## Table of Contents

**Chapter 8: Sequences and Infinite Series**

8.1 An Overview

8.2 Sequences

8.3 Infinite Series

8.4 The Divergence and Integral Tests

8.5 The Ratio and Comparison Tests

8.6 Alternating Series

**Chapter 9: Power Series**

9.1 Approximating Functions with Polynomials

9.2 Power Series

9.3 Taylor Series

9.4 Working with Taylor Series

**Chapter 10: Parametric and Polar Curves **

10.1 Parametric Equations

10.2 Polar Coordinates

10.3 Calculus in Polar Coordinates

10.4 Conic Sections

**Chapter 11: Vectors and Vector-Valued Functions**

11.1 Vectors in the Plane

11.2 Vectors in Three Dimensions

11.3 Dot Products

11.4 Cross Products

11.5 Lines and Curves in Space

11.6 Calculus of Vector-Valued Functions

11.7 Motion in Space

11.8 Length of Curves

11.9 Curvature and Normal Vectors

**Chapter 12: Functions of Several Variables**

12.1 Planes and Surfaces

12.2 Graphs and Level Curves

12.3 Limits and Continuity

12.4 Partial Derivatives

12.5 The Chain Rule

12.6 Directional Derivatives and the Gradient

12.7 Tangent Planes and Linear Approximation

12.8 Maximum/Minimum Problems

12.9 Lagrange Multipliers

**Chapter 13: Multiple Integration**

13.1 Double Integrals over Rectangular Regions

13.2 Double Integrals over General Regions

13.3 Double Integrals in Polar Coordinates

13.4 Triple Integrals

13.5 Triple Integrals in Cylindrical and Spherical Coordinates

13.6 Integrals for Mass Calculations

13.7 Change of Variables in Multiple Integrals

**Chapter 14: Vector Calculus**

14.1 Vector Fields

14.2 Line Integrals

14.3 Conservative Vector Fields

14.4 Green’s Theorem

14.5 Divergence and Curl

14.6 Surface Integrals

14.7 Stokes’ Theorem

14.8 Divergence Theorem