MATH 201 - Differential Equations (Section EB1, Fall 2019)

Time and Location

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

Instructor

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

Office hours

MWF 2:00 pm - 4:00 pm, or by appointment

Syllabus

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, R.K. Nagle, E.B. Saff, and A.D. Snider, Fundamentals of Differential Equations, henceforth abbreviated as [NSS].

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

Labs start NEXT week!

1 Wed
4
Sep
Introduction - What is a Differential Equation (DE)? [NSS] Ch. 1.
Please review the material from first-year calculus, as needed.
2 Fri
6 Sep
Initial value problems (IVP) and Boundary value problems (BVP).
First order ODE.
[NSS] Sec. 2.2.
Notes Week #1.
3 Mon
9 Sep
Separable equations.
Separable equations in disguise.
[NSS] Sec. 2.2, 2.6.
4 Wed
11 Sep
Linear first-order equations. [NSS] Sec. 2.3.
5 Fri
13 Sep
Exact equations. [NSS] Sec. 2.4.
Notes Week #2.
6 Mon
16 Sep
Linear second order equations. Wronski determinant. Fundamental sets of solutions. [NSS] Sec. 4.2, 4.7.
7 Wed
18 Sep
Homogeneous linear equations with constant coefficients. [NSS] Sec. 4.2, 4.3
8 Fri
20 Sep
Inhomogeneous linear equations with constant coefficients: Undetermined coefficients. [NSS] Sec. 4.4 - 4.6.
Notes Week #3.
9 Mon
23 Sep
Examples. [NSS] Sec. 4.5.
10 Wed
25 Sep
Variation of parameters. [NSS] Sec. 4.6.
11 Fri
27 Sep
Further examples. [NSS] Sec. 4.6, 4.7.
Notes Week #4.
12 Mon
30 Sep
Free and forced vibrations. [NSS] Sec. 4.9/4.10.
13 Wed
2 Oct
Resonance. Examples. [NSS] Sec. 4.10.
14 Fri
4 Oct
Euler equations. [NSS] Sec. 4.7.
Notes Week #5.
Sat
5 Oct
First midterm test !

Please see box on the left for details.
Good luck !!
15 Mon
7 Oct
Laplace Transform. Definition and basic properties. [NSS] Sec. 7.2/7.3.
16 Wed
9 Oct
A brief reminder of partial fractions.
17 Fri
11 Oct
Inverse Laplace transform.
[NSS] Sec. 7.4/7.5.
Notes Week #6.
Mon
14 Oct
No class. Happy Thanksgiving!
18 Wed
16 Oct
Solving IVPs using Laplace transform. [NSS] Sec. 7.5.
19 Fri
18 Oct
Unit step functions. Delayed signals. [NSS] Sec. 7.6.
Notes Week #7.
20 Mon
21 Oct
Convolution. [NSS] Sec. 7.8.
21 Wed
23 Oct
Applications of convolution. Impulses. [NSS] Sec. 7.8/7.9.
22 Fri
25 Oct
Dirac delta function. [NSS] Sec. 7.9.
Notes Week #8.
23 Mon
28 Oct
Systems of linear ODE. [NSS] Sec. 7.10.
24 Wed
30 Oct
A brief review of power series. [NSS] Sec. 8.2.
Thu
31 Oct
MATH 201 midterm review session:
at 5pm - 6:30pm
in CCIS 1-440.
25 Fri
1 Nov
Analytic functions. Solving linear ODE with power series. [NSS] Sec. 8.2 - 8.4.
Notes Week #9.
Sat
2 Nov
Second midterm test !

Please see box on the left for details.
Good luck !!
26 Mon
4 Nov
Examples of power series solutions of linear ODE. [NSS] Sec. 8.4.
27 Wed
6 Nov
Partial Differential Equations (PDE). Introductory remarks. [NSS] Ch. 10.
28 Fri
8 Nov
Boundary value problems for ODE (eigenvalue problems). [NSS] Sec. 10.2.
Notes Week #10.
29 Mon
18 Nov
Examples of eigenvalue problems. [NSS] Sec. 10.2.
30 Wed
20 Nov
An introduction to Fourier series. [NSS] Sec. 10.3.
31 Fri
22 Nov
More on Fourier series. Examples. [NSS] Sec. 10.3/10.4.
Notes Week #11.
32 Mon
25 Nov
The separation of variables method for the heat equation. [NSS] Sec. 10.5.
33 Wed
27 Nov
Examples. Variations of the method. [NSS] Sec. 10.5.
Please consider completing the online MATH 201 course survey. It only takes a few minutes. Thank you.
34 Fri
29 Nov
Further examples. [NSS] Sec. 10.5.
Notes Week #12.
35 Mon
2 Dec
The wave equation. The separation of variables method for the wave equation. [NSS] Sec. 10.6.
36 Wed
4 Dec
D'Alembert's form of the solution. [NSS] Sec. 10.6.
37 Fri
6 Dec
Examples.
Final housekeeping and exam information.
[NSS] Sec. 10.6.
Notes Week #13.
Good bye and good luck !!
Thu
12 Dec
MATH 201 review session:
6pm - 7:30pm in CCIS L2-200.
Fri
13 Dec
MATH 201 open house:
10am - 3pm in CAB 683.
Sat
14 Dec
Final exam !

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

Homework

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

Please submit your completed assignments into the MATH 201 assignment box on the third floor of CAB that has you lab instructor's name on it. The due date and time are indicated on each assignment problem sheet.

Midterm tests

The first midterm test will be held on Saturday, October 5th, 2019 at 1:00 pm. You will write the midterm in
ETLC 1-003 (last names A-S) or ETLC 1-007 (last names T-Z).

• Duration: 90 minutes.
• Material covered: Up to, and including, free vibrations (details announced 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.
• Sample MATH 201 midterms from previous years have been posted on eClass. Please look at them carefully.
• Good luck!

First midterm test average: 69.5%

Solutions for midterm I have been posted on eClass.

The second midterm test will be held on Saturday, November 2nd, 2019 at 1:00 pm. You will write the midterm in
ETLC 1-003 (last names A-S) or ETLC 1-007 (last names T-Z).

• Duration: 90 minutes.
• Material covered: Up to, and including, impulses/Dirac delta functions (details announced in class).
• Same format and procedures as on the first midterm !
• Sample MATH 201 midterms from previous years have been posted on eClass. Please look at them carefully.
• Good luck!

Second midterm test average: 74.0%

Solutions for midterm II have been posted on eClass.

Final exam

The final exam will be held on Saturday, December 13th, 2019 at 9:00 am in the Main Gym (Van Vliet building).

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

• 1,3,5, and 7.

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, but with a strong emphasis on material covered after the second midterm test, i.e., linear systems, Chapters V (power series solutions) 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.

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.