College Algebra, 1/e
Robert Blitzer, Miami-Dade Community College
Published October, 1997 by Prentice Hall Engineering/Science/Mathematics
Copyright 1998, 859 pp.
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Appropriate for courses in College Algebra. The goals
of the text are: 1) provide a solid algebraic foundation for students
who may take additional mathematics courses, 2) introduce algebraic
modeling and encourage students to use it to solve real world problems,
and 3) to foster the development of problem solving skills, critical
thinking and communication of mathematical ideas.
Modeling Real World Situations
- Emphasis is on the language of algebra as a tool for
solving problems related to everyday life.
- Problem Solving Strategies are introduced in chapter
one and are integrated thoughout the rest of the text.
- Many Applications, Examples and Exercises use current
data drawn from familiar sources such as the 1995 Statistical Abstract
of the U.S. published by the Census Bureau.
- Modeling is introduced in Chapter 1 and emphasized throughout
- Section 1.3 Linear and Quadratic Modeling.
- Section 3.7 Modeling with Rational Functions and
- Section 4.5 Modeling with Exponential and Logarithmic
- Real world sourced data, interpretation of data and visualization
is fully integrated.
Connecting with Other Disciplines
- Discover for Yourself exercises encourage students
to actively participate in the learning process as they read the book.
- Study Tips boxes offer suggestions for problem
solving, point out common student errors and provide informal tips
- The use of fine art, historical notes and interdisciplinary
connections are introduced in the context and applicability of algebra.
- The extensive collection of applications, including environmental
and financial issues promotes the problem-solving theme and demonstrates
the connections and relevancy to other disciplines.
- Since most students have a difficult time with word problems,
a great deal of attention has been placed on translating the words
and phrases of verbal models into algebraic equations.
- Most problem sets contain group activity problems. These
collaborative activities give students an opportunity to think, talk
and write about mathematics and to see other approaches to the same
Detailed Step-by-Step Explanations illustrate to
the student the mathematical process and thought behind each and every
step of the examples.
- Optional Graphing Calculator usage found throughout the
sections, examples and exercises. The grapher is introduced in the
prerequisites chapter and is used throughout the text to explore mathematical
ideas and to visualize the dynamics of the situation. TI-83 screen
shots are used thoughout the text for student support.
- Using Technology feature which includes screen
shots, makes visual solutions available to both students with graphers
and those without.
- Chapter Projects, extended one-page applications, conclude
each chapter. Most of these activities feature selected Internet websites
(available to students via the Prentice Hall/Blitzer website) for
student research and exploration.
Learning Objectives open each section. The objectives
are reinstated in the margin at the point of their use.
Problem Sets include the following categories: Practice,
Application, True-False Critical Thinking, Technology, Writing in
Mathematics, Open Ended Critical Thinking, and Group Activity.
Chapter Summaries are inclusive and appear at the conclusion
of each chapter - helping students pull together what they have learned
throughout the chapter.
(NOTE: Each chapter concludes with a Summary, Review Problems,
and a Chapter Test.)
Prerequisites: Fundamental Concepts of Algebra.
The Real Number System. Properties of Algebraic Expressions;
Exponents. Graphs and Graphing Utilities. Radicals and Rational Exponents.
Polynomials. Factoring. Rational Expressions. Complex Numbers.
1. Equations, Inequalities, and Mathematical Models.
Linear Equations. Quadratic Equations. Linear and Quadratic
Modeling. Other Types of Equations. Linear Inequalities. Polynomial
and Rational Inequalities.
2. Functions and Graphs.
Introduction to Functions. Linear Functions and Slope. Graphs
of Relations and Functions. Increasing and Decreasing Functions; Extreme
Values. Transformations of Functions. Combinations of Functions. Inverse
Functions. Cumulative Review Problems.
3. Modeling with Polynomial and Rational Functions.
Quadratic Functions. Polynomial Functions of Higher Degree
and Polynomial Variation. Zeros of Polynomial Functions. More on Zeros
of Polynomial Functions. Graphing Rational Functions. Modeling with
Rational Functions and Inverse Variation. Cumulative Review Problems.
4. Exponential and Logarithmic Functions.
Exponential Functions. Logarithmic Functions. Properties
of Logarithmic Functions. Exponential and Logarithmic Equations. Modeling
with Exponential and Logarithmic Functions. Cumulative Review Problems.
5. Matrices and Linear Systems.
Solving Linear Systems Using Substitution and Addition.
Matrix Solutions to Linear Systems. Inconsistent and Dependent Systems
and Their Applications. Matrix Operations and Their Applications.
Inverses of Matrices. Determinants and Cramer's Rule. Partial Fractions.
Systems of Linear Inequalities and Linear Programming. Cumulative
6. Conic Sections and Nonlinear Systems.
The Ellipse. The Hyperbola. The Parabola. Nonlinear Systems.
Cumulative Review Problems.
7. Sequences, Series, and Probability.
Sequences and Series. Arithmetic Sequences and Series. Geometric
Sequences and Series. Mathematical Induction. The Binomial Theorem.
Counting Principles, Permutations, and Combinations. An Introduction
Appendix: Review Problems Covering the Entire Book.