## Description

**This text is designed for the single variable component of a three-semester or four-quarter calculus course (math, engineering, and science majors).**

Calculus hasn’t changed, but your students have. Today’s students have been raised on immediacy and the desire for relevance, and they come to calculus with varied mathematical backgrounds. **Thomas’ Calculus: Early Transcendentals, Twelfth Edition**, helps your students successfully generalize and apply the key ideas of calculus through clear and precise explanations, clean design, thoughtfully chosen examples, and superior exercise sets. Thomas 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, and improved conceptual flow.

*This is the full version of the text contains Chapters 1-16. **ISBN-10:0321628837 | ISBN-13:9780321628831 Thomas Calculus Early Transcendentals, Single Variable) contains Chapters 1-11. The Multivariable version of the text contains Chapters 11-16. MyMathLab access is not included with this ISBN.*

## 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 Derivatives**

2.1 Rates of Change and Tangents to Curves

2.2 Limit of a Function and Limit Laws

2.3 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 Rules for Polynomials, Exponentials, Products, and Quotients

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'Hopital'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 and Fluid Forces

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

7.4 Relative Rates of Growth

**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. First-Order Differential Equations**

9.1 Solutions, Slope Fields, and Euler's Method

9.2 First-Order Linear Equations

9.3 Applications

9.4 Graphical Solutions of Autonomous Equations

9.5 Systems of Equations and Phase Planes

**10. Infinite Sequences and Series**

10.1 Sequences

10.2 Infinite Series

10.3 The Integral Test

10.4 Comparison Tests

10.5 The Ratio and Root Tests

10.6 Alternating Series, Absolute and Conditional Convergence

10.7 Power Series

10.8 Taylor and Maclaurin Series

10.9 Convergence of Taylor Series

10.10 The Binomial Series and Applications of Taylor Series

**11. Parametric Equations and Polar Coordinates**

11.1 Parametrizations of Plane Curves

11.2 Calculus with Parametric Curves

11.3 Polar Coordinates

11.4 Graphing in Polar Coordinates

11.5 Areas and Lengths in Polar Coordinates

11.6 Conic Sections

11.7 Conics in Polar Coordinates

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

12.1 Three-Dimensional Coordinate Systems

12.2 Vectors

12.3 The Dot Product

12.4 The Cross Product

12.5 Lines and Planes in Space

12.6 Cylinders and Quadric Surfaces

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

13.1 Curves in Space and Their Tangents

13.2 Integrals of Vector Functions; Projectile Motion

13.3 Arc Length in Space

13.4 Curvature and Normal Vectors of a Curve

13.5 Tangential and Normal Components of Acceleration

13.6 Velocity and Acceleration in Polar Coordinates

**14. Partial Derivatives**

14.1 Functions of Several Variables

14.2 Limits and Continuity in Higher Dimensions

14.3 Partial Derivatives

14.4 The Chain Rule

14.5 Directional Derivatives and Gradient Vectors

14.6 Tangent Planes and Differentials

14.7 Extreme Values and Saddle Points

14.8 Lagrange Multipliers

14.9 Taylor's Formula for Two Variables

14.10 Partial Derivatives with Constrained Variables

**15. Multiple Integrals**

15.1 Double and Iterated Integrals over Rectangles

15.2 Double Integrals over General Regions

15.3 Area by Double Integration

15.4 Double Integrals in Polar Form

15.5 Triple Integrals in Rectangular Coordinates

15.6 Moments and Centers of Mass

15.7 Triple Integrals in Cylindrical and Spherical Coordinates

15.8 Substitutions in Multiple Integrals

**16. Integration in Vector Fields**

16.1 Line Integrals

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

16.3 Path Independence, Conservative Fields, and Potential Functions

16.4 Green's Theorem in the Plane

16.5 Surfaces and Area

16.6 Surface Integrals

16.7 Stokes' Theorem

16.8 The Divergence Theorem and a Unified Theory

**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. Proofs of Limit Theorems

5. Commonly Occurring Limits

6. Theory of the Real Numbers

7. Complex Numbers

8. The Distributive Law for Vector Cross Products

9. The Mixed Derivative Theorem and the Increment Theorem

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

Pearson's Calculus Review Card, Multivariable for Thomas' Calculus, 12th Edition

ISBN-13: 978-0-321-60073-8

$5.00 | Add to Cart

ISBN-13: 978-0-321-60071-4

$40.00 | Add to Cart

Student Solutions Manual, Single Variable, for Thomas' Calculus: Early Transcendentals, 12th Edition

ISBN-13: 978-0-321-65692-6

$40.00 | Add to Cart

### Additional Course Materials

Insight Into Calculus: Using Texas Instruments Graphics Calculators

ISBN-13: 978-0-13-255365-0

$35.33 | Add to Cart

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: 9780321648426

Includes this title packaged with:

- MyMathLab -- Glue-in Access Card, 2nd Edition

. . Pearson Education

$255.67 | Add to Cart

Package ISBN-13: 9780321720085

Includes this title packaged with:

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

. . Pearson Education

$255.67 | Add to Cart

Package ISBN-13: 9780321907301

Includes this title packaged with:

- Just-in-Time Algebra and Trigonometry for Calculus, 4th Edition

Guntram Mueller, Ronald I. Brent

$255.67 | Add to Cart

Package ISBN-13: 9780321740960

Includes this title packaged with:

- Student Solutions Manual, Single Variable, for Thomas' Calculus: Early Transcendentals, 12th Edition

George B. Thomas, Maurice D. Weir, Joel R. Hass

$245.67 | Add to Cart

Package ISBN-13: 9780321692399

Includes this title packaged with:

- Student Solutions Manual, Multivariable, for Thomas' Calculus and Thomas' Calculus: Early Transcendentals, 12th Edition

George B. Thomas, Maurice D. Weir, Joel R. Hass - Student Solutions Manual, Single Variable, for Thomas' Calculus: Early Transcendentals, 12th Edition

George B. Thomas, Maurice D. Weir, Joel R. Hass

$249.00 | Add to Cart

Package ISBN-13: 9780321692405

Includes this title packaged with:

- Student Solutions Manual, Multivariable, for Thomas' Calculus and Thomas' Calculus: Early Transcendentals, 12th Edition

George B. Thomas, Maurice D. Weir, Joel R. Hass - Student Solutions Manual, Single Variable, for Thomas' Calculus: Early Transcendentals, 12th Edition

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

. . Pearson Education

$262.33 | 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 AccessMyMathLab with eBook -- Instant Access -- for Thomas' Calculus Early Transcendentals , 12th Edition

$95.20 | ISBN-13: 978-0-321-66519-5

Buy AccessMathXL -- Instant Access -- for Thomas' Calculus Early Transcendentals , 12th Edition

$102.85 | ISBN-13: 978-0-321-66520-1

#### 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.

Thomas' Calculus Early Transcendentals, CourseSmart eTextbook, 12th Edition

$96.99 | ISBN-13: 978-0-321-64093-2

### Print Choices

#### Alternative Options ?

Click on the titles below to learn more about these options.

Thomas' Calculus Early Transcendentals, Single Variable, 12th Edition

$122.67 | ISBN-13: 978-0-321-62883-1

Thomas' Calculus, Single Variable Plus MyMathLab/MyStatLab Student Access Kit, 12th Edition

$136.00 | ISBN-13: 978-0-321-64844-0

$171.33 | ISBN-13: 978-0-321-73603-1

$171.33 | ISBN-13: 978-0-321-73529-4

#### Loose Leaf Version ?

Books a la Carte are less-expensive, loose-leaf versions of the same textbook.

Thomas' Calculus, Early Transcendentals, Books a la Carte Edition, 12th Edition

$158.00 | ISBN-13: 978-0-321-73078-7

Thomas' Calculus, Early Transcendentals, Single Variable, Books a la Carte Edition, 12th Edition

$158.00 | ISBN-13: 978-0-321-73079-4