Higher Education

Precalculus: A Problems-Oriented Approach, 6th Edition

  • includes CD-ROM and iLrn™ Tutorial
  • David Cohen late of University of California, Los Angeles
  • ISBN-10: 0534402127  |  ISBN-13: 9780534402129
  • 1184 Pages
  • Previous Editions: 1997, 1987
  • © 2005 | Published
  • College Bookstore Wholesale Price = $286.50
  • Newer Edition Available
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About

Overview

David Cohen's PRECALCULUS: A PROBLEMS-ORIENTED APPROACH, Sixth Edition, focuses on teaching mathematics by using a graphical perspective throughout to provide a visual understanding of college algebra and trigonometry. The author is known for his clear writing style and the numerous quality exercises and applications he includes in his respected texts. In this new edition, graphs, visualization of data, and functions are now introduced much earlier and receive greater emphasis. Many sections now contain more examples and exercises involving applications and real-life data. While this edition takes the existence of the graphing calculator for granted, the material is arranged so that one can teach the course with as much or as little graphing utility work as he/she wishes.

Features and Benefits

  • The author has a remarkable writing style that is student friendly and yet mathematically honest.
  • The "Graphical Perspective" feature uses graphs to supplement the text discussion and encourage students to produce their own pictures of a graph.
  • There is a strong emphasis on graphs and visualization, with numerical, graphical, and algebraic viewpoints tightly linked throughout the text, to help students understand the material.
  • Coordinates and graphs are developed in Chapter 1.
  • Iteration is covered from numerical, graphical, and algebraic viewpoints.
  • Optional "Graphing Utility" exercises are available throughout the text.
  • Exercises range in difficulty from simple to more complex and are designated with an "A," "B," or "C" rating.

Table of Contents

1. FUNDAMENTALS.
Sets of Real Numbers. Absolute Value. Solving Equations (Review and Preview). Rectangular Coordinates. Visualizing Data. Graphs and Graphing Utilities. Equations of Lines. Symmetry and Graphs. Circles.
2. EQUATIONS AND INEQUALITIES.
Quadratic Equations: Theory and Examples. Other Types of Equations. Inequalities. More on Inequalities.
3. FUNCTIONS.
The Definition of a Function. The Graph of a Function. Shapes of Graphs. Average Rate of Change. Techniques in Graphing. Methods of Combining Function. Iteration. Inverse Functions.
4. POLYNOMIAL AND RATIONAL FUNCTIONS.
Applications to Optimization. Linear Functions. Quadratic Functions. Using Iteration to Model Population Growth (Optional Section). Setting up Equations That Define Functions. Maximum and Minimum Problems. Polynomial Functions. Rational Functions.
5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions. The Exponential Function y = ex. Logarithmic Functions. Properties of Logarithms. Equations and Inequalities with Logs and Exponents. Compound Interest. Exponential Growth and Decay.
6. TRIGONOMETRIC FUNCTIONS OF ANGLES.
Trigonometric Functions of Acute Angles. Algebra and the Trigonometric Functions. Right-Triangle Applications. Trigonometric Functions of Angles. Trigonometric Identities.
7. TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS.
Radian Measure. Radian Measure and Geometry. Trigonometric Functions of Real Numbers. Graphs of the Sine and the Cosine Functions. Graphs of y = A sin(Bx-C) and y = A cos(Bx - C). Simple Harmonic Motion. Graphs of the Tangent and the Reciprocal Functions.
8. ANALYTICAL TRIGONOMETRY.
The Addition Formulas. The Double-Angle Formulas. The Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations. The Inverse Trigonometric Functions.
9. ADDITIONAL TOPICS IN TRIGONOMETRY.
The Law of Sines and the Law of Cosines. Vectors in the Plane, a Geometric Approach. Vectors in the Plane, an Algebraic Approach. Parametric Equations. Introduction to Polar Coordinates. Curves in Polar Coordinates.
10. SYSTEMS OF EQUATIONS.
Systems of Two Linear Equations in Two Unknowns. Gaussian Elimination. Matrices. The Inverse of a Square Matrix. Determinants and Cramer's Rule. Nonlinear Systems of Equations. Systems of Inequalities.
11. ANALYTIC GEOMETRY.
The Basic Equations. The Parabola. Tangents to Parabolas (Optional). The Ellipse. The Hyperbola. The Focus-Directrix Property of Conics. The Conics in Polar Coordinates. Rotation of Axes.
12. ROOTS OF POLYNOMIAL EQUATIONS.
The Complex Number System. Division of Polynomials. Roots of Polynomial Equations: The Remainder Theorem and the Factor Theorem. The Fundamental Theorem of Algebra. Rational and Irrational Roots. Conjugate Roots and Descartes' Rule of Signs. Introduction to Partial Fractions. More About Partial Fractions.
13. ADDITIONAL TOPICS.
Mathematical Induction. The Binomial Theorem. Introduction to Sequences and Series. Arithmetic Sequences and Series. Geometric Sequences and Series. DeMoivre's Theorem.
Appendix 1: Using a Graphing Utility.
Appendix 2: Significant Digits and Calculators.
Tables.
Answers to Selected Exercises.
Index.

What's New

  • The role of the graphing utility has been expanded in this edition, with graphing utility material carefully integrated throughout the text. Graphing utility exercises are now integrated into the exercise sets with an icon to identify them. Reviewers praised Cohen's thoughtful approach to the optional use of technology, lauding his realistic use of modern technologies while maintaining a solid foundation in algebraic concepts.
  • Exercises have been rewritten, updating real data and applications throughout.
  • In addition to the "Writing Mathematics" sections, there are now "Projects" and "Mini Projects" at the ends of many sections. These give the students additional opportunities to discuss, explore, learn, and write mathematics.
  • The material on long division of polynomials has been moved to Chapter 12, preceding synthetic division.
  • Chapter 3 includes an expanded introduction to the function concept. Functions are introduced at length using algebraic, verbal, tabular, and graphical forms. Functions as models are introduced and used in examples and exercises. Implicit functions are introduced in the section PROJECT. Material on the average rate of change of a function (previously in section 3.2) has been expanded and there is an increased emphasis on applications.
  • New material includes: a discussion on the use of spreadsheets in generating scatter plots and regression lines, modeling real-life data with quadratic functions (Chapter 4); discussion on the use of graphing calculators and spreadsheets in computing matrix products and matrix inverses, including new examples and exercises using matrices to code and decode messages (Chapter 10); and new material in Chapter 11 on the perihelion and aphelion for an elliptical orbit.
  • Every new copy of this text is packaged with iLrn Tutorial, our suite of online, dynamic, customizable tutorial resources that puts tools for students' content mastery at their fingertips. By entering a PIN code packaged with their textbook, students gain access to text-specific tutorials with step-by-step explanations, exercises and quizzes, and vMentor--live, one-on-one online help from an experienced mathematics tutor. For instructors, iLrn offers highly customizable testing, course management, and diagnostic online resources that provide a dynamic way to power the course.
  • Our student mastery system also includes the Interactive Video Skillbuilder CD-ROM. Think of it as portable office hours! Free with every copy of this text, the Interactive Video Skillbuilder CD-ROM contains more than eight hours of video instruction and includes MathCue Tutorial Software.
  • Preloaded with content and available FREE via PIN code when packaged with this text, WebTutor ToolBox pairs all the content of this text's rich Book Companion Web Site with all the sophisticated course management functionality of a WebCT or Blackboard product. It's an ideal solution for online and distance learning needs.
  • A Book Companion Web Site accompanies this text and features a variety of teaching and learning resources. This Web site features everything from book-specific resources to newsgroups. It's a great way to make teaching and learning an interactive and intriguing experience.

Efficacy and Outcomes

Reviews

"The quantity and quality of the exercises are the reasons why I think that Cohen’s book is my favorite algebra and precalculus book ever…. Both the quantity and quality of the exercises of Cohen’s book are first class and the problems in each section are reflective of the concepts being taught. As far as I am concerned, the quality of both his algebra text and precalculus text are way above anything on the market that I’ve seen."

— Fred M. Schifando, Pennsylvania State University

"The mini projects are excellent and can be used for collaborative learning…. I think the writing style of an already well-written book has been improved."

— Richard Riggs, New Jersey City University

"This text is one of the most challenging precalculus books I have seen, but I like that because it gives students the opportunity to be very well prepared for calculus. The presentations are rigorous, precise, and detailed, but written in a way that students can follow fairly well. The exercises range from simple to complex and include not only applications to other disciplines but to other areas of mathematics as well." "One of the main reasons I continue to use this author’s texts is that I receive more compliments from my students on his books than I have on any other texts."

— Greg S. Deitrich, Florida Community College at Jacksonville

"Overall, the quantity and quality of the exercises in Cohen’s texts are outstanding. The different levels of exercises--A, B, and C levels--make an excellent transition from skill development to concept development."

— John Gosselin, University of Georgia

"The new authors have done a nice job in reorganizing the material in Chapter 6. Instructors familiar with earlier editions of Cohen’s books will find the transition seamless."

— Thomas J. Walters, University of California Los Angeles (retired)/Wilson High School

Supplements

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Student Supplements

Class Notes Guide  (ISBN-10: 0495112968 | ISBN-13: 9780495112969)

List Price = $58.95  | CengageBrain Price = $58.95  | College Bookstore Wholesale Price = $44.00

Meet the Author

Author Bio

David Cohen

David Cohen, a senior lecturer at UCLA, was the original author of the successful, well-respected precalculus series--COLLEGE ALGEBRA, ALGEBRA AND TRIGONOMETRY, PRECALCULUS: A PROBLEMS-ORIENTED APPROACH, and PRECALCULUS: WITH UNIT CIRCLE TRIGONOMETRY.