MATH 300 - Advanced Boundary Value Problems I
(Winter 2020)

Time and Location

Time: TR 12:30 - 1:50 pm
Room: SAB 325


Dr. Arno Berger (CAB 683,

Office hours

TR 3:00 pm - 5:00 pm, or by appointment


Please see this PDF document for all relevant details concerning MATH 300.

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, T. Hillen, I.E. Leonhard, H. van Roessel, Partial Differential Equations, henceforth abbreviated as [HLvR].

Lecture # Date Material covered / special events Remarks/ additional material
MATH 300 !!

1 Tue
Introduction to Partial Differential Equations (PDE).
Linear and quasi-linear equations.
[HLvR] Ch. 1.
2 Thu
9 Jan
Classification of linear second-order PDE: elliptic, hyperbolic, parabolic.
Deriving the heat equation.
[HLvR] Sec. 1.2, 1.8.
3 Tue
14 Jan
Deriving the wave equation.
Side conditions and steady-state solutions.
[HLvR] Sec. 1.3, 1.5, 1.9.

Homework 1 posted - due 28 Jan.
4 Thu
16 Jan
Separation of variables - a (p)review.
Piecewise continuous and piecewise smooth functions.
[HLvR] Sec. 1.6, 2.1.
5 Tue
21 Jan
Orthogonal and orthonormal systems. Abstract Fourier series. [HLvR] Sec. 2.3.
6 Thu
23 Jan
Properties of classical Fourier series. Example. [HLvR] Sec. 2.4, 2.5, 2.7.
7 Tue
28 Jan
Integrating and differentiating Fourier series. [HLvR] Sec. 2.6.

Homework 2 posted - due 11 Feb.
8 Thu
30 Jan
Fourier cosine and sine series. Gibbs phenomenon. Complex Fourier series. [HLvR] Sec. 2.4, 2.8.
9 Tue
4 Feb
Complex Fourier series.

Quiz #1.
[HLvR] Sec. 2.8.
10 Thu
6 Feb
Separation of variables. First examples. [HLvR] Sec. 3.1.
11 Tue
11 Feb
Eigenfunction expansions. Outline of method. First examples. [HLvR] Sec. 3.1, 3.2.
12 Thu
13 Feb
Eigenfunction expansions. Example and modification. [HLvR] Sec. 3.2.
  Have a great Reading Week.  

Homework 3 posted - due 10 Mar.
13 Tue
25 Feb
Simplified eigenfunction expansion.

Midterm information.
[HLvR] Sec. 3.2.

Practice Midterm posted - please have a look.
14 Thu
27 Feb
Difficulties with eigenvalue problems ...
Regular Sturm-Liouville (SL) problems.
[HLvR] Sec. 4.1.
15 Tue
3 Mar
More on SL problems. The magnificent SL theorem. Examples. [HLvR] Sec. 4.2, 4.3.
4 Mar
Special office hours:
3pm - 5pm in CAB 683.
MIDTERM TEST. Good luck!!
16 Tue
10 Mar
Rayleigh quotient. Examples. A singular SL problem. [HLvR] Sec. 4.4.

Homework 4 posted - due 24 Mar.
17 Thu
12 Mar
Basic definitions of Fourier Transform (FT). Examples.
[HLvR] Sec. 8.1.
Remote classes start.
18 Tue
17 Mar
Fourier integral (or inversion) theorem. Fourier cosine and sine transforms. [HLvR] Sec. 8.1.
19 Thu
19 Mar
Elementary properties of Fourier transform. Examples. [HLvR] Sec. 8.2.
20 Tue
24 Mar
Convolution. [HLvR] Sec. 8.2.

Homework 5 posted - due 7 Apr.
21 Thu
26 Mar
Applications of FT to (linear) PDE. [HLvR] Sec. 9.1.
22 Tue
31 Mar
Revisiting the wave and heat equations.

Quiz #2.
[HLvR] Sec. 9.1, 9.2.
23 Thu
2 Apr
One-sided heat equation. Poisson and Laplace equations. [HLvR] Sec. 9.2, 9.3.
24 Tue
7 Apr
Laplace equation in the upper half plane.
Final housekeeping and exam information.
[HLvR] Sec. 9.3.
Good bye and good luck !!
16 Apr
Final exam !

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


Throughout the semester a total of five homework assignments will be posted on eClass.

Three words about cheating:

    Don't Do It !!

Midterm test

The midterm test will be held on Thursday, March 5th, 2020 at 12:30 pm (in class).

Some details about the midterm:

  • Duration: 80 minutes.
  • Material covered: Up to, and including, Example III.8 (simplified eigenfunction expansion method) in class.
  • All problems on the current homework (#3) are relevant, and it is strongly recommended that you at least have a look at them prior to the test.
  • Some questions will be multiple-choice.
  • NO calculators, formula sheets etc.!
  • NO cell-phones, i-pods, or other electronics!
  • Please bring a valid ID with you.
  • A practice MATH 300 midterm can be found on eClass. Please look at it carefully, as the true midterm test will be very similar.
  • In case you need further practice material, chapters 2 and 3 of our textbook [HLvR] contain many worked examples; see also the problems listed on the last page of either chapter.
  • Good luck!

Midterm test average: 62%

Solutions and statistics for the midterm have been posted on eClass.

Final exam

The final exam will be organized as a 24hr take-home exam, ending on Thursday, April 16th, 2020, at 11:00 am.

Some details regarding the final:

  • Problem sheet posted on eClass at 11:00 am on Wednesday, April 15th.
  • Your work has to be submitted to Crowdmark no later than 11:00 am on Thursday, April 16th.
  • The exam covers the entire course.
  • Relevant resources: class notes (posted on eClass); assignments and solutions (also on eClass); chapters 1-4, 8, 9 in the textbook [HLvR].
  • Good luck!

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.