Answering Student Questions

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"In a compartment model, what doe a determinant of 0 mean?"
On page 612, the book explains that there are three possibilities when the determinant is 0. Matter gets stuck in compartment 1, matter gets stuck in compartment 2, or the matter in the system is a constant.

How do you compute the Hessian matrix of a function $f$?
The formula for the Hessian is on page 551 and the components of the matrix are second derivatives of $f$. If we write $\mathrm{Hess}f(x,y)=\begin{bmatrix} a & b \\ c & d \end{bmatrix} $, then compute $a$ by taking two derivatives in $x$, compute $d$ by taking two derivatives in $y$, and compute $b$ and $c$ by taking one derivative in $x$ and then taking a second derivative in $y$.

"One of the exercises generated a value of 2 for every boundary. Does that mean it is a max and min, or there is none?"
You have to compare the value 2 to the value obtained at the critical point on the interior. If the value of the critical point is greater than 2, then the minimum is attained all along the boundary and the maximum was attained at the critical point. If the value of the critical point is less than 2, then the opposite. In the situation that there are multiple critical points, then you must compare all the values attained.

Calculus II for Bio

Ask a math question of medium difficulty. Try looking through some and see if you can work out the answers. You'll need a writing utensil and some paper. Don't be lazy.

Here are two problems to get things started:
(Without looking in your book) Give an example of two $2\times 2$ matrices which do not commute.

If there was a $2\times 2$ matrix $A$ such that $A \cdot B = B \cdot A $ for all $2\times 2$ matrices $B$, what does $A$ look like?

Section 3 Comments 20130919

This section has a relaxed atmosphere which is conducive to learning.
This section is cool.
: Great! I definitely want students to come to a conducive-learning environment.

I don't like the quizzes. The homework is going to give me gray hairs at age 18. Tim/John*, you're a cool TA though.
*Inside joke
The section is helpful, but I don't like the quizzes. We should do more exercises.
Do the quizzes count as a grade?
: I don't like the quizzes either, but you probably need them.
: Yes, the quizzes are factored into your grade.

The differentials involving population are quite difficult.
: We'll have to talk about that some time.

I hate trigonometry.
: There's a saying: "Keep your friends close, and your enemies closer." You'll need trigonometry to answer calculus questions. So while you don't have to like it, you have to use it.

Note to Self

My students probably struggled with the last few topics covered in the semester as my coverage on those topics was not as thorough as my coverage on the rest of the topics covered in the semester.

On a related note, I occasionally ponder the possibility of covering less, but in greater detail.

On a different note, I think it's strange how many students ask for review sessions, but when I bring up the idea of extending class time or a separate hour (temporarily ignoring the issue of increasing credit) to my peers, there is the idea that students wouldn't agree to it. The problem with office hours is that students either have other classes schedule during that time or are afraid to come. Office hours by appointment is fine, as long as it isn't abused.

Maybe there should be a game. Played by a professor. Every time the professor says something that might be on the exam, students should say some key phrase like "That's magic!" Perhaps every once in a while, and especially the first week, this should be aided with a pause or a hand signal or a sign (much like an "Applause" sign).