# Calculus: Early Transcendentals, Multivariable

## Second EditionJon Rogawski

©2012What’s the ideal balance? How can you make sure students get both the computational skills they need and a deep understanding of the significance of what they are learning? With your teaching—supported by Rogawski’s

*Calculus*Second Edition—the most successful new calculus text in 25 years!Widely adopted in its first edition, Rogawski’s

Now Rogawski’s

*Calculus*worked for instructors and students by balancing formal precision with a guiding conceptual focus. Rogawski engages students while reinforcing the relevance of calculus to their lives and future studies. Precise mathematics, vivid examples, colorful graphics, intuitive explanations, and extraordinary problem sets all work together to help students grasp a deeper understanding of calculus.Now Rogawski’s

*Calculus*success continues in a meticulously updated new edition. Revised in response to user feedback and classroom experiences, the new edition provides an even smoother teaching and learning experience.## Table of Contents

**Chapter 10: Infinite Series**

10.1 Sequences

10.2 Summing an Infinite Series

10.3 Convergence of Series with Positive Terms

10.4 Absolute and Conditional Convergence

10.5 The Ratio and Root Tests

10.6 Power Series

10.7 Taylor Series

**Chapter 11: Parametric Equations, Polar Coordinates, and Conic Sections**

11.1 Parametric Equations

11.2 Arc Length and Speed

11.3 Polar Coordinates

11.4 Area and Arc Length in Polar Coordinates

11.5 Conic Sections

**Chapter 12: Vector Geometry**

12.1 Vectors in the Plane

12.2 Vectors in Three Dimensions

12.3 Dot Product and the Angle Between Two Vectors

12.4 The Cross Product

12.5 Planes in Three-Space

12.6 A Survey of Quadric Surfaces

12.7 Cylindrical and Spherical Coordinates

**Chapter 13: Calculus of Vector-Valued Functions**

13.1 Vector-Valued Functions

13.2 Calculus of Vector-Valued Functions

13.3 Arc Length and Speed

13.4 Curvature

13.5 Motion in Three-Space

13.6 Planetary Motion According to Kepler and Newton

**Chapter 14: Differentiation in Several Variables**

14.1 Functions of Two or More Variables

14.2 Limits and Continuity in Several Variables

14.3 Partial Derivatives

14.4 Differentiability and Tangent Planes

14.5 The Gradient and Directional Derivatives

14.6 The Chain Rule

14.7 Optimization in Several Variables

14.8 Lagrange Multipliers: Optimizing with a Constraint

**Chapter 15: Multiple Integration**15.1 Integration in Variables

15.2 Double Integrals over More General Regions

15.3 Triple Integrals

15.4 Integration in Polar, Cylindrical, and Spherical Coordinates

15.5 Applications of Multiplying Integrals

15.6 Change of Variables

**Chapter 16: Line and Surface Integrals**

16.1 Vector Fields

16.2 Line Integrals

16.3 Conservative Vector Fields

16.4 Parametrized Surfaces and Surface Integrals

16.5 Surface Integrals of Vector Fields

**Chapter 17: Fundamental Theorems of Vector Analysis**

17.1 Green’s Theorem

17.2 Stokes’ Theorem

17.3 Divergence Theorem

**Appendices**A. The Language of Mathematics

B. Properties of Real Numbers

C. Mathematical Induction and the Binomial Theorem

D. Additional Proofs of Theorems

E. Taylor Polynomials

**Answers to Odd-Numbered ExercisesReferencesPhoto CreditsIndex**