# Math Help - Teaching Calc 3/Analytic Geometry

1. ## Teaching Calc 3/Analytic Geometry

I know this isn't exactly the sort of question usually asked here, but I was hoping someone could help anyway...

I'm a "TA" at my university, but a very good teacher, so I am actually teaching Calculus 3 this semester. We are using Calculus: Early Transcendentals (6e) by Stewart.

I am "supposed" to cover chapters 12-16. But I think I'm going too slow; I'm only in section 13.3 (Arc Length and Curvature) right now.

I have a few questions to ask on how the class should be taught...

1. How much explanation would you give on definitions/theorems, in the way of proof, for example? Obviously I'm not proving every little thing (like properties of dot product for example lol...), but I really feel it is important for them to see the reasoning, the logic behind these things. I really don't like just stating something and moving on.
2. Are there any sections that can/should be skipped? I'm thinking 13.4 (Velocity and Acceleration Vectors) can mostly be avoided... maybe a quick mention of the relationship $\vec{r}^{\prime}(t)=\vec{v}(t),\vec{r}^{\prime\pri me}(t)=\vec{a}(t)$, but definitely skip stuff like Kepler's laws of motion.

1. Just looking ahead to chapter 14, Functions of 2 Variables and Partial Differentiation... How much detail is really necessary here? I mean limits, yes... the fact that you now have infinitely many paths on which to approach a point as opposed to just from the left or right. But in general proving that a particular limit DOES exist seems to be quite difficult, without resorting to the $\epsilon -\delta$ characterization (which I don't really want to spend time on...). But other than that, there are a ton of PAGES in chapter 14, but the material is not difficult. There's just a lot of it, and I don't want to continue falling further and further behind...

So... I don't know. What would you guys do?

2. ## Well

I´ll give you my perspective.

It´s imossible to cover all the material in Stewart (great book by the way) so you´ll have to skip alot, that´s a fact. It is also one of the problems young teachers face during their first years of their career, not enough time but alot to cover.

1. There are so many university-whatever homepages on the internet with lessonplans and stuff. Check them out to see what´s really important. Here´s just one example. You can always ask previous teachers at your university what, how and when.

2. The review sections in Stewart are quite good. They usually pic up the most important stuff. Try to cover as much as possible from there.

3. Make a semester plan for yourself, don´t be too time-optimistic.

4. Whatever you cover, do it properly. Don´t blame yourself if there´s not enough time to cover everything. There´s a reason why you already teach at at a university, you´re good and that´ll keep your students motivated. The more they understand after your lectures the more they will study on their own.

Don´t know if this made sense but just get that plan and then concentrate on what your good at.

-WS