$University of Illinois at Urbana-Champaign$

Math 241 Calculus III

Section ED1

Fall 2008

Tur/Thur 8-8:50am in 343 Altgeld 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 and the solution for worksheet Part I #2.
Dec. 2 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 Correction and solution for worksheet 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. 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

Solution for Part III.
Some suggestion of problems: Chapter 13.1 #21, 25, 28, 41, 44, 45, 51.

Oct. 7

For Part I problem 1, you may also make some observations to reduce the cases; see a different analysis of cases.
Note the observation is true in this problem, but not necessary others, in particular not 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.
Today we didn't have time to cover the relations of two lines, but you should read the book and try to do part II of the worksheet. We will discuss them briefly next time. To make sure you understand, you should hand them in, so I can help you to check.
Here is the notes I mentioned in the email.

Sep. 2

Here is the formula for distance between a point and a line. Click here
I did not 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 it in the detail during the class. 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