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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. This Enhanced Edition includes instant access to Enhanced WebAssign®, the most widely-used and reliable homework system. Enhanced WebAssign® presents thousands of problems, links to relevant textbook sections, video examples, problem-specific tutorials, and more, that help students grasp the concepts needed to succeed in this course. As an added bonus, the Start Smart Guide has been bound into this text. This guide contains instructions to help students learn the basics of WebAssign quickly.
- This Enhanced Edition includes instant access to Enhanced WebAssign®, the most widely-used and reliable homework system. Enhanced WebAssign® presents thousands of problems, links to relevant textbook sections, video examples, problem-specific tutorials, and more, that help students grasp the concepts needed to succeed in this course. As an added bonus, the Start Smart Guide has been bound into this text. This guide contains instructions to help students learn the basics of WebAssign quickly.
- 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.
- 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.
- "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.
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.
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.
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.
Online Instructor's Companion Web Site with Instructor's Guide
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.
Online Test Bank
This supplement includes test forms for every chapter of the text, and can be found on the instructor companion site.
Cengage Learning Testing, powered by Cognero Instant Access
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 the Instructor Companion Site at www.cengage.com/login
This carefully crafted guide helps students develop problem-solving skills while reinforcing their understanding with detailed explanations, worked-out examples, lists of key concepts to master, and practice problems. Each section of the main text has a corresponding section in the Study Guide.
Student Solutions Manual
This carefully crafted guide helps you develop problem-solving skills while reinforcing your understanding with detailed explanations, worked-out examples, lists of key concepts to master, and practice problems. Each section of the main text has a corresponding section in the Study Guide.
Student Solutions Manual
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.