Higher Education

Precalculus: Mathematics for Calculus, 7th Edition

  • James Stewart McMaster University
  • Lothar Redlin Pennsylvania State University, Abington Campus
  • Saleem Watson California State University, Long Beach
  • ISBN-10: 1305071751  |  ISBN-13: 9781305071759
  • 1088 Pages
  • Previous Editions: 2012, 2007
  • © 2016 | Published
  • College Bookstore Wholesale Price = $195.00
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About

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 book 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 text—is what makes this text the proven market leader.

Features and Benefits

  • 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.
  • The chapters on trigonometry are written so professors can begin with either the right triangle approach or the unit circle approach.
  • 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.
  • Discovery/Discussion/Writing problems at the end of every section encourage students to use and develop conceptual, critical thinking, and writing skills.
  • Discovery Projects engage students by providing a challenging but accessible set of activities that enable them (perhaps working in groups) to explore in greater depth an interesting aspect of the topic they have just learned.
  • Review Sections and Chapter Tests at the end of each chapter help students gauge their learning progress. Brief answers to the odd-numbered exercises in each section and to all questions in the Chapter Tests are provided at the back of the book.

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).

What's New

  • New Exercises: More than 20% of the exercises are new, and groups of exercises now have headings that identify the type of exercise. New Skills Plus exercises in most sections contain more challenging exercises that require students to extend and synthesize concepts.
  • Review Material: The review material at the end of each chapter now includes a summary of properties and formulas and a new Concept Check. Each Concept Check provides a step-by-step review of all the main concepts and applications of the chapter. Answers to the Concept Check questions are on tear-out sheets at the back of the book.
  • Discovery Projects: References to Discovery Projects, including brief descriptions of the content of each project, are located in boxes where appropriate in each chapter. These boxes highlight the applications of precalculus in many different real-world contexts. (The projects are located at the book companion website www.stewartmath.com).
  • Geometry Review: A new Appendix A contains a review of the main concepts of geometry used in this book, including similarity and the Pythagorean Theorem.
  • Chapter 1 Fundamentals: This chapter now contains two new sections: Section 1.5, "Complex Numbers" (formerly in Chapter 3), and Section 1.12, "Modeling with Variation."
  • Chapter 2 Functions: This chapter now includes the new Section 2.5, "Linear Functions and Models," which highlights the connection between the slope of a line and the rate of change of a linear function. These two interpretations of slope help prepare students for the concept of the derivative in calculus.
  • Chapter 3 Polynomial and Rational Functions: This chapter now includes the new Section 3.7, "Solving Polynomial and Rational Inequalities Graphically." Section 3.6, "Rational Functions," has a new subsection on rational functions with "holes." The sections on complex numbers and on variation have been moved to Chapter 1.
  • Chapter 4 Exponential and Logarithmic Functions: The chapter now includes two sections on the applications of these functions. Section 4.7, "Modeling with Exponential Functions," focuses on modeling growth and decay, Newton's Law of Cooling, and other such applications. Section 4.8, "Logarithmic Scales," covers the concept of a logarithmic scale with applications involving the pH, Richter, and decibel scales.
  • Chapter 5 Trigonometric Functions: Unit Circle Approach: This chapter includes a new subsection on the concept of phase shift as used in modeling harmonic motion.
  • Chapter 10 Systems of Equations and Inequalities: The material on systems of inequalities has been rewritten to emphasize the steps used in graphing the solution of a system of inequalities.

Alternate Formats

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  • Loose Leaf

    ISBN-10: 1305586026 | ISBN-13: 9781305586024

    List Price = $181.95  | CengageBrain Price = $181.95  | College Bookstore Wholesale Price = $136.50

Supplements

All supplements have been updated in coordination with the main title. Select the main title's "About" tab, then select "What's New" for updates specific to title's edition.

For more information about these supplements, or to obtain them, contact your Learning Consultant.

Instructor Supplements

Instructor's Web Site with Complete Solutions Manual  (ISBN-10: 1305253604 | ISBN-13: 9781305253605)

This manual, available on the Instructors Companion Site, contains solutions to all exercises from the text, including Chapter Review Exercises, and Chapter Tests.

Instructor's Web Site with Lesson Plans  (ISBN-10: 1305253825 | ISBN-13: 9781305253827)

Instructor's Web Site with Instructor's Guide  (ISBN-10: 1305254031 | ISBN-13: 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 Learning Testing, powered by Cognero Instant Access  (ISBN-10: 1305258533 | ISBN-13: 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-10: 1305253639 | ISBN-13: 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.

List Price = $108.95  | CengageBrain Price = $108.95  | College Bookstore Wholesale Price = $81.75

Note Taking Guide  (ISBN-10: 1305253833 | ISBN-13: 9781305253834)

List Price = $13.95  | CengageBrain Price = $13.95  | College Bookstore Wholesale Price = $10.50

Student Solutions Manual  (ISBN-10: 1305253612 | ISBN-13: 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.

List Price = $87.95  | CengageBrain Price = $87.95  | College Bookstore Wholesale Price = $66.00

DVD (Text Specific)  (ISBN-10: 1305254007 | ISBN-13: 9781305254008)

These text-specific DVDs cover all sections of the text—providing explanations of key concepts as well as examples, exercises, and applications in a lecture-based format.

List Price = $212.95  | CengageBrain Price = $212.95  | College Bookstore Wholesale Price = $157.75

Enhanced WebAssign Instant Access for Pre-Calculus & College Algebra, Single-Term Courses  (ISBN-10: 128585831X | ISBN-13: 9781285858319)

IMPORTANT: When purchasing this instant access code for Pre-Calculus & College Algebra, ensure that you are using it in one of the following courses: College Algebra, Trigonometry, Algebra and Trigonometry or Precalculus. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If your students need to retake the course and you are using the same book AND edition then they will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your Cengage Learning Consultant.

List Price = $94.00  | CengageBrain Price = $94.00  | College Bookstore Wholesale Price = $94.00

Instructor's Edition  (ISBN-10: 1305115279 | ISBN-13: 9781305115279)

Student Supplements

Study Guide  (ISBN-10: 1305253639 | ISBN-13: 9781305253636)

This carefully crafted guide helps you develop problem-solving skills while reinforcing your 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.

List Price = $108.95  | CengageBrain Price = $108.95  | College Bookstore Wholesale Price = $81.75

Note Taking Guide  (ISBN-10: 1305253833 | ISBN-13: 9781305253834)

List Price = $13.95  | CengageBrain Price = $13.95  | College Bookstore Wholesale Price = $10.50

Student Solutions Manual  (ISBN-10: 1305253612 | ISBN-13: 9781305253612)

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

List Price = $87.95  | CengageBrain Price = $87.95  | College Bookstore Wholesale Price = $66.00

DVD (Text Specific)  (ISBN-10: 1305254007 | ISBN-13: 9781305254008)

These text-specific DVDs cover all sections of the text—providing explanations of key concepts as well as examples, exercises, and applications in a lecture-based format.

List Price = $212.95  | CengageBrain Price = $212.95  | College Bookstore Wholesale Price = $157.75

Enhanced WebAssign Instant Access for Pre-Calculus & College Algebra, Single-Term Courses  (ISBN-10: 128585831X | ISBN-13: 9781285858319)

IMPORTANT: When purchasing this instant access code for Pre-Calculus & College Algebra, ensure that you are using it in one of the following courses: College Algebra, Trigonometry, Algebra and Trigonometry or Precalculus. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your instructor.

List Price = $94.00  | CengageBrain Price = $94.00  | College Bookstore Wholesale Price = $94.00

Meet the Author

Author Bio

James Stewart

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 Learning, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS, and CALCULUS: CONCEPTS AND CONTEXTS, as well as a series of precalculus texts.

Lothar Redlin

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 is currently Professor of Mathematics at The Pennsylvania State University, Abington Campus. His research field is topology.

Saleem Watson

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.