[Book Cover]

College Algebra, 1/e

Robert Blitzer, Miami-Dade Community College

Published October, 1997 by Prentice Hall Engineering/Science/Mathematics

Copyright 1998, 859 pp.
Cloth
ISBN 0-13-399940-8


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Summary

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.

Features


Problem Solving

  • 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.
Modeling Real World Situations
  • 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 the text.
  • Section 1.3 “Linear and Quadratic Modeling.”
  • Section 3.7 “Modeling with Rational Functions and Inverse Variation.”
  • Section 4.5 “Modeling with Exponential and Logarithmic Functions.”
  • Real world sourced data, interpretation of data and visualization is fully integrated.
Reasoning
  • “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 and suggestions.
Connecting with Other Disciplines
  • 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.
Communicating
  • 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 problem.
Technology
  • 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.
Mathematical Power
  • “Enrichment Essays” are interspersed throughout the text with further concepts and ideas appearing in the expository sections. These essays inspire non-trivial explorations of mathematical ideas with connections to other disciplines they might be more familiar with.

    = Additional Pedagogical Features:

Detailed Step-by-Step Explanations illustrate to the student the mathematical process and thought behind each and every step of the examples.
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.


Table of Contents
(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 Review Problems.

    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 to Probability.

    Appendix: Review Problems Covering the Entire Book.


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