MATH 201 - Differential Equations
(Sections EU1 and EV1, Winter 2017)

Time and Location

Section EU1

Time: MWF 10:00 - 10:50 am
Room: CAB 243

Section EV1

Time: MWF 2:00 - 2:50 pm
Room: ETLC E1-007


Dr. Arno Berger (CAB 683,

Office hours

MWF 11:30 am - 1:00 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 Mon
Introduction - What is a Differential Equation (DE)? [T] Ch. 1.
Please review the material from first-year calculus, as needed.
2 Wed
11 Jan
Initial value problems (IVP) and Boundary value problems (BVP).
First order ODE.
[T] Sec. 2.2.
3 Fri
13 Jan
Separable equations.
Separable equations in disguise.
[T] Sec. 2.4.
      Notes Week #1.
4 Mon
16 Jan
Linear first-order equations. [T] Sec. 2.1.
5 Wed
18 Jan
Exact equations. Integrating factors. [T] Sec. 2.5, 2.6.
6 Fri
20 Jan
Linear second order equations. Wronski determinant. Fundamental sets of solutions. [T] Sec. 5.1.
      Notes Week #2.
7 Mon
23 Jan
Homogeneous linear equations with constant coefficients. [T] Sec. 5.2.
8 Wed
25 Jan
Inhomogeneous linear equations with constant coefficients: Undetermined coefficients. [T] Sec. 5.3 - 5.5.
9 Fri
27 Jan
Variation of parameters. [T] Sec. 5.7.
      Notes Week #3.
10 Mon
30 Jan
Further examples. [T] Sec. 5.7.
11 Wed
1 Feb
Free vibrations. [T] Sec. 6.1/6.2.
12 Fri
3 Feb
Forced vibrations. Resonance. [T] Sec. 6.1/6.2.
      Notes Week #4.
13 Mon
6 Feb
Examples. [T] Sec. 6.1/6.2.
14 Wed
8 Feb
A brief review of power series. [T] Sec. 7.1.
15 Fri
10 Feb
Analytic functions. Solving linear ODE with power series. [T] Sec. 7.2/7.3.
      Notes Week #5.
16 Mon
13 Feb
Ordinary and singular points. [T] Sec. 7.2/7.3.
17 Wed
15 Feb
Examples. Euler equations. [T] Sec. 7.2 - 7.4.
18 Fri
17 Feb
Laplace Transform. Definition and basic properties. [T] Sec. 8.1.
      Notes Week #6.
  Have a great Reading Week.  
19 Mon
27 Feb
A brief reminder of partial fractions.  
20 Wed
1 Mar
Inverse Laplace transform.
[T] Sec. 8.2.
21 Fri
3 Mar
Solving IVPs by means of Laplace transform. [T] Sec. 8.3.
      Notes Week #7.
22 Mon
6 Mar
Discontinuous and delayed signals. [T] Sec. 8.4/8.5.
23 Wed
8 Mar
Periodic signals. [T] Sec. 8.4/8.5.
24 Fri
10 Mar
Periodic signals. Convolution. [T] Sec. 8.6.
      Notes Week #8.
11 Mar
Midterm test !

Please see box on the left for details.
Good luck !!
25 Mon
13 Mar
Applications of convolution. [T] Sec. 8.6.
26 Wed
15 Mar
Impulses. Dirac delta function. [T] Sec. 8.7.
27 Fri
17 Mar
Systems of linear differential equations.  
      Notes Week #9.
28 Mon
20 Mar
Partial Differential Equations (PDE). Introductory remarks. [T] Ch. 12.
29 Wed
22 Mar
Boundary value problems for ODE (eigenvalue problems). [T] Sec. 11.1.
30 Fri
24 Mar
Examples of eigenvalue problems. [T] Sec. 11.1.
      Notes Week #10.
31 Mon
27 Mar
An introduction to Fourier series. [T] Sec. 11.2.
32 Wed
29 Mar
More on Fourier series. Examples. [T] Sec. 11.2.
33 Fri
31 Mar
Fourier cosine and sine series. [T] Sec. 11.3.
      Notes Week #11.
34 Mon
3 Apr
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.
35 Wed
5 Apr
Examples. Variations of the method. [T] Sec. 12.1.
36 Fri
7 Apr
Examples. The wave equation. [T] Sec. 12.1/12.2.
      Notes Week #12.
37 Mon
10 Apr
The separation of variables method for the wave equation. [T] Sec. 12.2.
38 Wed
12 Apr
D'Alembert's form of the solution.
Final exam information.
[T] Sec. 12.2.
      Notes Week #13.
Good bye and good luck !!
13 Apr
Special MATH 201 office hours:
1pm - 3pm in CAB 683.

Special MATH 201 study session 3pm - 6pm in CAB 528.
18 Apr
Special MATH 201 office hours:
10am - 12pm in CAB 683.
18 Apr
Final exam !

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


Throughout the semester a total of four homework assignments will be administered through Crowdmark. You will receive all relevant information by email, but are welcome to check here for a heads-up.

Three words about cheating:

    Don't Do It !!

Midterm test

The midterm test will be held on Saturday, March 11th, 2017 at 10:00 am. Please see this document for relevant information.

You will write the midterm in ETLC E1-013 (Section EU1) or ETLC E1-017 (Section EV1).

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.
  • NO calculators, formula sheets etc.!
  • NO cell-phones, i-pods, or other electronics!
  • Please bring a valid ID with you.
  • Several MATH 201 midterms from previous years have been posted on eClass. Please look at them carefully.
  • Good luck!

The Decima Robinson Support Centre in CAB 528 is running specific MATH 201 Midterm Review Sessions between 4:00 pm and 7:00 pm on Thursday, March 9th; see here for details.

Midterm test average: 68.9%

Solutions have been posted on eClass.

Final exam

The final exam will be held on Tuesday, April 18th, 2017 at 2:00 pm in the Main Gym (Van Vliet building).

The following rows have been reserved for you (sections EU1 and EV1):

  • 1,2,3,4, 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 has been posted on eClass. Please review them carefully.

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.