Calculus,
5th Edition

Preface.
To the Student.
Diagnostic Tests.
A Preview of Calculus.
1. FUNCTIONS AND MODELS.
Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Exponential Functions. Inverse Functions and Logarithms. Parametric Curves. Laboratory Project: Running Circles around Circles. Review. Principles of Problem Solving.
2. LIMITS AND DERIVATIVES.
The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws.
2.4 Continuity. Limits Involving Infinity. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. Review. Focus on Problem Solving.
3. DIFFERENTIATION RULES.
Derivatives of Polynomials and Exponential Functions. Applied Project: Building a Better Roller Coaster. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Laboratory Project: Bézier Curves. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Inverse Trigonometric Functions and their Derivatives. Derivatives of Logarithmic Functions. Discovery Project: Hyperbolic Functions. Rates of Change in the Natural and Social Sciences. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. Review. Focus on Problem Solving.
4. APPLICATIONS OF DIFFERENTIATION.
Related Rates. Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. Derivatives and the Shapes of Curves. Graphing with Calculus and Calculators. Indeterminate Forms and l'Hospital's Rule. Writing Project: The Origins of l'Hospital's Rule. Optimization Problems. Applied Project: The Shape of a Can. Newton's Method. Antiderivatives. Review. Focus on Problem Solving.
5. INTEGRALS.
Areas and Distances. The Definite Integral. Evaluating Definite Integrals. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Integration by Parts. Additional Techniques of Integration. Integration Using Tables and Computer Algebra Systems. Discovery Project: Patterns in Integrals. Approximate Integration. Improper Integrals. Review. Focus on Problem Solving.
6. APPLICATIONS OF INTEGRATION.
More about Areas. Volumes. Discovery Project: Rotating on a Slant. Volumes by Cylindrical Shells. Arc Length. Discovery Project: Arc Length Contest. Average Value of a Function. Applied Project: Where to Sit at the Movies. Applications to Physics and Engineering. Discovery Project: Complementary Coffee Cups. Applications to Economics and Biology. Probability. Review. Focus on Problem Solving.
7. DIFFERENTIAL EQUATIONS.
Modeling with Differential Equations. Direction Fields and Euler's Method. Separable Equations. Applied Project: How Fast Does a Tank Drain? Applied Project: Which Is Faster, Going Up or Coming Down? Exponential Growth and Decay. Applied Project: Calculus and Baseball. The Logistic Equation. Predator-Prey Systems. Review. Focus on Problem Solving.
8. INFINTE SEQUENCES AND SERIES.
Sequences. Laboratory Project: Logistic Sequences. Series. The Integral and Comparison Tests; Estimating Sums. Other Convergence Tests. Power Series. Representations of Functions as Power Series. Taylor and Maclaurin Series. Laboratory Project: An Elusive Limit. Writing Project: How Newton Discovered the Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. Focus on Problem Solving.
9. VECTORS AND THE GEOMETRY OF SPACE.
Three-Dimensional Coordinate Systems. Vectors. The Dot Product. The Cross Product. Discovery Project: The Geometry of a Tetrahedron. Equations of Lines and Planes. Laboratory Project: Putting 3D in Perspective. Functions and Surfaces. Cylindrical and Spherical Coordinates. Laboratory Project: Families of Surfaces. Review. Focus on Problem Solving.
10. VECTOR FUNCTIONS.
Vector Functions and Space Curves. Derivatives and Integrals of Vector Functions. Arc Length and Curvature. Motion in Space: Velocity and Acceleration. Applied Project: Kepler's Laws. Parametric Surfaces. Review. Focus on Problem Solving.
11. PARTIAL DERIVATIVES.
Functions of Several Variables. Limits and Continuity. Partial Derivatives. Tangent Planes and Linear Approximations. The Chain Rule. Directional Derivatives and the Gradient Vector. Maximum and Minimum Values. Applied Project: Designing a Dumpster. Discovery Project: Quadratic Approximations and Critical Points. Lagrange Multipliers. Applied Project: Rocket Science. Applied Project: Hydro-Turbine Optimization. Review. Focus on Problem Solving.
12. MULTIPLE INTEGRALS.
Double Integrals over Rectangles. Iterated Integrals. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. Surface Area. Triple Integrals. Discovery Project: Volumes of Hyperspheres. Triple Integrals in Cylindrical and Spherical Coordinates. Applied Project: Roller Derby. Discovery Project: The Intersection of Three Cylinders. Change of Variables in Multiple Integrals. Review. Focus on Problem Solving.
13. VECTOR CALCULUS.
Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Green's Theorem. Curl and Divergence. Surface Integrals. Stokes' Theorem. Writing Project: Three Men and Two Theorems. The Divergence Theorem. Summary. Review. Focus on Problem Solving.
APPENDIXES.
A. Intervals, Inequalities, and Absolute Values.
B. Coordinate Geometry.
C. Trigonometry.
D. Precise Definitions of Limits.
E. A Few Proofs.
F. Sigma Notation.
G. Integration of Rational Functions by Partial Fractions.
H. Polar Coordinates.
I. Complex Numbers.
J. Answers to Odd-Numbered Exercises.

• James Stewart

  The late James Stewart received his M.S. from Stanford University and his Ph.D. from the University of Toronto. He conducted research at the University of London and was influenced by the famous mathematician George Polya at Stanford University. Dr. Stewart most recently served as a professor of mathematics at McMaster University, and his research focused on harmonic analysis. Dr. Stewart authored a best-selling calculus textbook series, including CALCULUS, CALCULUS: EARLY TRANSCENDENTALS and CALCULUS: CONCEPTS AND CONTEXTS as well as a series of successful precalculus texts.

• Kokoska

  Steve Kokoska received his undergraduate degree from Boston College and his M.S. and Ph.D. from the University of New Hampshire. He taught for 36 years and is now professor emeritus in the department of mathematical and digital sciences at Bloomsburg University. Dr. Kokoska has served as Chief Reader for the AP® calculus reading and as a member of the AP® Calculus Development Committee. He has been involved with calculus reform and the use of technology in the classroom for numerous years. He has written several technology supplements, an introductory statistics text and an AP® calculus text with Dr. Stewart. He has also given numerous presentations for the College Board and Texas Instruments, has presented workshops in China and Singapore, participated in several AP® calculus-focused webinar and has written and produced several calculus resources for Texas Instruments.

• NEW "A CLOSER LOOK" LEARNING FEATURE CLARIFIES KEY CONCEPTS: These helpful "A Closer Look" sections provide straightforward, itemized explanations of important concepts. This effective guidance enables students to connect with relevant theory.

• MORE DETAILED SOLUTIONS AND EXPLANATIONS ENHANCE THE EXAMPLES: This edition's examples now include more detailed solutions with explanations that further clarify most steps. This makes it easier for students to follow the logical steps to a solution and apply problem-solving techniques to this edition's exercises.

• "COMMON ERROR" MARGIN NOTES HELP STUDENTS AVOID SOME OF THE MOST FREQUENTLY MADE MISTAKES: These invaluable marginal notes remind students of the common errors while reinforcing the proper solution method.

• NEW AUTOMATICALLY-GRADED PROOF PROBLEMS IN WEBASSIGN BUILD STUDENT CONFIDENCE: Carefully crafted online proof problems within WebAssign help build student confidence. Your students develop an understanding of the entire process of writing proofs with important practice and instant feedback.

• NEW EXPANDED PROBLEMS IN WEBASSIGN INCLUDE MULTIPLE PARTS TO ENSURE UNDERSTANDING: These online Expanded Problems go beyond the basic exercises to ask students to show the specific steps of their work or to explain the reasoning behind the answers they've provided.

• NEW SUBSECTIONS DIVIDE LEARNING INTO SMALLER, MORE MANAGEABLE PIECES: Wherever possible, this edition's sections are divided into appropriate subsections -- smaller portions of concepts and practice -- to accommodate the way students learn today.

• CONTENT AND EXERCISES EMPHASIZE A CONCEPTUAL UNDERSTANDING: Engaging examples and exercises strengthen students' conceptual understanding and encourage a meaningful interpretation of results.

• PROBLEM-SOLVING EMPHASIS PREPARES STUDENTS FOR LONG-TERM SUCCESS: Problem-solving is introduced at the beginning and reinforced throughout. Students learn how to identify key words, expressions, and phrases, important concepts needed, and how to develop a vision for a solution.

• WEALTH OF EXERCISES REINFORCE STUDENTS' SKILLS AND CHALLENGE THEIR THINKING: A range of exercises reinforce the Rule of Four, enabling students to practice analytical skills and stress concepts through pattern recognition. Many of the problems are designed to challenge students and encourage creative thinking.

• WEALTH OF EXERCISES REINFORCE STUDENTS' SKILLS AND CHALLENGE THEIR THINKING: This edition includes a range of exercises that reinforce the Rule of Four, allow students to practice analytical skills and stress concepts through pattern recognition. Many of the problems are designed to challenge students and encourage creative thinking.

• Problem-Solving Approach There is a principal emphasis throughout the text on problem solving skills. Students will learn how to identify key words, expressions, and phrases, important concepts needed, and how to develop a vision for a solution.

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.

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