Math 1572H Honors Calculus Spring Semester 2002

Assignment 11 - Due Thursday 4/18/2002

Read: Simmons, Sections 14.5, 14.6, 16.1, 16.2.
I am tempted to specify section 14.7 also, and I will say something about it in class, but I will not set any questions on it. The techniques in it are important, but also I would say they are fairly obvious, if they turn out to be something you need to use. Like several other things we have done, proving that they work is less easy.

In Chapter 16 there is quite a lot of detail about polar coordinates that I do not think we need to know, for example, we do not need to remember the equations of cardioids, limacons, various spirals etc. On the other hand, in general terms I do think it is useful to have seen the sort of things that can be done in polar coordinates, especially how we deal with expressions involving derivatives.

Exercises:
Sec. 14.5: 1*, 2, 4, 9*, 10, 12, 15
Sec. 14.6: 1, 2b*, 3, 4*
Sec. 16.1: 1ab, 2cd, 7, 8*, 9b
Sec. 16.2: 2a, 4cefgklmn, 4k*, 4n*, 5fgh, 5h*, 6, 6e*, 10b*

At the end of section 14.5 there are many questions like numbers 1, 2, and 4, and I think you are meant to do all of them in the way which is suggested in the wording of question 1; in other words you are supposed to use the theory to find how many terms of the series you need to take to get the specified accuracy. The alternative you might think of is to add up a few terms of the series on your calculator, check to see if what you get lies within the specified range of what your calculator says is the true value, and stop there. This would not be using the theory!