## Description

**University Calculus, Early Transcendentals, Second Edition** helps readers successfully generalize and apply the key ideas of calculus through clear and precise explanations, clean design, thoughtfully chosen examples, and superior exercise sets. This text offers the right mix of basic, conceptual, and challenging exercises, along with meaningful applications. This significant revision features more examples, more mid-level exercises, more figures, improved conceptual flow, and the best in technology for learning and teaching.

This ISBN is the standalone book, if you want the Book/Acess Card order the ISBN below:

0321759907 / 9780321759900 University Calculus, Early Transcendentals plus MyMathLab Student Access Code Card

Package consists of

0321431308 / 9780321431301 MyMathLab/MyStatLab Access Card

0321654064 / 9780321654069 MyMathLab Inside Star

0321717392 / 9780321717399 University Calculus, Early Transcendentals

## Table of Contents

**1. Functions**

1.1 Functions and Their Graphs

1.2 Combining Functions; Shifting and Scaling Graphs

1.3 Trigonometric Functions

1.4 Graphing with Calculators and Computers

1.5 Exponential Functions

1.6 Inverse Functions and Logarithms

**2. Limits and Continuity**

2.1 Rates of Change and Tangents to Curves

2.2 Limit of a Function and Limit Laws

2.3 The Precise Definition of a Limit

2.4 One-Sided Limits

2.5 Continuity

2.6 Limits Involving Infinity; Asymptotes of Graphs

**3. Differentiation**

3.1 Tangents and the Derivative at a Point

3.2 The Derivative as a Function

3.3 Differentiation Rules

3.4 The Derivative as a Rate of Change

3.5 Derivatives of Trigonometric Functions

3.6 The Chain Rule

3.7 Implicit Differentiation

3.8 Derivatives of Inverse Functions and Logarithms

3.9 Inverse Trigonometric Functions

3.10 Related Rates

3.11 Linearization and Differentials

**4. Applications of Derivatives**

4.1 Extreme Values of Functions

4.2 The Mean Value Theorem

4.3 Monotonic Functions and the First Derivative Test

4.4 Concavity and Curve Sketching

4.5 Indeterminate Forms and L'Hôpital's Rule

4.6 Applied Optimization

4.7 Newton's Method

4.8 Antiderivatives

**5. Integration**

5.1 Area and Estimating with Finite Sums

5.2 Sigma Notation and Limits of Finite Sums

5.3 The Definite Integral

5.4 The Fundamental Theorem of Calculus

5.5 Indefinite Integrals and the Substitution Rule

5.6 Substitution and Area Between Curves

**6. Applications of Definite Integrals**

6.1 Volumes Using Cross-Sections

6.2 Volumes Using Cylindrical Shells

6.3 Arc Length

6.4 Areas of Surfaces of Revolution

6.5 Work

6.6 Moments and Centers of Mass

**7. Integrals and Transcendental Functions**

7.1 The Logarithm Defined as an Integral

7.2 Exponential Change and Separable Differential Equations

7.3 Hyperbolic Functions

**8. Techniques of Integration**

8.1 Integration by Parts

8.2 Trigonometric Integrals

8.3 Trigonometric Substitutions

8.4 Integration of Rational Functions by Partial Fractions

8.5 Integral Tables and Computer Algebra Systems

8.6 Numerical Integration

8.7 Improper Integrals

**9. Infinite Sequences and Series**

9.1 Sequences

9.2 Infinite Series

9.3 The Integral Test

9.4 Comparison Tests

9.5 The Ratio and Root Tests

9.6 Alternating Series, Absolute and Conditional Convergence

9.7 Power Series

9.8 Taylor and Maclaurin Series

9.9 Convergence of Taylor Series

9.10 The Binomial Series and Applications of Taylor Series

**10. Parametric Equations and Polar Coordinates**

10.1 Parametrizations of Plane Curves

10.2 Calculus with Parametric Curves

10.3 Polar Coordinates

10.4 Graphing in Polar Coordinates

10.5 Areas and Lengths in Polar Coordinates

10.6 Conics in Polar Coordinates

**11. Vectors and the Geometry of Space**

11.1 Three-Dimensional Coordinate Systems

11.2 Vectors

11.3 The Dot Product

11.4 The Cross Product

11.5 Lines and Planes in Space

11.6 Cylinders and Quadric Surfaces

**12. Vector-Valued Functions and Motion in Space**

12.1 Curves in Space and Their Tangents

12.2 Integrals of Vector Functions; Projectile Motion

12.3 Arc Length in Space

12.4 Curvature and Normal Vectors of a Curve

12.5 Tangential and Normal Components of Acceleration

12.6 Velocity and Acceleration in Polar Coordinates

**13. Partial Derivatives**

13.1 Functions of Several Variables

13.2 Limits and Continuity in Higher Dimensions

13.3 Partial Derivatives

13.4 The Chain Rule

13.5 Directional Derivatives and Gradient Vectors

13.6 Tangent Planes and Differentials

13.7 Extreme Values and Saddle Points

13.8 Lagrange Multipliers

**14. Multiple Integrals**

14.1 Double and Iterated Integrals over Rectangles

14.2 Double Integrals over General Regions

14.3 Area by Double Integration

14.4 Double Integrals in Polar Form

14.5 Triple Integrals in Rectangular Coordinates

14.6 Moments and Centers of Mass

14.7 Triple Integrals in Cylindrical and Spherical Coordinates

14.8 Substitutions in Multiple Integrals

**15. Integration in Vector Fields**

15.1 Line Integrals

15.2 Vector Fields and Line Integrals: Work, Circulation, and Flux

15.3 Path Independence, Conservative Fields, and Potential Functions

15.4 Green's Theorem in the Plane

15.5 Surfaces and Area

15.6 Surface Integrals

15.7 Stokes' Theorem

15.8 The Divergence Theorem and a Unified Theory

**16. First-Order Differential Equations (Online)**

16.1 Solutions, Slope Fields, and Euler's Method

16.2 First-Order Linear Equations

16.3 Applications

16.4 Graphical Solutions of Autonomous Equations

16.5 Systems of Equations and Phase Planes

**17. Second-Order Differential Equations (Online)**

17.1 Second-Order Linear Equations

17.2 Nonhomogeneous Linear Equations

17.3 Applications

17.4 Euler Equations

17.5 Power Series Solutions

**Appendices**

1. Real Numbers and the Real Line

2. Mathematical Induction

3. Lines, Circles, and Parabolas

4. Conic Sections

5. Proofs of Limit Theorems

6. Commonly Occurring Limits

7. Theory of the Real Numbers

8. Complex Numbers

9. The Distributive Law for Vector Cross Products

10. The Mixed Derivative Theorem and the Increment Theorem

11. Taylor's Formula for Two Variables

Enhance your learning experience with ** text-specific** study materials.

ISBN-13: 978-0-321-69462-1

$40.00 | Add to Cart

ISBN-13: 978-0-321-69454-6

$40.00 | Add to Cart

### These online resources are available at no cost.

Companion Website for Thomas' Calculus Series, 2nd Edition

This title is also sold in the various packages listed below. Before purchasing one of these packages, speak with your professor about which one will help you be successful in your course.

Package ISBN-13: 9780321793164

Includes this title packaged with:

- MathXL -- Valuepack Access Card (24-month access), 4th Edition

. . Pearson Education

$185.00 | Add to Cart

Package ISBN-13: 9780321780058

Includes this title packaged with:

- Student's Solutions Manual for University Calculus, Early Transcendentals, Single Variable, 2nd Edition

Joel R. Hass, Maurice D. Weir, George B. Thomas - MyMathLab -- Valuepack Access Card

. . Pearson Education

$188.33 | Add to Cart

## Purchase Info

### Digital Choices

#### MyLab & Mastering ?

MyLab & Mastering products deliver customizable content and highly personalized study paths, responsive learning tools, and real-time evaluation and diagnostics. MyLab & Mastering products help move students toward the moment that matters most—the moment of true understanding and learning.

Buy AccessMathXL -- Instant Access -- for University Calculus, Early Transcendentals , 2nd Edition

$60.50 | ISBN-13: 978-0-321-69453-9

Buy AccessNEW MyMathLab with Pearson eText -- Instant Access -- for University Calculus, Early Transcendentals, 2nd Edition

$95.20 | ISBN-13: 978-0-321-69455-3

#### eTextbook ?

With CourseSmart eTextbooks and eResources, you save up to 60% off the price of new print textbooks, and can switch between studying online or offline to suit your needs.

Once you have purchased your eTextbooks and added them to your CourseSmart bookshelf, you can access them anytime, anywhere.

University Calculus, Early Transcendentals, CourseSmart eTextbook, 2nd Edition

$68.99 | ISBN-13: 978-0-321-69458-4