## Mathematics 311, Sec. 200 (Honors), Spring 2004

SKIP PAST THE ANNOUNCEMENTS if you so desire. ._. (or to near the bottom)

#### Course procedures and announcements:

• May 14: It's official: Your grade is available in Vista, and I have updated the table below with the top and median scores in each category. Here are the formulas for the curves:
• Homework: Add 46, then multiply by 0.471.
• Total class participation: Multiply by 0.5, then add 20.
• Final exam: Multiply by 0.9, then add 27.
(Curves on the hour tests were additive and already included in the scores in Vista.) I don't remember a final exam where the scores were so tightly bunched; usually I need to squeeze the distribution much harder to avoid carnage. This result confirmed my impression that you, as a class, demonstrated an unusual depth of talent and motivation, even for an honors class. Therefore, I had little hesitation about giving grades that were a bit more generous than the raw numbers indicated (although I do wish that all the students with As would score as well on all tests as you each do on some).
• May 13: (scream2) Please study the solution to Qu. 7(b). NOBODY did it correctly. Note: (1) Finding the components of a vector with respect to the local polar basis is not at all the same thing as finding the polar coordinates of a point. The latter is a nonlinear transformation (r = square root of x2 + y2, etc.) ; the vector transformation is just a rotation. (2) If you use the Jacobian matrix of the polar coordinate transformation (in the right way) you will get the transformation of the vector from the Cartesian basis to the tangent-vector basis (dr/dr, etc.). To get to the basis of unit vectors you need to scale the theta component by 1/r. (That would be a legitimate third method of solution.)

Qu. 8 was also something of a disaster, but I had to grade it leniently. Only two people explicitly appealed to the equality of mixed partials, which is the crucial step in the proof. Most of you gave a proof by ambiguity of notation: a partial derivative of (f times the partial derivative of g) is not the same thing as (partial of f) times (partial of g); you were supposed to verify that all the second derivatives of g cancel!

I have corrected one misprint each in the solution to Qu. 4 (p. 3) and Qu. 7(b) (p. 5).

• May 12: (scream) Please study the solutions to Qu. 2 and Qu. 10(B)! Remember: (1) You can't apply Stokes's theorem until you have a CLOSED curve (the boundary of a surface). (2) A "semicircle" is a CURVE, not the half-moon-shaped surface it sits next to. You were not told to calculate a flux through the half-moon; use the cylindrical surface you were handed on a platter, where you already know the surface integral and which already has a closed curve as boundary where you can trivally evaluate all the extra line integrals. When you try to use the half-moon, you get the wrong answer because of the phenomenon that is the subject of Qu. 2(b).
• May 11: Final exam key is now posted.
• May 8 (updated May 14): Vista is now updated (except for the strange ordering of the items on the page you see; according to the local expert, that is a known bug that will be fixed in the next edition of the software). Here is some statistical information:

High Median Remarks
Grades A A 14 As (4 of them squeaky - you know who you are).
Hour test total 290 261 Includes 5 point curves on Tests B and C.
Final exam 192 168 Does not include curve.
Test average 96.52 88.10 Includes curve on final.
Homework 276 243 Scaled and curved to nominal max of 130.
Reviewing 66 59 Added and scaled/curved to nominal max of 70.
Other Class Participation 32 20
Total points 699 636
("Nominal" means that some students got more than 130 on homework, for example, because of extra credit points.)
• May 8: Extra time on final. Since our exam is the last of the day, I have no problem letting you work till 6:00. I thought you'd like to know that beforehand.
• May 4: Please DON'T erase your homework from the Web yet. You may have given me permission to copy it, but that doesn't mean that I have had time to do that yet. It will happen sometime later this week. (Note that calclab accounts will be nuked on May 14, so anything that YOU want to save should be downloaded elsewhither before then.)
• May 3: Notes on nabla in curvilinear coordinates
• Apr. 25: Grader jobs for fall
• Apr. 25: Transparencies on Vector calculus and the topology of domains in 3-space (J. Cantarella et al., Amer. Math. Monthly 109 (2002), 409-442). (Updated 8 Nov 2010)
• Apr. 20: Another Math Club meeting, April 26.
• Apr. 3: Sophomore Mathematics Contest April 13, 7-9 p.m., Milner 317. Cash prizes! You are eligible if you are a second-year undergraduate student (even if your classification is U3).
• Mar. 10: Notes on Green functions
• Feb. 27: Notes on hyperbolic functions and the twin paradox
• Feb. 19: Just Say No to .doc files! How to get PDF or PostScript out of Word.
• Feb. 17: Annoyed by the poor quality of your on-screen output from LyX? Here's what to do!
• Jan. 13: Here are Chapters 1 and 2, in case you have not yet been able to buy the book. (Do not expect this service in the future.)
• STUDENT-WRITTEN ON-LINE SOLUTIONS MANUAL
• Fall 96 home page (See this for sample summary reports and fragments of a student-generated solutions manual for odd-numbered exercises (available after the homework is due). DISCLAIMER
• Fall 98 home page (See this for sample summary reports and fragments of a student-generated solutions manual for even-numbered exercises).) DISCLAIMER
• Spring 99 home page (See this for sample summary reports and fragments of a student-generated solutions manual for even-numbered exercises).) DISCLAIMER
• Spring 00 home page (See this for sample summary reports and fragments of a student-generated solutions manual for odd-numbered exercises).) DISCLAIMER
• Spring 02 home page (See this for sample summary reports and items that fill in the gaps in the student-generated solutions manual).) DISCLAIMER
• Course handout ._._. DVI format ._._. Acrobat format
• Web and TeX information: I really want to encourage and help you to put your work on the Web, and to read what others have put there, and also to discuss mathematics with specificity in e-mail and your reviews and reports. I have compiled some links (not recently updated) that may be useful. (More useful would be for the state of the technology to advance so that the process becomes easy and natural for all concerned. That is happening slowly.)
• Information on the Web about putting math on the Web. I urge all of you to read at least the first two items (the one from Swarthmore, and the one from Karl's Calculus Tutor about e-mail). The later items become increasingly technical, and often refer to "solutions" that are not useful to us now because not every reader has the necessary software. The whole page will be of interest to those who might be interested in helping develop the higher education of the future. (See also Pilant's Web course if you have time to browse.)
• Information about DVI viewers. If you are unable to read the excellent homework papers of TeX users such as Chris Wood (M. 311, s00) and Andrew Barkley (M. 311, f98), you should read this!
• On-line introductions to TeX. If you want to learn to use TeX yourself, here is free documentation!
• TeX10x
• Groups (revised 1/26) ._._. TeX source (ASCII readable) ._._. DVI format ._._. PDF format
• e-mail: fulling@calclab.math.tamu.edu

#### Course content by weeks:

1. Sections 1.1-1.4
2. Sections 2.1-2.3
3. Sections 2.4-3.2
4. Sections 3.3-3.5
5. Section 4.1
6. Sections 4.2-4.4
7. Sections 4.5, 5.1
8. Sections 5.2-5.4
9. Sections 5.5, 6.1
10. Sections 6.2-6.4
11. Sections 7.1-7.4
12. Sections 7.5-7.6
13. Sections 8.1-8.2

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#### Things of tangential interest:

• Related course materials on the Web
• A generic Frequently Asked Questions List for mathematics
• Prof. Pilant's course on Web Technology for Communicating Mathematics -- especially
• Arithmetic with large integers by means of the Chinese remainder theorem and object oriented programming (fun stuff from Math. 302)
• The W. L. Putnam Undergraduate Mathematics Competition. Winners are often not math majors!
• Internet Awareness Week (1995) and TeX Users Group (1999) talks.

Go to home pages: Fulling ._._. Calclab ._._. Math Dept ._._. University

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Last updated Tue 18 Jan 05