Table of Contents
 9 • Introduction to Differential Equations

10 • Infinite Series
 Representing Sequences
 Convergent and Divergent Sequences
 Recursive Formula of a Sequence
 Monotone Convergence Theorem
 Partial Sums
 The nth Term Divergence Test
 Infinite Geometric Series
 Integral Test for Series
 Harmonic and pSeries
 Comparison Test for Series
 Limit Comparison Test
 Conditional and Absolute Convergence
 Alternating Series Test
 Ratio Test
 Root Test
 Power Series and Radius of Convergence
 Operations on Power Series
 Differentiating and Integrating Power Series
 Maclaurin Series
 Taylor Series
 Taylor Polynomials Approximation to a Function
 The Binomial Theorem

11 • Parametric Equations, Polar Coordinates, and Conic Sections
 Conversion between Parametric and Rectangular Equations
 Parametric Equations and Curves in Two Dimensions
 Second Derivatives of Parametric Equations
 Derivatives of Parametric Equations
 Area Enclosed by Parametric Curves
 Arc Length of Parametric Curves
 Surface of Revolution of Parametric Curves
 Polar Coordinates
 Conversion between Rectangular and Polar Equations
 Graphing Polar Curves
 Area Bounded by Polar Curves
 Arc Length of a Polar Curve
 Equation of a Parabola
 Equation of an Ellipse
 Equation of a Hyperbola

12 • Vector Geometry
 Polar Form of a Vector
 Magnitude of a 2D Vector
 Scalars, Vectors, and Directed Line Segments
 Vectors Applications
 Vector Operations in 2D
 Components of a Vector
 Graphical Operations on Vectors
 Points, Midpoints, and Distances in Space
 Equation of a Straight Line in Space: Cartesian and Vector Forms
 Angle between Two Straight Lines in Space
 Dot Product in 3D
 Angle between Two Vectors in Space
 Vector Projection
 Cross Product in 3D
 Scalar Triple Product
 Equation of a Plane: Vector, Scalar, and General Forms
 Equation of a Plane: Intercept and Parametric Forms
 Equation of a Straight Line in Space: Parametric Form
 Parallel and Perpendicular Vectors in Space
 Intersection of Planes
 Cylindrical and Spherical Coordinates
 13 • Calculus of VectorValued Functions
 14 • Differentiation in Several Variables
 15 • Multiple Integration
 16 • Line and Surface Integrals
 17 • Fundamental Theorems of Vector Analysis