Higher Education

Algebra and Trigonometry, 2nd Edition

  • includes Video Skillbuilder CD-ROM and CengageNOW, iLrn™ Homework Student Version, Personal Tutor with SMARTHINKING Printed Access Card
  • James Stewart McMaster University
  • Lothar Redlin Pennsylvania State University, Abington Campus
  • Saleem Watson California State University, Long Beach
  • ISBN-10: 0495013579  |  ISBN-13: 9780495013570
  • 1088 Pages
  • Previous Editions: 2001
  • © 2007 | Published
  • College Bookstore Wholesale Price = $266.75
  • Newer Edition Available
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About

Overview

This best selling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, so that when students finish the course, they have a solid foundation in the principles of mathematical thinking. This comprehensive, evenly paced book provides complete coverage of the function concept and integrates substantial graphing calculator materials that help students develop insight into mathematical ideas. The authors' attention to detail and clarity, as in James Stewart's market-leading Calculus text, is what makes this text the 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 authors introduce the graphing calculator early, so it can be used to graph and solve equations prior to the introduction of functions. Material that deals with graphing devices is labeled with an icon so that those who prefer not to use the graphing calculator can easily skip this material.
  • The chapters on trigonometry have been 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 problems at the end of every section encourage conceptual, critical thinking, and writing skills.
  • Special projects are included in each chapter to engage students and make them active learners by having them work (perhaps in groups) on extended projects that give a feeling of substantial accomplishment when completed.
  • 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 given at the back of the book.
  • This edition is fully supported with iLrn™ (part of the CengageNOW suite of technology products). Providing instructors and students with unsurpassed control, variety, and all-in-one utility, iLrn is a powerful and fully integrated teaching and learning system. iLrn ties together five fundamental learning activities: diagnostics, tutorials, homework, quizzing, and testing.

Table of Contents

P. PREREQUISITES.
Modeling the Real World. Real Numbers. Integer Exponents. Rational Exponents and Radicals. Algebraic Expressions. Discovery Project: Visualizing a Formula. Factoring Algebraic Expressions. Rational Expressions. Chapter P Review. Chapter P Test. Focus on Problem Solving: General Principles.
1. EQUATIONS AND INEQUALITIES.
Basic Equations. Modeling with Linear Equations. Discovery Project: Equations Through the Ages. Quadratic Equations. Complex Numbers. Other Types of Equations. Inequalities. Absolute Value Equations and Inequalities. Chapter 1 Review. Chapter 1 Test. Focus on Modeling: Making the Best Decisions.
2. COORDINATES AND GRAPHS.
The Coordinate Plane. Discovery Project: Visualizing Data. Graphs of Equations in Two Variables. Graphing Calculators: Solving Equations and Inequalities Graphically. Lines.Modeling: Variation. Chapter 2 Review. Chapter 2 Test. Focus on Modeling: Fitting Lines to Data.
3. FUNCTIONS.
What is a Function? Graphs of Functions. Discovery Project: Relations and Functions. Increasing and Decreasing Functions: Average Rate of Change. Transformations of Functions. Quadratic Functions: Maxima and Minima. Combining Functions. Discovery Project: Iteration and Chaos. One-to-One Functions and Their Inverses. Chapter 3 Review. Chapter 3 Test. Focus on Modeling: Modeling With Functions.
4. POLYNOMIAL AND RATIONAL FUNCTIONS.
Polynomial Functions and Their Graphs. Dividing Polynomials. Real Zeros of Polynomials. Discovery Project: Zeroing in on a Zero. Complex Zeros and the Fundamental Theorem of Algebra. Rational Functions. Chapter 4 Review. Chapter 4 Test. Focus on Modeling: Fitting Polynomial Curves to Data.
5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
Exponential Functions. Discovery Project: Exponential Explosion. Logarithmic Functions. Laws of Logarithms. Exponential and Logarithmic Equations. Modeling with Exponential and Logarithmic Functions. Chapter 5 Review. Chapter 5 Test. Focus on Modeling: Fitting Exponential and Power Curves to Data.
6. TRIGONOMETRIC FUNCTIONS OF ANGLES.
Angle Measure. Trigonometry of Right Triangles. Trigonometric Functions of Angles. Discovery Project: Similarity. The Law of Sines. The Law of Cosines. Chapter 6 Review. Chapter 6 Test. Focus on Modeling: Surveying.
7. TRIGONOMETRIC FUNCTIONS OF REAL NUMBERS.
The Unit Circle. Trigonometric Functions of Real Numbers. Trigonometric Graphs. Discovery Project: Predator-Prey Models. More Trigonometric Graphs. Modeling Harmonic Motion. Chapter 7 Review. Chapter 7 Test. Focus on Modeling: Fitting Sinusoidal Curves to Data.
8. ANALYTIC TRIGONOMETRY.
Trigonometric Identities. Addition and Subtraction Formulas. Double-Angle, Half-Angle, and Sum-Product Identities. Inverse Trigonometric Functions. Discovery Project:Where to Sit at the Movies. Trigonometric Equations. Chapter 8 Review. Chapter 8 Test. Focus on Modeling: Traveling and Standing Waves.
9. POLAR COORDINATES AND VECTORS.
Polar Coordinates. Graphs of Polar Equations. Polar Form of Complex Numbers; DeMoivre''s Theorem. Discovery Project: Fractals. Vectors. The Dot Product. Discovery Project: Sailing Against the Wind. Chapter 9 Review. Chapter 9 Test. Focus on Modeling: Mapping the World.
10. SYSTEMS OF EQUATIONS AND INEQUALITIES.
Systems of Equations. Systems of Linear Equations in Two Variables. Systems of Linear Equations in Several Variables. Discovery Project: Best Fit versus Exact Fit. Systems of Linear Equations: Matrices. The Algebra of Matrices. Discovery Project: Will the Species Survive? Inverses of Matrices and Matrix Equations. Discovery Project: Computer Graphics I. Determinants and Cramer''s Rule. Partial Fractions. Systems of Inequalities. Chapter 10 Review. Chapter 10 Test. Focus on Modeling: Linear Programming.
11. ANALYTIC GEOMETRY.
Parabolas. Ellipses. Hyperbolas. Discovery Project: Conics in Architecture. Shifted Conics. Rotation of Axes. Discovery Project: Computer Graphics II. Polar Equations of Conics. Plane Curves and Parametric Equations. Chapter 11 Review. Chapter 11 Test. Focus on Modeling: The Path of a Projectile.
12. SEQUENCES AND SERIES.
Sequences and Summation Notation. Arithmetic Sequences. Geometric Sequences. Discovery Project: Finding Patterns. Mathematics of Finance. Mathematical Induction. The Binomial Theorem. Chapter 12 Review. Chapter 12 Test. Focus on Modeling: Modeling with Recursive Sequences.
13. COUNTING AND PROBABILITY.
Counting Principles. Permutations and Combinations. Probability. Discovery Project: Small Samples, Big Results. Binomial Probability. Expected Value. Chapter 13 Review. Chapter 13 Test. Focus on Modeling: The Monte Carlo Method.

What's New

  • All of the chapters (other than Chapter "P" Prerequisites) are now followed by a "Focus on Modeling" section. Chapter "P" Prerequisites is now the only chapter be followed by a "Problem Solving" section.
  • There are six new "Focus on Modeling" sections, containing high-interest applications ranging from surveying to architecture.
  • Each exercise section now contains a special group heading for "Applications" exercises, to give these more prominence and to make them easier to assign. Each such exercise has a title to clarify its purpose at a glance.
  • One of the very long chapters (Chapter 9, Analytic Trigonometry) has been shortened, and the extra material from it, plus some related sections from the Analytic Geometry chapter (previously Chapter 11), have been combined into a new, more logically structured Chapter 9: Polar Coordinates and Vectors.
  • This edition includes several new Discovery Projects, for example the Discovery Project in 3.2 on "Relations and Functions," which was added to satisfy those users who asked for some material on relations.
  • More than 20% of the exercises are new, including many more application exercises. Many others have been updated and revised.
  • Each chapter now begins with a one-page "Chapter Overview" to introduce the ideas of the chapter and indicate how they can be applied to the real world.

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  • Non-Media Version

    ISBN-10: 0495016764 | ISBN-13: 9780495016762

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Bundle: Text + Student Solutions Manual

ISBN-10: 0495147710 | ISBN-13: 9780495147718

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This Bundle Includes:

  • Algebra and Trigonometry
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  • Student Solutions Manual
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CengageNOW™, Personal Tutor, iLrn™ Homework Student Version Instant Access Code  (ISBN-10: 0495171174 | ISBN-13: 9780495171171)

By purchasing the 1pass Instant Access for this text, students not using a new text can access iLrn™ Tutorial and Personal Tutor with a single password at academic.cengage.com.

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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.