Unit 9: Intro to Vector Calculus

Unit 9: Intro to Vector Calculus

• FriDay 34: Remember Vectors? How About Algebra 1?

  • • Video 1: Class Picture. Please Send me a Selfie

    • Video 1.5: Quick Introduction

    • Video 2: Remember Vectors?

    • Video 3: Equations of Lines in Vector Space

    • Video 4: Angles between Vectors

    • Video 5: Remeber Matrices?

    • Video 6: Dot Product

    • Video 7: Orthoganal Vectors

    • Video 8: Another Example

    • Video 9: Generalization of Equations of Lines in Vector Form

    • Video 10: Scalar Multiplication

    • Video 11: Unit Vectors

    • Video 12: Linear Combinations of Vectors

      • • Vector Notes Sheet

        • Vector Worksheet 1

          • • Vector Worksheet 1 Answers

• MonDay 35: More Algebra 1 in Vector Space

  • • Video 1: Let's Race!

    • Video 2: Standard Cartesian Form

    • Video 3: Converting from Cartesian to Vector

    • Video 4: Converting from Vector to Cartesian

    • Video 5: Perpendicular Bisectors

    • Video 6: Vector Projection and Scalar Projection

    • Video 7: Distance from a Point to a Line (Vector)

    • Video 8: Distance from a Point to a Line (Cartesian)

      • • Vector Notes Sheet

        • Vector Worksheet 2

          • • Vector Worksheet 2 Answers

• Day 36: You Asked For It! More Algebra 1!

  • • Video 1: How Many Ways Can You Solve a 2x2 System of Equations?

    • Video 2: Solving Systems of Equations using Vector Methods BEST METHOD EVER!

    • Video 3: One More Example

      • • Vector Notes Sheet

        • Vector Worksheet 3 (Designed when there a few more topics discussed. Skip what you don't know)

          • • Vector Worksheet 3 Answers

        • Vector Worksheet 4 (Designed when there a few more topics discussed. Skip what you don't know)

          • • Vector Worksheet 4 Answers

        • If you are NOT planning to take the AP exam in May, please return your books and calculators as soon as you can.

• Day 37: Cross Product

  • • Video 1: Solving a 3x3 System with 3D Vectors Part 1

    • Video 2: Solving a 3x3 System with 3D Vectors Part 2

    • Video 3: Solving a 3x3 System (Nifty Method)

    • Video 4: Our First Cross Product

    • VIdeo 5: Cross Product to Solve for z

    • Video 6: Second Cross Product

    • Video 7: Cross Product to Solve for x

    • Video 8: Third Cross Product

    • Video 9: Cross Product to Solve for y

      • • Create and Solve an Infinite Number of 3x3 Systems

          • • Answers (check your own answers...)

    • Video 10: Equations of Lines in 3D and 4D

      • • If you are NOT planning to take the AP exam in May, please return your books and calculators as soon as you can.

• Day 38: 3D Vectors

  • • Video 1: How do you draw 3D? How do you draw 4D or 5D?

    • Video 2: Transitioning from 2D to 3D

    • Video 3: Finding the Norm of a 3D Vector

    • Video 4: The Definition of a Plane (An Undefined Term)

    • Video 5: An Equation of a Plane

    • Video 6: Example

      • • Be able to find the norm of a 3D vector

        • Be able to add, subtract, and compute the dot product of any two 3D vectors

        • Practice calculating the cross product of two 3D vectors. Do an infinite number of these

        • If you are NOT planning to take the AP exam in May, please return your books and calculators as soon as you can.

• FriDay 39: Equations of Planes, BIG PROBLEM #1

  • • Video 1: Given 3 Points, Find the Equation of a Plane

    • Video 2: One of Many Examples

      • • Practice BIG PROBLEM #1 an infinite number of times (given 3 points, find the equation of the plane that contains them). Be sure to VERIFY

        • If you are NOT planning to take the AP exam in May, please return your books and calculators as soon as you can.

        • We are skipping Big Problem #2, so you won't be able to do all of the following:

        • Vector Worksheet 5

          • • Vector Worksheet 5 Answers

        • Vector Worksheet 6

          • • Vector Worksheet 6 Answers