M408R is a 1-semester survey of calculus. As such, it covers more ground than the first semester of a 2-sememster sequence, but with a very different emphasis. We will cover Chapters 1-6 of Callahan, and part of Chapter 11.
Goals for the class:
a) Learning the key ideas of calculus, which I call the six pillars.
1. Close is good enough (limits)
2. Track the changes (derivatives)
3. What goes up has to stop before is can come down (max/min)
4. The whole is the sum of the parts (integrals)
5. The whole change is the sum of the partial changes (fundamental theorem)
6. One variable at a time.
b) Learning how to analyze a scientific situation and model it mathematically.
c) Learning to analyze a mathematical model using calculus.
d) Learning how to apply the results of the model back into the real world.
e) Learning enough formulas and calculational methods to make the other goals possible. There are three questions associated with every mathematical idea in existence:
1. What is it?
2. How do you compute it?
3. What is it good for?
Compared to most math classes, we're going to spend a lot more time on the first and third questions, but we still need to address the second. You can't spend all your time looking at the big picture! You need some practice sweating the details, too