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Precalculus: Mathematics for Calculus, 7th Edition

James Stewart | Lothar Redlin | Saleem Watson

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Overview

This bestselling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, providing students with a solid foundation in the principles of mathematical thinking. Comprehensive and evenly paced, the content provides complete coverage of the function concept, and integrates a significant amount of graphing calculator material to help students develop insight into mathematical ideas. The authors' attention to detail and clarity—the same as found in James Stewart's market-leading Calculus products—is what makes this the proven market leader.

James Stewart, McMaster University

The late James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He did research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Stewart was most recently Professor of Mathematics at McMaster University, and his research field was harmonic analysis. Stewart was the author of a best-selling calculus textbook series published by Cengage, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.

Lothar Redlin, Pennsylvania State University, Abington Campus

The late Lothar Redlin grew up on Vancouver Island, received a Bachelor of Science degree from the University of Victoria, and a Ph.D. from McMaster University in 1978. He subsequently did research and taught at the University of Washington, the University of Waterloo, and California State University, Long Beach. He was most recently Professor of Mathematics at The Pennsylvania State University, Abington Campus. His research field was topology.

Saleem Watson, California State University, Long Beach

Saleem Watson received his Bachelor of Science degree from Andrews University in Michigan. He did graduate studies at Dalhousie University and McMaster University, where he received his Ph.D. in 1978. He subsequently did research at the Mathematics Institute of the University of Warsaw in Poland. He also taught at The Pennsylvania State University. He is currently Professor of Mathematics at California State University, Long Beach. His research field is functional analysis. Watson is a co-author on Stewart's best-selling Calculus franchise.

WebAssign is a flexible and fully customizable online instructional solution that puts powerful tools in the hands of teachers, enabling you to realize your teaching goals and instantly assess individual student performance to help students learn math, not just do online homework.

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  • Mathematics in the Modern World vignettes show that mathematics is a living science crucial to the scientific and technological progress of recent times, as well as to the social, behavioral, and life sciences.
  • Real-world applications from engineering, physics, chemistry, business, biology, environmental studies, and other fields demonstrate how mathematics is used to model real-life situations.
  • Each approach to trigonometry is accompanied by the applications appropriate for that approach, clarifying the reason for different approaches to trigonometry.
  • Mathematics in the Modern World vignettes show that mathematics is a living science crucial to the scientific and technological progress of recent times, as well as to the social, behavioral, and life sciences.
  • Focus on Modeling sections illustrate modeling techniques as well as how mathematics can be applied to model real-life situations. These sections, as well as others, are devoted to teaching students how to create their own mathematical models, rather than using prefabricated formulas.
  • Real-world applications from engineering, physics, chemistry, business, biology, environmental studies, and other fields demonstrate how mathematics is used to model real-life situations.
  • Each approach to trigonometry is accompanied by the applications appropriate for that approach, clarifying the reason for different approaches to trigonometry.

Precalculus: Mathematics for Calculus

TABLE OF CONTENTS

Preface.
To the Student.
Prologue: Principles of Problem Solving.
1. FUNDAMENTALS.
Chapter Overview.
1.1 Real Numbers. 1.2 Exponents and Radicals. 1.3 Algebraic Expressions. 1.4 Rational Expressions. 1.5 Equations. 1.6 Complex Numbers. 1.7 Modeling with Equations. 1.8 Inequalities. 1.9 The Coordinate Plane; Graphs of Equations; Circles. 1.10 Lines. 1.11 Solving Equations and Inequalities Graphically. 1.12 Modeling Variation. Chapter 1 Review. Chapter 1 Test.
FOCUS ON MODELING: FITTING LINES TO DATA.
2. FUNCTIONS.
Chapter Overview.
2.1 Functions. 2.2 Graphs of Functions. 2.3 Getting Information from the Graph of a Function. 2.4 Average Rate of Change of a Function. 2.5 Linear Functions and Models. 2.6 Transformations of Functions. 2.7 Combining Functions. 2.8 One-to-One Functions and Their Inverses. Chapter 2 Review. Chapter 2 Test.
FOCUS ON MODELING: MODELING WITH FUNCTIONS.
3. POLYNOMIAL AND RATIONAL FUNCTIONS.
3.1 Chapter Overview. 3.2 Quadratic Functions and Models. 3.3 Polynomial Functions and Their Graphs. 3.4 Dividing Polynomials. 3.5 Real Zeros of Polynomials. 3.6 Complex Zeros and the Fundamental Theorem of Algebra. 3.7 Rational Functions. 3.8 Polynomial and Rational Inequalities. Chapter 3 Review. Chapter 3 Test.
FOCUS ON MODELING: FITTING POLYNOMIAL CURVES TO DATA.
4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Chapter Overview.
4.1 Exponential Functions. 4.2 The Natural Exponential Function. 4.3 Logarithmic Functions. 4.4 Laws of Logarithms. 4.5 Exponential and Logarithmic Equations. 4.6 Modeling with Exponential Functions. 4.7 Logarithmic Scales. Chapter 4 Review. Chapter 4 Test.
FOCUS ON MODELING: FITTING EXPONENTIAL AND POWER CURVES TO DATA.
5. TRIGONOMETRIC FUNCTIONS: UNIT CIRCLE APPROACH.
Chapter Overview.
5.1 The Unit Circle. 5.2 Trigonometric Functions of Real Numbers. 5.3 Trigonometric Graphs. 5.4 More Trigonometric Graphs. 5.5 Inverse Trigonometric Functions and Their Graphs. 5.6 Modeling Harmonic Motion. Chapter 5 Review. Chapter 5 Test.
FOCUS ON MODELING: FITTING SINUSOIDAL CURVES TO DATA.
6. TRIGONOMETRIC FUNCTIONS: RIGHT TRIANGLE APPROACH.
Chapter Overview.
6.1 Angle Measure. 6.2 Trigonometry of Right Triangles. 6.3 Trigonometric Functions of Angles. 6.4 Inverse Trigonometric Functions and Triangles. 6.5 The Law of Sines. 6.6 The Law of Cosines. Chapter 6 Review. Chapter 6 Test.
FOCUS ON MODELING: SURVEYING.
7. ANALYTIC TRIGONOMETRY.
Chapter Overview.
7.1 Trigonometric Identities. 7.2 Addition and Subtraction Formulas. 7.3 Double-Angle, Half-Angle, and Sum-Product Formulas. 7.4 Basic Trigonometric Equations. 7.5 More Trigonometric Equations. Chapter 7 Review. Chapter 7 Test.
FOCUS ON MODELING: TRAVELING AND STANDING WAVES.
8. POLAR COORDINATES AND PARAMETRIC EQUATIONS.
Chapter Overview.
8.1 Polar Coordinates. 8.2 Graphs of Polar Equations. 8.3 Polar Form of Complex Numbers; DeMoivre's Theorem. 8.4 Plane Curves and Parametric Equations. Chapter 8 Review. Chapter 8 Test.
FOCUS ON MODELING: The Path of a Projectile.
9. VECTORS IN TWO AND THREE DIMENSIONS .
Chapter Overview.
9.1 Vectors in Two Dimensions. 9.2 The Dot Product. 9.3 Three –Dimensional Coordinate Geometry. 9.4 Vectors in Three Dimensions. 9.5 The Cross Product. 9.6 Equations of Lines and Planes. Chapter 9 Review. Chapter 9 Test.
FOCUS ON MODELING: VECTOR FIELDS.
10. SYSTEMS OF EQUATIONS AND INEQUALITIES.
Chapter Overview.
10.1 Systems of Linear Equations in Two Variables. 10.2 Systems of Linear Equations in Several Variables. 10.3 Matrices and Systems of Linear Equations. 10.4 The Algebra of Matrices. 10.5 Inverses of Matrices and Matrix Equations. 10.6 Determinants and Cramer's Rule. 10.7 Partial Fractions. 10.8 Systems of Non-Linear Equations. 10.9 Systems of Inequalities. Chapter 10 Review. Chapter 10 Test.
FOCUS ON MODELING: LINEAR PROGRAMMING.
11. CONIC SECTIONS.
Chapter Overview. 11.1 Parabolas. 11.2 Ellipses. 11.3 Hyperbolas. 11.4 Shifted Conics. 11.5 Rotation of Axes. 11.6 Polar Equations of Conics. Chapter 11 Review. Chapter 11 Test.
FOCUS ON MODELING: CONICS IN ARCHITECTURE.
12. SEQUENCES AND SERIES.
Chapter Overview. 12.1 Sequences and Summation Notation. 12.2 Arithmetic Sequences. 12.3 Geometric Sequences. 12.4 Mathematics of Finance. 12.5 Mathematical Induction. 12.6 The Binomial Theorem. Chapter 12 Review. Chapter 12 Test.
FOCUS ON MODELING: MODELING WITH RECURSIVE SEQUENCES.
13. LIMITS: A PREVIEW OF CALCULUS.
Chapter Overview. 13.1 Finding Limits Numerically and Graphically. 13.2 Finding Limits Algebraically. 13.3 Tangent Lines and Derivatives. 13.4 Limits at Infinity: Limits of Sequences. Areas. Chapter 13 Review. Chapter 13 Test.
FOCUS ON MODELING: INTERPRETATIONS OF AREA.
APPENDIX A: Geometry Review.
APPENDIX B: Calculations and Significant Figures (available on website).
APPENDIX C: Graphing with a Graphing Calculator (available on website).
APPENDIX D: Using the TI-83/84 Graphing Calculator (available on website).

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Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.

FOR INSTRUCTORS

Instructor's Web Site with Instructor's Guide

ISBN: 9781305254039
This helpful teaching companion contains points to stress, suggested time to allot, text discussion topics, core materials for lectures, workshop/discussion suggestions, group work exercises in a form suitable for handout, solutions to group work exercises, and suggested homework problems.

Cengage Testing, powered by Cognero® Instant Access

ISBN: 9781305258532
Cengage Learning Testing Powered by Cognero is a flexible, online system that allows you to author, edit, and manage test bank content; create multiple test versions in an instant; and deliver tests from your LMS, your classroom or wherever you want. This is available online via www.cengage.com/login.

Study Guide

ISBN: 9781305253636
This carefully crafted learning resource helps students develop their problem-solving skills while reinforcing their understanding with detailed explanations, worked-out examples, listings of key ideas to master, and practice problems. Each section of the main text has a corresponding section in the Study Guide.

Student Solutions Manual

ISBN: 9781305253612
Contains fully worked-out solutions to all of the odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an answer.