MATH 201 - Differential Equations (Sections EU1 and EV1, Winter 2019)

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: CAB 243

Instructor

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

Office hours

MWF 11:30 am - 1:00 pm, or by appointment

Syllabus

A PDF document containing all you want to know about this semester's version of MATH 201 is available here.

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.E. Boyce and R.C. DiPrima, Elementary Differential Equations with Boundary Value Problems, henceforth abbreviated as [BDP].

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

Labs start 14 Jan (i.e., NEXT week!).
1 Mon 7
Jan
Introduction - What is a
Differential Equation (DE)?
[BDP] Ch. 1.

from first-year calculus, as needed.
2 Wed 9
Jan
Initial value problems (IVP) and Boundary value problems (BVP).
First order ODE.
[BDP] Sec. 2.2.
3 Fri
11 Jan
Separable equations.
Separable equations in disguise.
[BDP] Sec. 2.2.
Notes Week #1.
4 Mon 14 Jan Linear first-order equations. [BDP] Sec. 2.1.
5 Wed 16 Jan Exact equations. Integrating factors. [BDP] Sec. 2.6.
6 Fri
18 Jan
Linear second order equations. Wronski determinant. Fundamental sets of solutions. [BDP] Ch. 3.
Notes Week #2.
7 Mon 21 Jan Homogeneous linear equations with constant coefficients. [BDP] Sec. 3.1/3.
8 Wed 23 Jan Inhomogeneous linear equations with constant coefficients: Undetermined coefficients. [BDP] Sec. 3.5.
9 Fri
25 Jan
Examples. [BDP] Sec. 3.5.
Notes Week #3.
10 Mon
28 Jan
Further examples. [BDP] Sec. 3.5.
11 Wed
30 Jan
Free vibrations. [BDP] Sec. 3.7.
12 Fri
1 Feb
Forced vibrations. Resonance. [BDP] Sec. 3.8.
Notes Week #4.
13 Mon
4 Feb
Examples. [BDP] Sec. 3.8.
14 Wed
6 Feb
A brief review of power series. [BDP] Sec. 5.1.
15 Fri
8 Feb
Analytic functions. Solving linear ODE with power series. [BDP] Sec. 5.1-3.
Notes Week #5.
16 Mon
11 Feb
Ordinary and singular points. [BDP] Sec. 5.3.
17 Wed
13 Feb
Examples. Euler equations. [BDP] Sec. 5.4.
18 Fri
15 Feb
Laplace Transform. Definition and basic properties. [BDP] Sec. 6.1.
Notes Week #6.
19 Mon
25 Feb
A brief reminder of partial fractions.
20 Wed
27 Feb
Inverse Laplace transform.
[BDP] Sec. 6.1.
21 Fri
1 Mar
Solving IVPs by means of Laplace transform. [BDP] Sec. 6.2.
Notes Week #7.
22 Mon
4 Mar
Discontinuous and delayed signals. [BDP] Sec. 6.3/4.
Tue
5 Mar
MATH 201 review session with Dr. Allegretto:
5pm - 6:30pm in ETLC E1-001.
23 Wed
6 Mar
Periodic signals. [BDP] Sec. 6.3/4.
Thu
7 Mar
MATH 201 review session with Dr. Allegretto:
5pm - 6:30pm in ETLC E1-001.
24 Fri
8 Mar
Periodic signals. Convolution. [BDP] Sec. 6.6.
Notes Week #8.
Sat
9 Mar
Midterm test !

Please see box on the left for details.
Good luck !!
25 Mon
11 Mar
Applications of convolution. [BDP] Sec. 6.6.
26 Wed
13 Mar
Impulses. Dirac delta function. [BDP] Sec. 6.5.
27 Fri
15 Mar
Systems of linear differential equations. [BDP] Ch. 7.
Notes Week #9.
28 Mon
18 Mar
Partial Differential Equations (PDE). Introductory remarks. [BDP] Ch. 10.
29 Wed
20 Mar
Boundary value problems for ODE (eigenvalue problems). [BDP] Sec. 11.1.
30 Fri
22 Mar
Examples of eigenvalue problems. [BDP] Sec. 11.1.
Notes Week #10.
31 Mon
25 Mar
An introduction to Fourier series. [BDP] Sec. 10.2.
32 Wed
27 Mar
More on Fourier series. Examples. [BDP] Sec. 10.3.
33 Fri
29 Mar
Fourier cosine and sine series. Examples. [BDP] Sec. 10.4.
Notes Week #11.
34 Mon
1 Apr
The separation of variables method for the heat equation. [BDP] Sec. 10.5.
35 Wed
3 Apr
Examples. Variations of the method. [BDP] Sec. 10.6.
Please consider completing the online MATH 201 course survey. It only takes a few minutes. Thank you.
36 Fri
5 Apr
Examples. The wave equation. [BDP] Sec. 10.6/10.7.
Notes Week #12.
37 Mon
8 Apr
The separation of variables method for the wave equation. [BDP] Sec. 10.7.

Final Exam Review session with Dr. Allegretto
5pm - ??pm in Tory Lec 11.
Tue
9 Apr
Special MATH 201 study session 4:30pm - 7:30pm in CAB 528.
38 Wed
10 Apr
D'Alembert's form of the solution.
Final exam information.
[BDP] Sec. 10.7.

Final Exam Review session with Dr. Allegretto
5pm - ??pm in Tory Lec 11.
Notes Week #13.
Good bye and good luck !!
Fri
11 Apr
Special MATH 201 office hours:
10am - 12pm in CAB 683.

Final exam !

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

Midterm test

The midterm test will be held on Saturday, March 9th, 2019 at 2:00 pm. You will write the midterm in ETLC E1-013 (Section EU1) or ETLC E1-017 (Section EV1).

• 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.
• 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 welcoming MATH 201 students preparing for the midterm; see here for details.

Two MATH 201 review sessions will be held by retired math professor Dr. Allegretto on Tuesday and Thursday (March 5 and 7) at 5:00-6:30pm in ETLC E1-001. This is an excellent opportunity to get your last-minute questions answered, so you should make an effort to attend.

Midterm test average: 75.65%

Solutions have been posted on eClass.

Final exam

The final exam will be held on Friday, April 12th, 2019, at 2:00 pm in the Main Gym (Van Vliet building).

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.

The Decima Robinson Support Centre in CAB 528 is running a dedicated MATH 201 study session on Tuesday (April 9) between 4:30-7:30pm.

Two MATH 201 Final Exam review sessions will be held by retired math professor Dr. Allegretto on Monday and Wednesday (April 8 and 10) at 5:00-6:30pm in Tory Lec 11. This is an excellent opportunity to get your last-minute questions answered, so you should make an effort to attend.

Other material

A free textbook that covers the material of MATH 201 (and much more) is W.F. Trench, Elementary Differential Equations with Boundary Value Problems; it contains LOTS of practice problems and is available here.

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.