Common
webpage
for Sections 101104 of MATH 215 and MATH 255
Information for Section 102 only
Instructor: Dr. TaiPeng Tsai, Math building
room 109, phone 6048222591, ttsai at math.ubc.ca.
Lectures: Mon Wed Fri 9am10am,
LSK
200
Office hours:
Tue 11am12:15pm, Thu 2pm3:15pm,
and by appointment
(Tsai's schedule).
Announcements:
 12.02 and 12.04
 Final Exam: Thu Dec 17, 8:30am11am, MATH 100.
 Office hours during final exam weeks: Mon Wed Fri 2pm2:30pm, and by
appointment.
 All past exams
in the Math Department archive
 Math Learning Centre in LSK 301
and 302, where you can study and find a TA to answer your questions.
 UBC Math Club at
Math Annex Room 1119:
Exam package with detailed solutions for $10.
 Old quiz/exam are placed in folders outside my office, MATH 109.
 11.30

Remark from the TA on HW8:
I marked all of the questions and the
points are 6, 3, 3, 3 and 4 respectively and 1 extra point is for the completion.
Students may have problems in drawing the phase portrait. In general they just
consider which eigenvetcor is the dominating vector. Moreover, for the (f) part in
q1, many students are able to find the phase portrait is an ellipse, but they made
mistakes in determining the direction of the long (short) axis. And to find a
particular solution for an ODE system, some students forget to divide the matrix by
the determinant when computing the inverse matrix.
 11.25


The final answer in the very last line of my Example 2 on Friday Nov 20 lecture is
wrong. Please see
corrected Example 2.
The answer I gave was still a valid particular solution. It was obtained by
using a definite integral to compute u(t) so that
u(0)=0, as explained in the bottom of page 1 of the above note.
 11.09


Remark from the TA on HW7:
I marked
all of the questions and the points are 2, 3, 3, 4, 3 and 3 correspondingly.
Some students use 0 as an eigenvector in q4 which is wrong and for the last
question some students find out the amount of the pollutant not the
concentration. Moreover, for a ODE system with repeated eigenvalue "a", we
should add a te^(at) term.
 11.18


We returned MT2 today. The average is 26.77 out of 40, i.e. 66.94%. The standard deviation is 22.64%.
 11.09


Remark from the TA on HW6:
I choose Question 1, 2, 5, 6, 7, 9
and 10. The points are 2, 2, 3, 3, 3, 2 and 3 respectively. Many students have a
problem with Question 5 and 6. For example, the f(t) is a piecewise function with
f(t)=2 when t<=2 and f(t)=t when t>=2; some students caculate the Laplace transform
on
2 and t seperately and add them up, which is wrong. The correct idea is to desrcibe
f(t) by using the unit step function u(t) and do the Laplace transform.
 11.06


Extra office hours next week for MT2: Monday Nov 9, 3:30pm5pm. (Regular office hours:
Tue 11am12:15pm, Thu 2pm3:15pm)
 11.02


Midterm Exam 2
will cover Chapters 2 and 6, except sections 2.3, 6.2.4, 6.3.3 and 6.4.4.

Remark from the TA on HW5:
I choose problem 1, 2, 3, 6, 7, 8, 9 and 10; the scores are 2,
3, 2, 3, 2, 2, 2 and 2 respectively. Most of students make a mistake when
writing a particular solution in terms of integrals in problem 3, that is,
they
use same parameters (or variables) t inside the integral, like $
y(t)=e^{2t}\int
g(t)e^{2t} dt$ instead of$ y(t)=e^{2t}\int^{t} g(s)e^{2s} ds$. And for
problem
10, many students forgot to consider the case when s=2.
 10.19


Remark from the TA on HW4:
I chose question 1, 2, 4, 5, 6, 7
and 9; the marks are 2, 2, 3, 3, 3, 3 and 2 respectively with 2 points for
completion. Most of students have difficulty in question 6 and 7, they
should notice that the reason for having 2 cases (k=1, k not equal 1)
comes
from the general solution y_c, which some students haven't calculated.
Also,
some students may feel confused about the term "general solution" in
question 9. The answer should be y_c + y_p instead of y_c.
Tsai's comment: Always find y_c first when solving nonhomogeneous problems, then
compare it with the source term.
 10.19


Remark from the TA on HW3:
I choose question 1,3,4,5,6,7 and 8. The points for
them are 2,3,2,2,3,3 and 2 respectively. And 3 points are for the completion. Most
students
have problems with question 3,7 and 8. For the question 3, students usually could find out
the characteristic function has two repeated roots 1/2, so they should try exp(1/2*x) and
x*exp(1/2*x); for question 7, students may follow the hint by trying y=x^p,then
y'(x)=p*x^(p1) and similarly for y''(x), then they could get p=2 or 2, so
y=C1*x^2+C2*x^(2); for question 8, w is angular frequency not the ordinary frequency,
hence
w=2Pi*f.
 10.16


Midterm Exam I has average 27.40/40 = 68.50% and standard deviation 18.02%.
 10.14


The final exam time has been announced to be Thursday, Dec 17, 8:30am11am.
 10.05


Remark from the TA on HW2:
I chose question 1, 3, 4, 7, 8 and 9. (Two
point for each problem, and 8 points for completeness.)
Students usually have difficulties in
forming an ODE in question 1; for the question 3 and 4, many students think that
phi(x,y) is the general solution of ODE while y(x) should be; for the question
9,
some students have problems in finding the limit by using the diagram.
 10.02


Remark from the TA on HW1:
The grading is over 20 points: Problems 13, 610 had value of 1 point each. Problems
1112 had value of 2 points each and problems 45 had value of 4 points each.
 09.01


Welcome to MATH 215/255 Section 102!
Check this page frequently regarding any announcement for the section.