Math 1571H Honors Calculus Fall Semester 2001

Remember: The exam on methods of differentiation is on Thursday October 25 in recitation. No calculators or books or notes are allowed. You have to do at least 6 of 8 differentiation questions correctly to pass. I have decided that 30 minutes is a reasonable time in which to do this exam. Here are some last minute practice questions to look over: page 97 nos. 22, 27, page 112 nos. 19, 20, 29, 30 page 113 nos. 34, 40, 42, page 114 no. 46, page 288 nos. 1 - 6, 22 - 24.

Assignment 8 - Due Thursday 11/1/2001

Read: Simmons Sections 4.4, 4.5, 4.6. We are going to omit Section 4.7.

Exercises:
4.4: 2, 3, 4*, 5*, 11*, 15, 22*
4.5: 2, 4*, 5, 8, 17*
4.6: 1, 2a*, 5, 9, 10*, 13


Assignment 9 - Due Thursday 11/8/2001

Read: Simmons Sections 5.3, 5.4.
We will be doing questions from section 5.2, but I recommend that if you do read section 5.2 then try not to get hung up on things like the meaning of the term 'differential' on page 164, because it is not precisely explained, and indeed it is problematic to give it a precise meaning. We don't have to work with the notion of differentials as they do in this book. I will show you in class how to do the things they do in section 5.2 without using the differential notation. I take the view that writing things down as differentials is a useful informal way to go about doing some calculations, but in our finished written work we should avoid writing them down. It seems to me that this view is in accordance with history, as described on pages 168 and 169 (and those are two good pages to read).

In section 5.3 differentials are used at the top of page 174 to introduce integration by substitution, but it seems to me that what Simmons writes there does not have a sound basis. You should really read about 2/3 of the way down page 176 to get a proper justification for integration by substitution. My advice is: be wary. And if something does not seem clear in what you read, try to skip over it.

Another warning about section 5.3. On page 171 I would not say that both the formulas (4) are correct. The second formula with the constant c is the one we should use.


Exercises:
5.2: 16, 22*, 24, 27
5.3: 8, 14, 26, 32*, 38, 40, 42*, 44, 48, 50, 52, 54, 56, 58*, 62, 63, 66b*, 69
5.4: 4, 5, 6*, 9, 10*, 11, 12, 13, 20*

Office Hours: I realize that my office hours as advertised in the schedule are not much use to you. In fact I am generally in my office (350 Vincent Hall, 625 3491, webb@math.umn.edu) on M, W and F between 11:15 - 12:15 and 2:30 - 4:30. This week I am substituting for someone else at 3:35 - 4:25, but that only applies to this Wednesday and Friday. Also I may start attending a class which runs 2:30 - 3:20, in which case I will be in my office 3:30 - 4:30. Do drop by. It is a good idea if you can to telephone in advance, or warn me in some way, so that you can be sure I will be there.