taking mathematics. In her free time she likes to travel, read, knit and spend time throughout the U.S. with her children.
