MATH 201 - Differential Equations
(Section EB1, Fall 2017)

Time and Location

Time: MWF 12:00 - 12:50 pm
Room: NRE 2-001


Dr. Arno Berger (CAB 683,

Office hours

MWF 2:00 pm - 3:30 pm, or by appointment


Please see this PDF document for all relevant details concerning MATH 201.

Material covered in class (Course Diary)

I plan to keep an up-to-date list of the topics, examples etc. covered in class. Unless stated otherwise, reference numbers refer to our textbook, W. F. Trench, Elementary Differential Equations with Boundary Value Problems, henceforth abbreviated as [T], which is freely available here.

Lecture # Date Material covered / special events Remarks/ additional material
MATH 201 !!

1 Wed
Introduction - What is a Differential Equation (DE)? [T] Ch. 1.
Please review the material from first-year calculus, as needed.
2 Fri
8 Sep
Initial value problems (IVP) and Boundary value problems (BVP).
First order ODE.
[T] Sec. 2.2.
      Notes Week #1.
3 Mon
11 Sep
Separable equations.
Separable equations in disguise.
[T] Sec. 2.2, 2.4.
4 Wed
13 Sep
Linear first-order equations. [T] Sec. 2.1.
5 Fri
15 Sep
Exact equations. Integrating factors. [T] Sec. 2.5, 2.6.
      Notes Week #2.
6 Mon
18 Sep
Linear second order equations. Wronski determinant. Fundamental sets of solutions. [T] Sec. 5.1.
7 Wed
20 Sep
Homogeneous linear equations with constant coefficients. [T] Sec. 5.2.
8 Fri
22 Sep
Inhomogeneous linear equations with constant coefficients: Undetermined coefficients. [T] Sec. 5.3 - 5.5.
      Notes Week #3.
9 Mon
25 Sep
Variation of parameters. [T] Sec. 5.7.
10 Wed
27 Sep
Further examples. [T] Sec. 5.7.
11 Fri
29 Sep
Free and forced vibrations. Resonance. [T] Sec. 6.1/6.2.

Two nice YouTube videos on the topic of resonances:

Tacoma Bridge Collapse.
Wine Glass Resonance.
      Notes Week #4.
12 Mon
2 Oct
Examples. [T] Sec. 6.1/6.2.
13 Wed
4 Oct
A brief review of power series. [T] Sec. 7.1.
14 Fri
6 Oct
Analytic functions. Solving linear ODE with power series. [T] Sec. 7.2/7.3.
      Notes Week #5.
9 Oct
No class. Happy Thanksgiving!
15 Wed
11 Oct
Ordinary and singular points. [T] Sec. 7.2/7.3.
16 Fri
13 Oct
Examples. Euler equations. [T] Sec. 7.2 - 7.4.
      Notes Week #6.
17 Mon
16 Oct
Laplace Transform. Definition and basic properties. [T] Sec. 8.1.
18 Wed
18 Oct
A brief reminder of partial fractions.  
19 Fri
20 Oct
Inverse Laplace transform.
[T] Sec. 8.2.
      Notes Week #7.
21 Oct
Midterm test !

Please see box on the left for details.
Good luck !!
20 Mon
23 Oct
Solving IVPs by means of Laplace transform. [T] Sec. 8.3.
21 Wed
25 Oct
Discontinuous and delayed signals. [T] Sec. 8.4/8.5.
22 Fri
27 Oct
Periodic signals. [T] Sec. 8.4/8.5.
      Notes Week #8.
23 Mon
30 Oct
Convolution. [T] Sec. 8.6.
24 Wed
1 Nov
Applications of convolution. Impulses. [T] Sec. 8.6/8.7.
25 Fri
3 Nov
Dirac delta function. [T] Sec. 8.7.
      Notes Week #9.
26 Mon
6 Nov
Systems of linear differential equations. [T] Ch. 10.
27 Wed
8 Nov
Partial Differential Equations (PDE). Introductory remarks. [T] Ch. 12.
28 Fri
10 Nov
Boundary value problems for ODE (eigenvalue problems). [T] Sec. 11.1.
      Notes Week #10.
  Have a great Reading Week.  
29 Mon
20 Nov
Examples of eigenvalue problems. [T] Sec. 11.1.
30 Wed
22 Nov
An introduction to Fourier series. [T] Sec. 11.2.
31 Fri
24 Nov
More on Fourier series. Examples. [T] Sec. 11.2.
      Notes Week #11.
32 Mon
27 Nov
Fourier cosine and sine series. [T] Sec. 11.3.
33 Wed
29 Nov
The separation of variables method for the heat equation. [T] Sec. 12.1.
    Please consider completing the online MATH 201 course survey. It only takes a few minutes. Thank you.
34 Fri
1 Dec
Examples. Variations of the method. [T] Sec. 12.1.
      Notes Week #12.
35 Mon
4 Dec
Examples. The wave equation. [T] Sec. 12.1/12.2.
36 Wed
6 Dec
The separation of variables method for the wave equation. [T] Sec. 12.2.
37 Fri
8 Dec
D'Alembert's form of the solution.
Final exam information.
[T] Sec. 12.2.

Extended MATH 201 office hours:
2pm - 5pm in CAB 683.

      Notes Week #13.
Good bye and good luck !!
11 Dec
Special MATH 201 office hours:
2pm - 5pm in CAB 683.

MATH 201 review session:
6pm - ?pm in CCIS L1-140.
11 Dec
Final exam !

Please see box on the left for details.
Good luck !!


Throughout the semester a total of six homework assignments; please see the course information for further details.

Three words about cheating:

    Don't Do It !!

Midterm test

The midterm test will be held on Saturday, October 21st, 2017 at 1:00 pm. You will write the midterm in
NRE 1-001 (last names A-K) or NRE 1-003 (last names L-Z).

Some details about the midterm:

  • Duration: 90 minutes.
  • Material covered: Up to, and including, power series solutions of linear differential equations, i.e., Chapters I to IV in class.
  • Some questions may be multiple choice.
  • NO calculators, formula sheets etc.!
  • NO cell-phones, i-pods, or other electronics!
  • Please bring a valid ID with you.
  • Three MATH 201 midterms from previous years have been posted on eClass. Please look at them carefully.
  • Good luck!

Midterm test average: 55.7%

Solutions have been posted on eClass.

Final exam

The final exam will be held on Tuesday, December 12th, 2017 at 2:00 pm in the Main Gym (Van Vliet building).

The following rows have been reserved for you (section EB1):

  • 1,3, and 5.

Please make sure you are seated in one of the correct rows.

Some details concerning the final:

  • Duration: 120 minutes.
  • Material covered: Basically everything covered in class after the midterm test, i.e., Chapters V (Laplace transform) and VI (PDE, including eigenvalue problems and Fourier series).
  • A table of Laplace transform will be provided (and is available on eClass beforehand).
  • NO calculators, formula sheets etc.!
  • NO cell-phones, i-pods, or other electronics!
  • Please bring a valid ID with you.
  • Good luck!

A few sample finals have been posted on eClass. Please review them carefully. This year's exam will be very similar.

Other material

Need help? The Decima Robinson Support Centre in CAB 528 offers free drop-in help sessions, Monday to Friday, 9:00 am to 3:00 pm. It's a great, friendly place, though quite busy at times.