$University of Illinois at Urbana-Champaign$

Math 241 Calculus III

Section ED6

Fall 2008

Tue/Thur 10-10:50am in 108 David Kinley Hall

Office: 341 Illini Hall
Office Hours: Monday 1-2, Thursday 11-12
Text: Multivariable Calculus: Early Transcendental Functions, Third Edition , by Smith and Minton. ISBN 0-07-287029-X. We will cover chapters 10-14.
E-mail: ctsai6@uiuc.edu

For more course policies and information, please go to Professor Hildebrand-Math 241

Course Syllabus

Announcements

Dec. 9 The solution for worksheet.
Dec. 5 The solution for worksheet 11/20 which I may have promised before.
Dec. 4 The solution for worksheet Part II.
Nov. 18 Good luck!! Here is the solution, and I provide two ways to do PartI #1.
Nov. 6 Solution for worksheet Part II 2 and Part III.
Nov. 4 Solution for worksheet Part II 2(a).
Oct. 30 Solution for worksheet Part II & III.
Oct. 28

Bring today's worksheet on Thursday, and we will discuss Part II.
You should go ahead and try it, and here is the answer for them:
#1. a³π(2-sqrt{2})/3
#2. (0, 0, 3a(2+sqrt{2})/16)
#3. a²π(2-sqrt{2})
#4. a²π/(sqrt{2})
Some suggestion of problems:
Chapter 13.5 #11, 13, 19, 30, 41, 42.
Chapter 13.6 #17, 19, 37, 41.

Oct. 23 Solution for Part II. Oct. 14

I will have an extra office hour tomorrow (Wednesday 10/15 11am).
Some suggestion of problems:
Chapter 13.2 #7, 14, 17, 25, 28, 45, 51.
Chapter 13.3 #3, 5, 10, 11, 13, 15, 22, 25, 28, 32

Oct. 9 Some suggestion of problems: Chapter 13.1 #21, 25, 28, 41, 44, 45, 51.

Oct. 7

For Part I problem 1, we made some observations to reduce the cases. The observation is true in this problem, but not necessary others, in particular problem 11 p.1020.
Some suggestion of problems: Chapter 12.8 #6, 17, 26, 29, 39.

Oct. 2

Some suggestion of problems:Chapter 12.7 #1, 5, 8, 23, 26.
In Part II, you will not get back to the example we did in class, if you are thinking of data as the total amount of hotdogs at the time. In fact, you will have (0,0),(1,1),(2,2) and (3,5). In order to get (0,0),(1,1),(2,1) and (3,3), we are thinking of the amount per minute. Sorry, the question is not well-phrased.

Sep. 30

Solutaion for Part II.
The examples were discussed at the end, and they are similar to #55 in chapter 12.6.
Some suggestion of problems:(If you have any question, you can always email me or come to my office hour.)
Chap.12.5-#8, 18, 23, 27
Chap.12.6-#8, 9, 17, 23, 36, 43, 55(change the degree of 10/6 to 45/30).

Sep. 11 Solutaion for #29. Someone mentioned it's much easier to use the cross product method, so you should try it! (Remember you need 3-dim vectors to do cross product.) Sep. 4

If you are still confused with the distance formula, you can look up the note under Sep. 2.
For those left early, you should try to do the part II on your own to see if you understand the relations of lines. You can hand it in next class if you want to.
Here is the notes of the last five minutes of the class.

Sep. 2

Here is the formula for distance between a point and a line. Click here
I didn't talk about it today. It is a similar idea to how we get the formula of area.
We will do it together with distance between two lines (in Chap10.5). Please let me know if you have any question.
Some suggestion of problems: Chap.10.4-#9,#14,#15,#48,#50,#55,#61

Aug. 28

Some suggestion of problems: Chap.10.3-#8,#18,#22,#27,#28,#30,#31

Aug. 26

Here is something I didn't explain clearly during the class and I might confuse some of you. Please let me know if you have any question. Click here
Two equivalent ways to write the polar form of a vector v=⟨a,b⟩:
- v=product of the magnitude of v and the unit vector of the same direction as v.
- v=||v||⟨cosθ,sinθ⟩ where θ=tan^-1(b/a).
If you are interested in doing some more problems, you can always try the problems which are in the same block as homework problems and they will be similar to homework problems.
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Some suggestions: Chap.10.1-#14,#17,#23,#27
                   Chap.10.2-#7,#15,#20,#30,#47
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Last updated: 12/10/08