# Summer Preparation for Calculus III

There are two topics that I don't want to have to go over from scratch. You have seen them before, but you need to review them to be ready when we start. We will start with questions on these topics.
## Complex Numbers

Go through the Complex Numbers unit from Khan Academy (20 videos). If you remember complex numbers pretty well you may fast-forward the basic stuff, but make sure you know:

- multiplication and division
- representation of complex numbers in polar form (i. e. magnitude and angle, aka magnitude and phase)
- the complex plane (aka the Argand diagram)
- using the complex plane for multiplication and division

## Matrices

The main points about matrices:

- A matrix represents a transformation
- Multiplying a matrix times a vector, as in
**Ax**, means creating a linear combination of the columns of **A**, using the components of **x** as weights for the columns
- In the product of a matrix times a matrix
**C=BA**, each column of **C** is the matrix-vector product of **B** times the corresponding column of **A**.

**If you didn't learn matrices here at RCHS**, you learned a different way of multiplying matrices and you didn't learn to think of a matrix as a collection of column vectors. Also, the statements made above might not mean much to you. **You need to forget your old way and learn the new way of thinking about matrices**.

Slowly read pages 2-14 of our linear-algebra book. I mean slowly! This is math.

**Read no more than 30 minutes per day**. You can't concentrate any longer than that, and it may take some practice to get to 30 minutes. (Most professional mathematicians don't try to do math more than 4 hours per day, some much less).

**Don't skim**! Read every line. After you read a line, stop and make sure you agree with it. Go no faster than:

- page 2: 10 minutes
- page 3: 10 minutes
- page 4: 10 minutes
- page 5: 15 minutes
- page 6: 15 minutes
- pages 7-8: 30 minutes total
- pages 9-10: 30 minutes total
- page 11: 20 minutes
- page 12: 30 minutes
- page 13: 30 minutes
- page 14 (top half): 10 minutes