## MATH 317 Sep-Dec 2016 Announcements

11.28
• Comments from TA on H8:
• I marked problems 4,6,8,9,11 (4pts each).
• For problems 8 & 9, students should be clear exactly how and at what point in their computations they are applying Stokes' theorem (for instance why two surface integrals are the same, or writing a surface integral as a line integral, etc.)
• Also it is important to make sure that if you define a surface e.g. H, or some other object, then H is precisely defined somewhere.
• In problem 11, the most common mistake was to use the wrong orientation, resulting in -pi instead of pi.

11.25
• Presentation by Science Teaching and Learning Fellow (STLF) Sophie Burrill sburrill@math.ubc.ca
Sophie is carrying out an evaluation of our Math major program and, as part of her project, she'd like to run a focus group with 3rd yr math majors so she is looking for volunteers.

• USRA: The NSERC Undergraduate Student Research Awards (USRA) provide summer research experience with stipend. If you are interersted in such oppurtunities in math, please visit UBC MATH NSERC USRA page, and reports from previous years.
Benefits:
1. It is a great experience: What is math research like? How do mathematicians think and act when doing research?
2. It helps you to decide if you want to go to graduate school in math.
3. It gives closer contact with faculty members, and they can writer more "useful" recommendation letters in the future.
4. It is a big bonus when you apply for graduate programs.

11.21
• Many TA hours in MLC have been shifted to the final exam weeks. As a result, the MLC is open for very limited hours for the next two weeks (see details at the MLC website). On the other hand, the MLC will stay open until December 20th.

• You can find old math final exams at Math Department exam archive. You can also buy exam packages with solutions at UBC Math Club.

• Comments from TA on H7:
• I marked problems 2,4,9,11,12. Problems 4,9,11 were 4pts each, while problem 2 was 3pts, and problem 12 was 5pts.
• General remark: When writing down a parametrization (of a surface, etc.) don't forget to include the appropriate values each parameter can take (e.g. 0 < \theta < 2*pi).
• Problem 12: Quite a few students did not attempt this problem. Also, there seemed to be some misunderstanding as there are actually three surfaces to consider: S_1 on the cylinder, S_2 on the plane z = y, and S_3 on the plane z = 0. Many students only computed the surface integral for S_1.
• Additionally, one needs to be careful when parametrizing S_1, since the cylinder is not centred at the origin of the xy-plane (the y-coordinate is shifted to the right by 2).

11.19
• The final exam will take place on Thursday December 15 8:30am-11am at GEOG 100.

11.14
• The average of MT2, the second midterm exam, is 25.8 out of 40, or 64.5%. The following is the distribution, together with MT1 for comparison.
 0-5 6-10 11-15 16-20 21-25 26-30 31-35 36-40 total average max standard deviation MT1 0 0 3 5 15 18 33 30 104 30.8 40 6.6 MT2 0 0 4 14 37 29 11 9 104 25.8 40 6.0 pb1 8.9 10 1.6 pb2 3.8 10 2.8 pb3 7.5 10 2.2 pb4 5.5 10 1.9

11.07
• Comments from TA on H6:
• I marked problems 1,2,6,9,10. Problems 1 & 10 were 3 marks, 2 & 4 were 4 marks, and 6 was 6 marks (2 for each figure).
• For problem 2, I deducted a mark if the argument for part (b) wasn't precise enough (particularly I was looking for "integral over C = sum over integrals over C_i").
• In problem 6, I deducted points if no explanation or a vague one was given. There were answers that said "the curl(F) is counter-clockwise", or something like that, however it does not strictly make sense to speak of a *vector* (field) in this way (though of course curl(F) is related to rotation in some sense). In a similar way it doesn't make sense to say "curl(F) < 0".
• In problem 10, some students forget that the divergence of a vector field must be a scalar (e.g. some answers were div(curl(G)) = (1,1,1))

11.04
• Office hour before MT2: Monday 1-1:50pm, Tuesday 10:30-11:50am.
• MT2 will not cover the proof of Green Theorem in §16.4, in particular the concept of "simple regions". MT2 will also not cover the vector forms of the Green Theorem, which is included in §16.5 to make connnection to later sections (16.8 and 16.9).
• The concept of "simply connnected region" is covered. It is different from "simple regions".

10.31
• Comments from TA on H5:
• I marked problems 4,5,7,10,12. Problems 4,5 & 12 were 4pts each, while problem 7 was 3 pts and problem 12 was 5 pts.
• Almost everyone had no trouble with 4,5,10 & 12. Problem 7 was the only source of a bit of difficulty, in particular, the set (iii) is *not* simply connected as it is missing the origin. Also, a set can be neither open nor closed (as is the case for (iii), (iv) ).

10.25
• Comments from TA on H4:
• A general comment for the questions (especially problem 3) is that solutions should be written with enough detail to indicate that the student has a 100% understanding of their solution.
• Quite often I saw too few steps being given in computations giving the *impression* that the solution was acquired elsewhere and copied down. (I do not mean that, for example, an integration-by-parts should be given in excruciating step-by-step detail, but enough to be convincing). A one-line answer is probably not enough.
• One point for problem 9 (conservative vector fields) is that some students said the function F "was open and connected" (or something to that effect). This is actually a condition for the *domain* of the function.

10.17
• Comments from TA on H3:
• I marked 1, 2, 4, 9, and 11. Problems 2, 9, & 11 were 4 pts each, while problem 1 was 3pts and problem 4 was 5 pts.
• Problem 1: The main issue was mixing up indefinite versus definite integrals.
More precisely, if e.g. v(t) = \int a(t) d t + C, then the integration constant C is not necessarily v(0).
• Problem 2: It is probably better to leave the gravitational constant g as just 'g' until the very end of the computation, and then substitute its value. I accepted various values of g = 9.8, 10, etc.
• Problem 4: It is important to specify the orientation that is used (directions NWSE with respect to positive x and positive y), otherwise there is a bit of ambiguity where the ball lands. Also, the comment for Problem 2 applies here too.

10.14
• The average of MT1, the first midterm exam, is 30.82 out of 40, or 77.0%. The following is the distribution:
 0-5 6-10 11-15 16-20 21-25 26-30 31-35 36-40 total 0 0 3 5 15 18 33 30 104

• Our TA marked problems 1 and 2 of MT1. His comments on problem 1(b):

A remark on my marking scheme for question 1 (b) (computing d/dt|_{t = 1} [u(t) x v(t)]): There were a quite a few students who "came up" with a v(t) that satisfied the requirements of v(1) and v'(1), and then with this explicit v(t),
• either took the cross-product of u(t) x v(t), and then the derivative, or
• just used d/dt [u(t) x v(t)]) = u'(t) x v(t) + u(t) x v'(t)

Either way, (providing no mistakes) obviously they will get the correct answer when evaluating at t = 1. But there is some sort of reasoning error that we can determine v(t) just from v(1) & v'(1).

If everything was otherwise correct, I gave 4/5. If there were more errors, it would be 2/5 or 3/5 (depending on severity).

10.12
• The final exam will take place on Thursday December 15 at 8:30am. Location TBA.
• Midterm Exam I will be returned on Friday (Oct 14).
• Office hour tomorrow (Oct 13) is moved to 11am.

10.07
• Midterm Exam I will be returned next Wendesday or Friday.

10.03
• Pictures to H1 solution added.
• Comments from our TA for HW2:
• I marked questions 1 (3pts), 4, 5, 9 (4 pts each), and 12 (5 pts).
• Question 1: Many students were treating derivatives (e.g. dr/ds) as if they were actually fractions ("dr divided by ds"). This is fine for heuristics, but the chain rule and inverse function theorem are the tools for a rigorous proof.
• Question 9: It is not enough just to find where k'(x) = 0. One needs to say a little bit more to conclude that a local extrema x_0 where k'(x_0) = 0 is actually a global maximum for k. (I deducted 1pt for this omission.) Note that the first (or second) derivative tests provide *local* information. To conclude *global* information, one needs to analyze the behaviour of k(x) at +infinity and -infinity.
• Question 12: I think some students got bogged down in algebra, because calculating the vector B exactly seems rather unpleasant. (However, we only need some vector parallel to B, to define the osculating plane.)

09.28
• Midterm exam 1 next Wednesday will cover §13.1-§13.4 and §16.1. It will not cover decomposition of acceleration and Kepler's Law in §13.4. Formulas for MT1, 2013 MT1, practice problems for §13.4 and §16.1 and their solutions are posted. Our MT1 will take 50 minutes with similar format as the 2013 MT1.

09.26
• Comments from our TA for HW1:
• Questions 4,5,9,10, and 12 were marked (4 pts each, for a total of 20 pts)
• Question 4: The most common mistake was to forget that the intersection of the surfaces must occur when y = 0.
• Question 5: The most common error was, when getting to the equation 1 + y = x^2, to try and parametrize by y = t (t \in R). But this will not work because 1 + y >= 0.
• Question 9, 10: It is important pay careful attention to what the question is asking. Question 10 in particular asks for the angle to the nearest degree. Many students gave instead arccos(1/sqrt(6)), or 65.9, or other variants. (I did not penalize this.)
• Question 12: The (very few) computational mistakes were with finding the integration constant.
• Additional Comment: A reminder that assignments need to be stapled.

09.16
• There was a typo in H1 problem 6: cot should be cos. 25% bonus will be given to first email pointing out a math error.
• Office hours:   Tue 10:30-11:50am, Wed 11:00-11:50am, Thu 2:00-2:50pm, and by appointment (Tsai's schedule).

09.14
• H1 is posted
• The Math Learning Centre (MLC) starts operation today, Monday-Friday, 11am- 6pm. The MLC is a space for undergraduate students to study math together, with friendly support from tutors, who are graduate and undergraduate students in the math department.

09.12
• Office hours for this week: Tue and Thu, 11am-12pm (this week only).

09.08
09.05
• Welcome to MATH 317 !