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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


Instructor

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


Office hours

MWF 11:30 am - 1:00 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, 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 Mon
9
Jan 		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.
Sat
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 !!
Thu
13 Apr 		Special MATH 201 office hours:
1pm - 3pm in CAB 683.

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

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

Homework

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.