Review

Vectors

The Dot Product

The Cross Product

Matrices

Representations of Lines and Planes

Coordinate Systems

Coordinate Systems and Functions

Functions

Graphing Functions

Quadric Surfaces

Cylindrical Coordinates

Spherical Coordinates

Topology

Curves and Surfaces

Parametric Curves

Velocity, Speed, and Acceleration

Properties of Velocity and Speed

The Length of a Curve

Arclength Function

Curvature

Defining the Moving Frame

Moving Frame Computations

Decomposition of Acceleration

Limits and Derivatives

Partial Derivatives

Geometric Interpretation of Partial Derivatives

Higher Order Partial Derivatives

Introduction to Limits

Evaluating Limits

Continuity and Limits in General

Geometry of Differentiability

Differentiability of Functions of Two Variables

The Gradient

Differentiability in General

Differentiation Properties

Chain Rule

Directional Derivatives

The Gradient and Level Sets

Implicit Curves and Surfaces

Behavior of Functions

Taylor Polynomials

Quadratic Forms

The Hessian Matrix

Local Extrema

Absolute Extrema

Optimization with Constraints

Lagrange Multipliers

Homework

Homework 1: Coordinates

Homework 2: Graphing

Homework 3: Parametrized Curves

Homework 4: Arclength and Curvature

Homework 5: Moving Frames and Acceleration

Homework 6: Limits

Homework 7: Partial Derivatives

Homework 8: Differentiability

Homework 9: Properties of Derivatives

Homework 10: Directional Derivatives

Homework 11: Taylor’s Theorem

Homework 12: Extrema

Winter Assignment: Substitution and Lagrange Multipliers

Practice Problems

Practice Problems: Review

Practice Problems: Coordinate Systems

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