First Day of Class: Calculus II and Linear Algebra

I gave myself the gift this semester of no lower-level classes. I think I'll have more mature students, and I hope to have a great time with them.


Calculus II
I've taught this the previous two semesters, so it should be a breeze. We've switched to a new text, but I don't think that will have much effect on my teaching. I have a big class this time (36 or more), unlike the past two semesters. But putting students in groups of 4 makes it so much easier to learn their names.

We did the axes exercise (mentioned here), and I once again loved how it got them talking to one another and reminded me how weak they are on things I think of as pretty basic. (How would you label the axes?)

We also worked on the Calculus Review sheet I've used each term. Part of their homework is to make a list of 5 Calculus I problems that they can't do, and share it with their group tomorrow.


Linear Algebra
It's been over a decade since I've taught Linear, and I knew I needed lots of work on the material over the holidays to be well-prepared to teach it. That task is done.

We're using the text by David Lay (Linear Algebra and Its Applications, 4th edition), and it starts out tougher than many texts. He says, "I think that students' opinions of the course are set somewhere in the first two weeks, and they need to feel the conceptual emphasis early." (page xv, Notes to the Instructor) My colleagues have told me that our students have done especially well with this text. One thing that threw me at first was (from page 35, in section 1.4):

"If A is an mxn matrix, with columns a1, ..., an, and if x is in Rⁿ, then the product of A and x, denoted by Ax, is the linear combination of the columns of A using the corresponding entries in x as weights; that is,

I don't think I had ever seen that before. I've been talking with Owen Thomas (aka vlorbik) about this course, and he grabbed right onto that when I mentioned it - he loved it. I think I will too, once I get used to thinking this way.

After doing the axes exercise, I gave my students a warmup sheet which was a review of what they've seen before regarding systems of equations.  Of course it wasn't the breeze I thought it would be, so we're already 'behind'. That's ok. Class went well. I had fun showing them three axes on the edges of my desk and in the air.


Pre-Calculus
We did the axes exercise, and compared the different forms the equation of a line can take.

I'm tired - headed home...