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Precalculus, 7th Edition

David Cohen, Theodore B. Lee, David Sklar

Copyright 2012
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Precalculus 7th Edition by David Cohen/Theodore B. Lee/David Sklar

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Overview
Meet the Authors
What's New
Features
Table of Contents
Pricing

Overview

Written by David Cohen and co-authors Theodore B. Lee and David Sklar, PRECALCULUS, Seventh Edition, focuses on the use of a graphical perspective to provide a visual understanding of college algebra and trigonometry. Cohen's texts are known for their clear writing style and outstanding, graded exercises and applications, including many examples and exercises involving applications and real-life data. Graphs, visualization of data, and functions are introduced and emphasized early on to aid student understanding. Although the text provides thorough treatment of the graphing calculator, the material is arranged to allow instructors to teach the course with as much or as little graphing utility work as they wish.

Meet the Authors

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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.

Theodore B. Lee

David Sklar

What's New

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In addition to being honed in numerous sections to improve clarity, this edition combines material from PRECALCULUS: A PROBLEMS-ORIENTED APPROACH with that of PRECALCULUS: WITH UNIT-CIRCLE TRIGONOMETRY, 4th Edition--creating a single book that accommodates the introduction of trigonometry with either a right triangle approach or a unit-circle approach.
This edition's broader content allows instructors wishing to introduce trigonometry via right triangles to do so by covering Chapters 6 through 10. Instructors wishing to introduce trigonometry via the unit circle may do so by skipping Chapter 6 and then covering Chapters 7 through 10.
Section 1.7 presents rewritten coverage of symmetry that features an increased emphasis on geometry.
In Section 2.4, the "table" presentation of non-linear inequalities is complemented with a sign chart on a number line.
In Section 3.4, "Techniques in Graphing," material on graphing techniques has been rewritten to include coverage of vertical and horizontal scaling of graphs.
Section 3.5, 'Methods of Combining Functions," includes new material of an abstract nature in discussing combinations of two even functions, two odd functions, or an even function and an odd function to determine whether properties are "preserved."
In Section 3.6, the presentation of inverse functions has been rewritten to emphasize the connection between a one-to-one function and its inverse function.
Section 4.6 includes a more detailed discussion and analysis of limiting behavior without using limits or limit notation. Enhanced discussion of limiting behavior (developed in Sections 4.6 and 4.7) continues in Sections 5.1 through 5.3 with the analysis of asymptote and other end behavior of graphs of exponential and logarithmic functions.

Features

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Thorough treatment of the role of the graphing utility is carefully integrated throughout the text. Graphing utility exercises are identified in the exercise sets with an icon. Reviewers have praised this book's thoughtful approach to the optional use of technology, lauding the way it covers the realistic use of modern technologies while providing a solid foundation in algebraic concepts.
"Writing Mathematics" sections and "Projects" (the latter now referenced in the book and available online) give students opportunities to discuss, explore, learn, and write about mathematics.
Functions, introduced in Chapter 3, are presented at length using algebraic, verbal, tabular, and graphical forms. Functions as models are introduced and used in examples and exercises.
This text has been lauded for its remarkable writing style, which 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.

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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 Functions. Iteration. Inverse Functions.
4. POLYNOMIAL AND RATIONAL FUNCTIONS: APPLICATIONS TO OPTIMIZATION.
Linear Functions. Quadratic Functions. Using Iteration to Model Populations Growth (Optional Section). Setting Up Equations That Devine 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. AN INTRODUCTION TO TRIGONOMETRY VIA RIGHT TRIANGLES.
Trigonometric Functions of Acute Angles. Right-Triangle Applications. Trigonometric Functions of Angles. Trigonometric Identities.
7. THE TRIGONOMETRIC FUNCTIONS.
Radian Measure. Trigonometric Functions of Angles. Evaluating the Trigonometric Functions. Algebra and the Trigonometric Functions. Right-Triangle Trigonometry.
8. GRAPHS OF TRIGONOMETRIC FUNCTIONS.
Trigonometric Functions of Real Numbers. Graphs of the Sine and 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.
9. ANALYTICAL TRIGONOMETRY.
The Addition Formulas. The Double-Angle Formulas. The Product-to-Sum and Sum-to-Product Formulas. Trigonometric Equations. The Inverse Trigonometric Functions.
10. ADDITIONAL TOPICS IN TRIGONOMETRY.
Right-Triangle Applications. 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.
DeMoivre's Theorem.
11. 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.
12. THE CONIC SECTIONS.
The Basic Equations. The Parabola. Tangents to Parabolas (Optional Section). The Ellipse. The Hyperbola. The Focus-Directrix Property of Conics. The Conics in Polar Coordinates. Rotation of Axes.
13. ROOTS OF POLYNOMIAL EQUATIONS.
Division of Polynomials. The Remainder Theorem and the Factor Theorem. The Fundamental Theorem of Algebra. Rational and Irrational Roots. Conjugate Roots and Descartes's Rule of Signs. Introduction to Partial Fractions. More About Partial Fractions.
14. ADDITIONAL TOPICS IN ALGEBRA.
Mathematical Induction. The Binomial Theorem. Introduction to Sequences and Series. Arithmetic Sequences and Series. Geometric Sequences and Series. Introduction to Limits.
Appendix A.1: Significant Digits.
Appendix A.2: √2 is Irrational.
Appendix A.3: The Complex Number System.
Answers.
Index.