# Calculus I: Math 151-007, Fall 2007

Instructor: Michael Pelsmajer
[Departmental webpage] [Personal webpage]

Generic Syllabus (Feb.'06)
Course Information (Sept.7 updates: recitation moved to LS 240, recitation guidelines added)

Thursday October 4 class is in Siegal Hall, room 237
No class Friday Oct 5; hand in HW by 11:25am in E1 room 210, box "CHEN"
Class Thursday October 11 is in LS 240 (recitation)
Thursday October 24, class is in Siegal Hall, room 237.
Thursday November 1 is in LS 240 (recitation)
Thursday November 8 is in LS 240 (recitation/exam review)
Thursday November 15 is in Siegal Hall, room 237.
Thursday November 29 is in LS 240.

### Thursday December 6 is in Siegal Hall, room 237.

For some really spot-on tips, etc., I can enthusiastically recommend How to Ace Calculus: A Streetwise Guide. The quality of the advice is very high. Excerpts are available on the website so that you can see roughly what it's about.

I have also collected notes on how to succeed in Calculus.

## Exams

The first exam will be Friday, September 28.
If you need to catch up, you better start right away. (9/21/07)
Study without the book open in front of you; be able to solve problems under exam-like conditions. You will only have a pencil/pen & paper. (9/24/07)
The second exam was be Friday, November 9.
The only remaining exam is the final.

## Trig Review Homework (optional for most)

Assigned Friday August 24, due Thursday August 30
From Appendix D (Stewart), do #1, 3, 9, 13, 15, 17, 19, 21(Hint: Pi/2 is approximately...?), 25, 27, 29, 32, 33

Assigned Friday September 7, due Thursday September 20
From Appendix D (Stewart), do 45-50, 59, 61, 63, 65, 67, 69, 71, 73, 75

## Homework

HW assigned Wednesday, December 5:
Look at picture in Section 6.3
On p368, do #3, 21, 25
On p378, do #7, 9

HW assigned Tuesday, December 4:
Look at the other pictures in sections 6.2 & 6.3, and read(review) p365-366.
On p362, do #3, 11, 15, 17

HW assigned Friday, November 30:
Look at pictures on p354-356 & 361-362!
On p362, do #51, 53, 57,
#65(Hint for part a: Set up the integral for part b, and compare to the integral you'd get for a usual cylinder. It should be very revealing!)
and #66.

HW assigned Wednesday, November 28:
On p352, #5, 11, 17-20, 23(hint: to find intersection, rewrite sin2x using trig identity)
Tip (that I should have mentioned during class): You don't necessarily have to do the entire sketch before finding the intersection point. Rather, carefully finding all intersection points can help you to make the sketch. (Or, at least they can help verify that the sketch is correct).

HW assigned Monday, November 26:
On p338, do #9, 15, 19, 25, 29, 39, 43, 47, 50
Note: Some problems have more than one letter; only one is the variable, the others are constants
Also, do these two problems:
(*) What if we changed the limits of #47 to be: 0,2 ?
(**) What if we changed #25 to be a definite integral from 0 to 2pi?

(No class Friday, November 23 due to Thanksgiving Break)

HW assigned Wednesday, November 21:
Read Example 5 on p326, all of p327, and Example 7 on p329.
On p322, do #27, 29, 31, 37, 40
On p329, do #2, 3, 5, 9, 37, 41, 47, 50, 52, 59, 60

HW assigned Monday, November 19:
On p310, do #43, 47-49, 53
On p321, do #3, 6, 7, 9, 11, 13, 16, 19, 23-26

HW assigned Friday, November 16:
On p310, do #17, 19, 29, 30, 33, 34,
and redo #34 but with the upper and llower limits switched.

HW assigned Wednesday, November 14:
On p298, Do #1a, 5ab

HW assigned Monday, November 12:
On p279, do #3, 9, 11, 13, 15, 21, 29, 35, 39, 53, and 57 and 69.

On Friday, hand in HW that was assigned on November 2 and 5. (Although you may wish to do the HW assigned November 7, that material will not be on Exam 2, so that stuff is not due until the next week.)

HW assigned Wednesday, November 7:
Read p271-272, which gives a reasonable "rule of thumb" for how you can (hopefully) attain a certain level of accuracy.
You can and should use a calculator (or Maple), and Formula 2 (p270) for most of these problems!
On p272, do #1(part b, explain in terms of what Newton's Method would produce),
and #4, 5, 8, 11(Hint: To get started, write the number equal to x, and rewrite that as a polynomial equal to zero.)
and #15(Hint: First, rewrite it in the form "f(x)=0" for some function f.),
and #21(Hint: it's like Example 3),
and #29.

HW assigned Monday, November 5:
On p263, do #34, 36, 37, 45, 47

HW assigned Friday, November 2:
On p262, do #2, 3, 7, 9, 11, 19, 22, 23 On p265, do #55; for part b, note that revenue = (demand)x(price).

HW assigned Wednesday, October 31:
On p241, do #18-23, 25, 27, 30, 55
Optional: Read Examples 2 & 3, p246-247.
On p248, using my guidelines, do #5, 11, 15, 20, 23, 25, 38
(Recitation tomorrow, LS 240 !)

HW assigned Monday, October 29:
Read Example 4 on p234 and, if needed, Examples 8-10 on p236
On p240, do #3, 9, 11, 13, 15, 17, 23, 25, 27

HW assigned Friday, October 26:
On p227, do #1, 9c, 21, 23, 25, 27, 32, 33(ab)cd, 37

HW assigned Wednesday, October 24:
Read Example 5, p218, and on p220, do #23
On p227, do #5, 9ab, 12ab, 13ab, 31ab, 33ab, 39ab (For most of these problems, part "c" and/or "d" will be assigned next time. Leave room for that, and make a photocopy of your homework for yourself before handing it in!)

HW assigned Monday, October 22:
Try reading the proof of Rolle's Theorem - it's really not that bad, and you've heard it once already. In fact, this is one of the few times when I will recommend that you read the entire section through (section 4.2).
On p219, do #5, 7, 11, 13, 15, 17-18(like in class, but you also need to show that there exists a root - do you remember how you might do that?),
19, 25, 32

HW assigned Wednesday, October 17:
Read the yellow dots on p205, read The Closed Interval Method on p209, and read example 10 on p210.
On p211, do #5-13, 27, 33-37, 39, and (using the closed interval method:) #45, 51

HW assigned Monday, October 15:
On p133, do #39-42
On p180, do #11, 13, 17 (Note: "answers" in the back of book are more like hints)
On p193, do #1-4, 23-28, 41a

HW assigned Friday, October 12:
On p186, do #13, 21, 24, 29, 31-33, 36, 39
(Reading examples on p183-186 may help, but it's optional.)

HW assigned Wednesday, October 10:
On p461, do #3, 5, 22, 23, 30, 31, 39, 40. (Note that "arctan x" is the same as "tan-1x".)
On p186, do #1, 3, 7

HW assigned Monday, October 8:
Read the bottom of p385, then this: A function is one-to-one exactly when it has an inverse (i.e., when the inverse exists), which is true exactly when it passes the horizontal line test.
On p391, do #5-14, 18-20, 25, 31, 35, 37-41
On p461, do #1, 7, 25

(No HW will be assigned Friday, October 5)

HW assigned Wednesday, October 3:
On p169, do #7, 15, 19, 21, 23-25, 29, 39, 51

HW assigned Monday, October 1:
p161, do #3-7, 11, 15, 17, 20-24, 29, 34, 37, 39, 40, 44, 47, 49, 63, 73, 84

(No HW assigned Friday, September 28)

HW assigned Monday September 24:
p144, do #33, 35, 37, 55, 65, 71
p154, do #1, 3, 5, 7, 9, 13, 15, 17, 21, 23, 39-41, 43, 44, 46, 48
(It's a lot, I know.)

HW assigned Friday September 21:
Now you can and should use the formulas summarized on p144.
Read formulas at the end of p144. (These are written in rather compact form - full versions are written throughout section 3.3.)
Read examples 6,7,10,11 from section 3.3.
p144, do #1-21, 63, 99.
Also read the proofs of the Sum Rule and Product Rule.

HW assigned Wednesday September 19:
On p131 do #1, 4-11, 17, 23, 33, 35

HW assigned Monday September 17:
Finish/correct previous HW and
Read VELOCITIES p114-115 (not Example 3) and RATES OF CHANGE p117-119.
On p119 do #21, 26, 30-36, 43, 51, 52

HW assigned Friday September 14:
On p107 do #44(clearly!), 45(you must pick a,b well), 46, 47, 48(first rewrite it as f(x)=0)
For this part of the homework, do not use any advanced techniques for taking derivatives! Sorry, but there's a good reason.) Read p116, and on p119 do #1, 3(must show both methods for part a!), 7, 8(easier w/definition 1), 9ab, 11, 12

HW assigned Wednesday September 12:
On p105 do #3, 5-7, 31, 33, 37-39

HW assigned Monday September 10:
On p95 do #1-4, 13, 20, 21

HW assigned Friday September 7:
Read examples 7,8,9,11 from section 2.3
On p85, do #11-19, 21, 23, 25, 27, 35-37, 39-44, 46

HW assigned Wednesday September 5:
On p74, do #4-7, 13-16(clarity is essential!), 25-32

(Labor Day)

HW assigned Friday August 31:
Read Section 2.1, and on p65 do #5

Reminder: On Friday, August 30, all HW is to be handed in, and there will be a quiz. (Try to done by Wednesday night, so you have time to seek me or visit the Academic Resource Center if necessary.)

HW assigned Wednesday, August 29:
On p35, do #6, 7, 15a, 17
On p43, do #3-7, 13, 17, 34-36, 41-45, 49, 51

HW assigned Monday, August 27:
Read section 1.1 (long, I know)
On pA15 do #3, 9, 23, 25, 29, 31, 45, 47, 51
On p22 do #1, 2, 5-8, 22, 27-33, 36-39, 41, 49, 51, 52, 56

HW assigned Friday, August 24:
Read A Preview of Calculus, read the links on this webpage, and examples 3,4 from Appendix A.
(Due Monday, but not handed in until Friday Aug 31):
Which of the problems on p9 do you find interesting - say, if you had to a substantial project on it?
From Appendix A, do #1, 9, 11, 21, 23, 25, 31, 33, 35, 37
(answers without explanation are on pA122)

## Maple Labs

October 4
Start here, find "Just enough Maple", and from there go through The Guide, #2.

Then, Lab #1. (Right click & save, etc.) Try to finish it by Monday.

Although this is said in The Guide, let me repeat it here:

Do not struggle for hours by yourself without making progress. Get help.

October 25
Lab #2 (Right click & save, etc.)
At various points in the lab, you will probably want to refer back to The Guide: Fasshauer's Introduction and also the Maple Tips.

November 15
Lab #3 (Right click & save, etc.)

December 5
Lab #4 (Right click & save, etc.)