Pub. Date:
Benjamin-Cummings Publishing Company
Precalculus: Graphs and Models / Edition 2

Precalculus: Graphs and Models / Edition 2

by Marvin L. Bittinger, Penna, Ellenbogen, Beecher
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Product Details

ISBN-13: 9780201662382
Publisher: Benjamin-Cummings Publishing Company
Publication date: 10/01/2000
Edition description: Older Edition
Product dimensions: 7.87(w) x 9.84(h) x (d)

About the Author

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. His hobbies include hiking in Utah, baseball, golf, and bowling. Professor Bittinger has also had the privilege of speaking at many mathematics conventions, most recently 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 four granddaughters.

Judy Beecher has an undergraduate degree in mathematics from Indiana University and a graduate degree in mathematics from Purdue University. She has taught at both the high school and college levels with many years of developmental math and precalculus teaching experience at Indiana University–Purdue University Indianapolis. In addition to her career in textbook publishing, she spends time traveling, enjoying her grandchildren, and promoting charity projects for a children's camp.

David Ellenbogen has taught math at the college level for twenty-two 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 also taught at St. Michael's College and The University of Vermont. Professor Ellenbogen has been active in the Mathematical Association of Two Year Colleges since 1985, having served on its Developmental Mathematics Committee and as a delegate, and has been a member of the Mathematical Association of America since 1979. He has authored dozens of publications on topics ranging from prealgebra to calculus and has delivered lectures at numerous conferences on the use of language in mathematics. Professor Ellenbogen received his BA in mathematics from Bates College and his MA in community college mathematics education from The University of Massachusetts at Amherst. A co-founder of the Colchester Vermont Recycling Program, Professor Ellenbogen has a deep love for the environment and the outdoors, especially in his home state of Vermont. In his spare time, he enjoys playing keyboard in the band Soularium, volunteering as a community mentor, hiking, biking, and skiing. He has two sons, Monroe and Zack.

Judy Penna received her undergraduate degree in mathematics from Kansas State University and her graduate degree in mathematics from the University of Illinois. Since then, she has taught at Indiana University–Purdue University Indianapolis and at Butler University, and continues to focus on writing quality textbooks for undergraduate mathematics students. In her free time she likes to travel, read, knit, and spend time with her children.

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.
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 Models.
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.
Logarithmic Functions andGraphs.
Properties of Logarithmic Functions.
Solving Exponential and Logarithmic Equations.
Applications and Models: Growth and Decay.

5. The Trigonometric Functions.
Trigonometric Functions of Acute Angles.
Applications of Right Triangles.
Trigonometric Functions of Any Angle.
Radians, Arc Length, and Angular Speed.
Circular Functions: Graphs and Properties.
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.
The Law of Sines.
The Law of Cosines.
Complex Numbers: Trigonometric Form.
Polar Coordinates and Graphs.
Vectors and Applications.
Vector Operations.

8. Systems 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. Conic Sections.
The Parabola.
The Circle and the Ellipse.
The Hyperbola.
Nonlinear Systems of Equations.

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.

A. Descartes' Rule of Signs.
B. Determinants and Cramer's Rule.
C. Parametric Equations.

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