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MATH 300 - Advanced Boundary Value Problems I
(Fall 2021)


Time and Location

Time: MWF 1:00 - 1:50 pm
Room: ETLC E1-017


Instructor

Dr. Arno Berger (CAB 683, berger@ualberta.ca)


Office hours

MWF 3:00 pm - 5:00 pm or by appointment


Syllabus

NOTE: All information on this site also is available from the official course site on eClass.

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 the recommended (though not formally required) 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
    WELCOME TO
MATH 300 !!
1 Wed
1
Sep 		Introduction to Partial Differential Equations (PDE).
Linear and quasi-linear equations. 		[HLvR] Ch. 1.
2 Fri
3
Sep 		Classification of linear second-order PDE: elliptic, hyperbolic, parabolic. [HLvR] Sec. 1.2.
Mon
6
Sep 		No class. Happy Labour Day!
3 Wed
8
Sep 		Deriving the heat and wave equations.
Side conditions and steady-state solutions. 		[HLvR] Sec. 1.3, 1.5, 1.9.
4 Fri
10
Sep 		Side conditions and steady-state solutions. Examples. [HLvR] Sec. 1.3, 1.5.
5 Mon
13
Sep 		Separation of variables - a (p)review.
Piecewise continuous and piecewise smooth functions. 		[HLvR] Sec. 1.6, 2.1.
6 Wed
15
Sep 		Orthogonal and orthonormal systems. Abstract Fourier series. [HLvR] Sec. 2.3.
7 Fri
17
Sep 		Review of abstract Fourier series. Examples. [HLvR] Sec. 2.3.
(class on zoom)
8 Mon
20
Sep 		Integrating Fourier series. [HLvR] Sec. 2.6.
9 Wed
22
Sep 		Differentiating Fourier series. [HLvR] Sec. 2.6.
10 Fri
24
Sep 		Fourier cosine and sine series. Gibbs phenomenon. [HLvR] Sec. 2.4, 2.8.
11 Mon
27
Sep 		Complex Fourier series. [HLvR] Sec. 2.8.
12 Wed
29
Sep 		Separation of variables. First examples. [HLvR] Sec. 3.1.
13 Fri
1
Oct 		Eigenfunction expansions. Outline of method. First examples. [HLvR] Sec. 3.1, 3.2.
14 Mon
4
Oct 		Eigenfunction expansions. Further examples. [HLvR] Sec. 3.2.
15 Wed
6
Oct 		Eigenfunction expansions. Modificatios and simplifications. [HLvR] Sec. 3.2.
16 Fri
8
Oct 		Eigenfunction expansions. Even more examples. [HLvR] Sec. 3.2.
Mon
11 Oct 		No class. Happy Thanksgiving!
17 Wed
13
Oct 		Simplified eigenfunction expansion.

Midterm information. 		[HLvR] Sec. 3.2.

Practice Midterm I posted on eClass - please have a look.
18 Fri
15
Oct 		Limitations of the eigenfunctions expansion method. [HLvR] Sec. 4.1.
19 Mon
18
Oct 		Regular Sturm-Liouville (SL) problems. The magnificent SL theorem. Examples. [HLvR] Sec. 4.2, 4.3.
Wed
20
Oct 		MIDTERM TEST 1. Good luck!!

Model solutions posted on eClass.
20 Fri
22
Oct 		Rayleigh quotient. Examples. [HLvR] Sec. 4.4.
21 Mon
25
Oct 		Two singular SL problems. Motivating the Fourier Transform (FT).
 [HLvR] Sec. 4.4, 8.1.
22 Wed
27
Oct 		Basic definitions of Fourier Transform. Examples.
[HLvR] Sec. 8.1.
23 Fri
29
Oct 		Fourier integral (or inversion) theorem. Fourier cosine and sine transforms. [HLvR] Sec. 8.1.
24 Mon
1
Nov 		Elementary properties of Fourier transform. Examples. [HLvR] Sec. 8.2.
25 Wed
3
Nov 		Convolution. [HLvR] Sec. 8.2.
26 Fri
5
Nov 		Applications of convolution. The error function. [HLvR] Sec. 8.2, 9.2.
  Have a great Reading Week.  
27 Mon
15
Nov 		Applying Fourier Transform to PDE. First Examples. [HLvR] Sec. 9.1.
28 Wed
17
Nov 		Fourier Tansform for the wave and heat equations. [HLvR] Sec. 9.1, 9.2.
29 Fri
19
Nov 		More on the heat equation. [HLvR] Sec. 9.2.
30 Mon
22
Nov 		Poisson and Laplace equations. [HLvR] Sec. 6.1, 9.3.
Wed
24
Nov 		MIDTERM TEST 2. Good luck!!

Model solutions posted on eClass.
31 Fri
26
Nov 		Poisson equation on a rectangle. Engineering interpretation. [HLvR] Sec. 5.4, 9.3.
    Please consider completing the online MATH 300 course survey. It only takes a few minutes. Thank you.
32 Mon
29
Nov 		Laplace equation in the upper half plane. Examples. [HLvR] Sec. 9.3.
33 Wed
1
Dec 		More examples. Deriving the Poisson integral formula again. [HLvR] Sec. 9.3.
34 Fri
3
Dec 		Laplace equation in an infinite strip. [HLvR] Sec. 9.3.
35 Mon
6
Dec 		General observations regarding Poisson integral formulae.
Final housekeeping. 		[HLvR] Sec. 9.3.
Good bye and good luck !!
Mon
13 Dec 		Pre-exam "open house":
10am - 3pm in CAB 683 and on zoom - please use the sign-up sheet on eClass.
Tue
14 Dec 		Final exam !
2-4pm in ETLC E1-017
(our usual classroom)

Please see information on eClass for details. 		Good luck !!
       

Homework

Throughout the semester a total of five homework assignments will be posted on eClass and announced in class, as appropriate. Assignments are due on Wednesday, at 6 pm. Please submit your work to Assign2 via eClass.

Three words about cheating:

    Don't Do It !!

Midterm tests

The midterm tests will be held on Wednesday, 20 October 2021 and on Wednesday, 24 November 2021 at 1:00 pm (in class). Details regarding both tests will be announced in class and on eClass.

Final exam

The final exam is scheduled for Tuesday, 14 December 2021, at 2:00 pm. Details will be announced in class and on eClass.

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.