## Table of Contents

1. FUNCTIONS AND LIMITS.

Functions and Their Representations. A Catalog of Essential Functions. The Limit of a Function. Calculating Limits. Continuity. Limits Involving Infinity.

2. DERIVATIVES.

Derivatives and Rates of Change. The Derivative as a Function. Basic Differentiation Formulas. The Product and Quotient Rules. The Chain Rule. Implicit Differentiation. Related Rates. Linear Approximations and Differentials.

3. APPLICATIONS OF DIFFERENTIATION.

Maximum and Minimum Values. The Mean Value Theorem. Derivatives and the Shapes of Graphs. Curve Sketching. Optimization Problems. Newton's Method. Antiderivatives.

4. INTEGRALS.

Areas and Distances. The Definite Integral. Evaluating Definite Integrals. The Fundamental Theorem of Calculus. The Substitution Rule.

5. INVERSE FUNCTIONS.

Inverse Functions. The Natural Logarithmic Function. The Natural Exponential Function. General Logarithmic and Exponential Functions. Exponential Growth and Decay. Inverse Trigonometric Functions. Hyperbolic Functions. Indeterminate Forms and l'Hospital's Rule.

6. TECHNIQUES OF INTEGRATION.

Integration by Parts. Trigonometric Integrals and Substitutions. Partial Fractions. Integration with Tables and Computer Algebra Systems. Approximate Integration. Improper Integrals.

7. APPLICATIONS OF INTEGRATION.

Areas between Curves. Volumes. Volumes by Cylindrical Shells. Arc Length. Area of a Surface of Revolution. Applications to Physics and Engineering. Differential Equations.

8. SERIES.

Sequences. Series. The Integral and Comparison Tests. Other Convergence Tests. Power Series. Representing Functions as Power Series. Taylor and Maclaurin Series. Applications of Taylor Polynomials.

9. PARAMETRIC EQUATIONS AND POLAR COORDINATES.

Parametric Curves. Calculus with Parametric Curves. Polar Coordinates. Areas and Lengths in Polar Coordinates. Conic Sections in Polar Coordinates.

10. VECTORS AND THE GEOMETRY OF SPACE.

Three-Dimensional Coordinate Systems. Vectors. The Dot Product. The Cross Product. Equations of Lines and Planes. Cylinders and Quadric Surfaces. Vector Functions and Space Curves. Arc Length and Curvature. Motion in Space: Velocity and Acceleration.

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. Lagrange Multipliers.

12. MULTIPLE INTEGRALS.

Double Integrals over Rectangles. Double Integrals over General Regions. Double Integrals in Polar Coordinates. Applications of Double Integrals. Triple Integrals. Triple Integrals in Cylindrical Coordinates. Triple Integrals in Spherical Coordinates. Change of Variables in Multiple Integrals.

13. VECTOR CALCULUS.

Vector Fields. Line Integrals. The Fundamental Theorem for Line Integrals. Green's Theorem. Curl and Divergence. Parametric Surfaces and Their Areas. Surface Integrals. Stokes' Theorem. The Divergence Theorem.

Appendix A. Trigonometry.

Appendix B. Proofs.

Appendix C. Sigma Notation.

## Products Included

## Instructor Supplements

# Instructor Supplements

All supplements have been updated in coordination with the main title. Select the main title's "About the Solution" 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.**

###
Single Variable Essential Calculus
(ISBN-10: 1133112765 | ISBN-13: 9781133112761)

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Solution Builder
(ISBN-10: 1133490956 | ISBN-13: 9781133490951)

This online instructor database offers complete worked solutions to all exercises in the text, allowing you to create customized, secure solutions printouts (in PDF format) matched exactly to the problems you assign in class. Visit Cengage.com/solutionbuilder for more information.

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Instructor's Guide
(ISBN-10: 1133525172 | ISBN-13: 9781133525172)

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PowerLecture with ExamView®
(ISBN-10: 1133525652 | ISBN-13: 9781133525653)

This CD-ROM (or DVD) provides the instructor with dynamic media tools for teaching, including Microsoft® PowerPoint® lecture slides and figures from the book. Create, deliver, and customize tests (both print and online) in minutes with ExamView® Computerized Testing Featuring Algorithmic Equations. You can also link to Solution Builder's online solutions manual, which allows you to easily build solution sets for homework or exams.

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Complete Solutions Manual
(ISBN-10: 1133365124 | ISBN-13: 9781133365129)

This manual includes worked out solutions to every exercise in Essential Calculus, 2e.

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Student Solutions Manual
(ISBN-10: 1133490948 | ISBN-13: 9781133490944)

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.

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Enhanced WebAssign Instant Access for Calculus, Multi-Term Courses
(ISBN-10: 1285858255 | ISBN-13: 9781285858258)

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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.
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## Student Supplements

# Student Supplements

All supplements have been updated in coordination with the main title. Select the main title's "About the Solution" 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.**

###
Single Variable Essential Calculus
(ISBN-10: 1133112765 | ISBN-13: 9781133112761)

Get the calculus textbook specifically designed for science or engineering majors. SINGLE VARIABLE ESSENTIAL CALCULUS, Second Edition, presents what you need to know about calculus in simple and concise terms. Diagnostic tests at the beginning of the text give you the opportunity to get up to speed on mathematical skills needed for calculus--helping you begin the course with confidence. Each chapter concludes with a thorough review to make sure you've mastered the material. SINGLE VARIABLE ESSENTIAL CALCULUS is the ideal text to help you get ready for your upper level science or engineering courses.

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(ISBN-10: 1133510612 | ISBN-13: 9781133510611)

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List Price = $145.00
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Student Solutions Manual
(ISBN-10: 1133490948 | ISBN-13: 9781133490944)

This manual includes worked out solutions to every odd-numbered exercise in Essential Calculus, 2e.

List Price = $74.95
| CengageBrain Price = $74.49
| College Bookstore Wholesale Price = $55.25

###
Enhanced WebAssign Instant Access for Calculus, Multi-Term Courses
(ISBN-10: 1285858255 | ISBN-13: 9781285858258)

IMPORTANT: When purchasing this instant access code for Calculus, ensure that you are using it in a Calculus course. 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 = $110.00
| CengageBrain Price = $110.00
| College Bookstore Wholesale Price = $110.00

###
Enhanced WebAssign - Start Smart Guide for Students
(ISBN-10: 0495384798 | ISBN-13: 9780495384793)

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