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


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 - 3:30 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, 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
    WELCOME TO
MATH 201 !!
1 Wed
6
Sep 		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.
Mon
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.
Sat
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 !!
Mon
11 Dec 		Special MATH 201 office hours:
2pm - 5pm in CAB 683.

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

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

Homework

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.