There are many different ways that students learn and learn effectively for them as an individual, especially when it comes to class notes vs in-class participation. To help I have provided you with options on how you can take notes in-class.

Option 1: I have provided my note outlines below each section that you can fill in during class. I will do my best to follow the outline but I may not get to all the examples. This should allow you more time to digest the material, ask questions during class, while still practicing writing the mathematics.

Option 2: I have also provided my filled in notes to the outlines complete with important points I'll address in class. This can serve you in two ways. If you miss a class you have the complete notes to look over (I would recommend that you fill out the outline using my notes so that you digest the material since you missed class). Also, if you are one who doesn't learn by taking note but rather by actively participating with the lectures then these notes can provide you with a reference outside of class.

Option 3: You can take your notes however best suits you. Don't feel limited but make sure it works for you. My recommendation for most students would be option 1 using option 2 when you miss class.

Chapter 12 Vectors and Geometry of Space

  • Section 12.1: Three Dimensional Coordinate Systems

    • -2D vs. 3D
    - Surfaces in Space
    - Distance Formula
    - Equation of a Sphere

    Visit: Online 3D graphing Calculator

    Notes Outline: Section 12.1
    Filled Notes: Section 12.1

  • Section 12.2: Vectors

    • - Vector Addition
    - Scalr Multiplication
    - Vector Components and Length
    - Properties of Vectors
    - Standard Basis Vectors
    - Forces as Vectors

    Notes Outline: Section 12.2
    Filled Notes: Section 12.2

  • Section 12.3: The Dot Product

    • - Dot Product of Vectors
    - Properties of Dot Product
    - Angle Between Vectors
    - Direction Angles
    - Projections

    Notes Outline: Section 12.3
    Filled Notes: Section 12.3

  • Section 12.4: The Cross Product

    • - Cross Product of Vectors
    - Angle Between Vectors
    - Area of Parallelograms
    - Cross Product Properties
    - Volume of parallelpipeds
    - Torque

    Notes Outline: Section 12.4
    Filled Notes: Section 12.4

  • Section 10.1: Curves Defined by Parametric Equations

    • - Definition
    - Parametrizing
    - Graphing

    Visit: Wolfram Alpha Parametric Ploter

    Notes Outline: Section 10.1
    Filled Notes: Section 10.1

  • Section 12.5: Equations of Lines and Planes

    • - Vector Equation of a Line
    - Parametric Equations for a Line
    - Symetric Equations of a Line
    - Line Segment
    - Vector Equation of a Plane
    - Scalar Equation of a Plane
    - Distance Between a Point and a Plane

    Visit: CPM 3D Plotter

    Notes Outline: Section 12.5
    Filled Notes: Section 12.5

  • Section 10.5: Conic Sections

    • - Parabolas
    - Ellipses
    - Hyperbolas
    - Shifted Conic Sections

    Activity: Foam Conic Sections

    Notes Outline: Section 10.5
    Filled Notes: Section 10.5

  • Section 12.6: Cylinders and Quadric Surfaces

    • - Cylinders
    - Rulings and Traces
    - Ellipsoids
    - Elliptic Paraboloid
    - Hyperbolic Paraboloid
    - Cone
    - Hyperboloid of One Sheet
    - Hyperboloid of Two Sheets

    Visit: Quadric Surfaces 3D Applet

    Notes Outline: Section 12.6
    Filled Notes: Section 12.6

  • Chapter 12 Test Review

    • Practice Problems
    Solutions

Chapter 13 Vector Functions

Chapter 14 Partial Derivatives

Chapter 15 Multiple Integrals

Chapter 16 Vector Calculus

Final Review