Table of Contents

9 Introduction to Differential Equations
 9.1 Solving Differential Equations
 9.2 Models Involving 𝑦′ = 𝑘(𝑦 − 𝑏)
 9.3 Graphical and Numerical Methods
 9.4 The Logistic Equation
 9.5 FirstOrder Linear Equations

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 and Strategies for Choosing Tests
 10.6 Power Series
 10.7 Taylor Series

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

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 3Space
 12.6 A Survey of Quadric Surfaces
 12.7 Cylindrical and Spherical Coordinates

13 Calculus of VectorValued Functions
 13.1 VectorValued Functions
 13.2 Calculus of VectorValued Functions
 13.3 Arc Length and Speed
 13.4 Curvature
 13.5 Motion in 3Space
 13.6 Planetary Motion According to Kepler and Newton

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

15 Multiple Integration
 15.1 Integration in Two 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 Multiple Integrals
 15.6 Change of Variables

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

17 Fundamental Theorems of Vector Analysis
 17.1 Green’s Theorem
 17.2 Stokes’ Theorem
 17.3 Divergence Theorem