Common webpage for Sections 101-104 of MATH 215 and MATH 255

Information for Section 102 only

Instructor: Dr. Tai-Peng Tsai, Math building room 109, phone 604-822-2591, ttsai at

Lectures: Mon Wed Fri 9am-10am, LSK 200

Office hours: Tue 11am-12:15pm, Thu 2pm-3:15pm, and by appointment (Tsai's schedule).


12.02 and 12.04
  • Final Exam: Thu Dec 17, 8:30am-11am, MATH 100.

  • Office hours during final exam weeks: Mon Wed Fri 2pm-2:30pm, 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.

  • 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.

  • 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.

  • 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.

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

  • 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.

  • Extra office hours next week for MT2: Monday Nov 9, 3:30pm-5pm. (Regular office hours: Tue 11am-12:15pm, Thu 2pm-3:15pm)

  • 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.

  • 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.

  • 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^(p-1) 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.

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

  • The final exam time has been announced to be Thursday, Dec 17, 8:30am-11am.

  • 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.

  • Remark from the TA on HW1:
    The grading is over 20 points: Problems 1-3, 6-10 had value of 1 point each. Problems 11-12 had value of 2 points each and problems 4-5 had value of 4 points each.

  • Welcome to MATH 215/255 Section 102!
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