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).


  • 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.

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