# MATH 201 - Differential Equations (Section EB1, Fall 2015)

## Time and Location

Time: MWF 12:00 - 12:50 pm
Room: N-RE 2-001

## Instructor

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

## Office hours

MWF 4:15 - 6:00 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. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems (10th ed.), henceforth abbreviated as [BDP].

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

1 Wed
2
Sep
Introduction - What is a Differential Equation (DE)? Please review the material from first-year calculus, as needed.
2 Fri
4 Sep
Initial value problems (IVP) and Boundary value problems (BVP).
First order ODE. Separable equations.
[BDP] Sec. 2.2.
Notes Week #1.
Mon
7 Sep
No class - Labour Day.
3 Wed
9 Sep
Separable equations in disguise. [BDP] Sec. 2.2.
The MATH 201 homework has gone live, and your first assignment of homework is waiting for you, see the box on the left for details.
4 Fri
11 Sep
Linear first-order equations. [BDP] Sec. 2.1.
Notes Week #2.
5 Mon
14 Sep
Exact equations. [BDP] Sec. 2.6.
6 Wed
16 Sep
Linear second order equations. Wronski determinant. Fundamental sets of solutions. [BDP] Sec. 3.2.
7 Fri
18 Sep
Homogeneous linear equations with constant coefficients. [BDP] Sec. 3.1/3.3/3.4.
Notes Week #3.
8 Mon
21 Sep
Inhomogeneous linear equations with constant coefficients: Undetermined coefficients. [BDP] Sec. 3.5.
9 Wed
23 Sep
Variation of parameters. [BDP] Sec. 3.6.
10 Fri
25 Sep
Further examples. [BDP] Sec. 3.5/3.6.
Notes Week #4.
11 Mon
28 Sep
Free and forced vibrations. [BDP] Sec. 3.7/3.8.
12 Wed
30 Sep
Examples. [BDP] Sec. 3.7/3.8.
13 Fri
2 Oct
A brief review of power series. [BDP] Sec. 5.1.
Notes Week #5.
14 Mon
5 Oct
Basic facts about power series. Analytic functions. [BDP] Sec. 5.1.
15 Wed
7 Oct
Ordinary and singular points. [BDP] Sec. 5.2/5.3.
16 Fri
9 Oct
Examples. [BDP] Sec. 5.2/5.3.
Notes Week #6.
Mon
12 Oct
No class. Happy Thanksgiving !
17 Wed
14 Oct
Euler equations. [BDP] Sec. 5.4.
18 Fri
16 Oct
Laplace Transform. Definition and basic properties. [BDP] Sec. 6.1.
Notes Week #7.
19 Mon
19 Oct
A brief reminder of partial fractions.
20 Wed
21 Oct
Inverse Laplace transform.
[BDP] Sec. 6.2.
Thu
22 Oct
Do not forget:
Midterm review session, 5-7 pm in CCIS L2-190.
21 Fri
23 Oct
Solving IVPs by means of Laplace transform. [BDP] Sec. 6.2.
Notes Week #8.
Sat
24 Oct
Midterm test !

Please see box on the left for details.
Good luck !!
22 Mon
26 Oct
Discontinuous and delayed signals. [BDP] Sec. 6.3/6.4.
23 Wed
28 Oct
Periodic signals. [BDP] Sec. 6.3/6.4.

Midterm test returned -
please see box on the left.
24 Fri
30 Oct
Periodic signals. Convolution. [BDP] Sec. 6.4/6.6.
Notes Week #9.
25 Mon
2 Nov
Applications of convolution. [BDP] Sec. 6.6.
26 Wed
4 Nov
Impulses. Dirac delta function. [BDP] Sec. 6.5.
27 Fri
6 Nov
Systems of linear differential equations.
Notes Week #10.

28 Mon
16 Nov
Partial Differential Equations (PDEs). Introductory remarks. [BDP] Ch. 10.
29 Wed
18 Nov
Boundary value problems for ODEs (eigenvalue problems). [BDP] Sec. 10.1.
30 Fri
20 Nov
Examples of eigenvalue problems. [BDP] Sec. 10.1.
Notes Week #11.
31 Mon
23 Nov
An introduction to Fourier series. [BDP] Sec. 10.2.
32 Wed
25 Nov
More on Fourier series. Examples. [BDP] Sec. 10.3.
33 Fri
27 Nov
Fourier cosine and sine series. [BDP] Sec. 10.4.
Notes Week #12.
34 Mon
30 Nov
The separation of variables method. [BDP] Sec. 10.5.
Please consider completing the online MATH 201 course survey. It only takes a few minutes. Thank you.
35 Wed
2 Dec
Examples. Variations of the method. [BDP] Sec. 10.6.
36 Fri
4 Dec
Examples. [BDP] Sec. 10.6.
Notes Week #13.
37 Mon
7 Dec
Example with heat sources.
Final exam information.
[BDP] Sec. 10.6.
Notes Week #14.
Good bye and good luck !!
Wed
9 Dec
Do not forget:
Final review session, 4-6 pm in ETLC 1-003.
Fri
18 Dec
Special MATH 201 office hours:
10am - 3pm in CAB 683.
Sat
19 Dec
Final exam !

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

#### Homework

Homework problems are being posted weekly on WileyPLUS.

Please see this YouTube video, especially if you haven't used WileyPLUS before. Please note that our section is EB1. Correspondingly, our class section URL is edugen.wileyplus.com/
edugen/class/cls471866/.

Note: There is a free online access to WileyPLUS provided by the University on campus. This no-cost option is sufficient to complete the homework assignments for Math 201. However, it can be accessed only from these designated computer labs on campus, and it does not allow usage of any other online Wiley study tools.

#### Midterm test

The midterm test will be held on Saturday, October 24th, 2015 at 1:00 pm. You will write the midterm in N-RE 2-001 (our usual class room; last names A - K) or N-RE 2-003 (last names L - Z).

A midterm review session will be held for all sections on Thursday, 22 Oct, 5-7 pm in CCIS L2-190. Please make an effort to attend!
The material for this review session can be found here.

Need some practice material? The following is taken from last year's midterm: Midterm test 2014.

Some of you have asked for additional practice material for homogeneous and Bernoulli equations. You may want to check out this for Bernoulli equations; for homogeneous equations, try this and this (the latter also has some other substitutions).

• 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.
• Good luck!

The Math and Applied Sciences Centre is also offering a review session.

#### Midterm test - Solutions

Solutions have been posted on eClass.

#### Final exam

The final exam will be held on Saturday, December 19th, 2015 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, but with a strong emphasis on the material covered in class after the midterm test.
• A table of Laplace transform will be provided (from [BDP]).
• NO calculators, formula sheets etc.!
• NO cell-phones, i-pods, or other electronics!
• Please bring a valid ID with you.
• Good luck!

A review session will be held for all sections on Wednesday, 9 Dec, 4:00-6:00pm in ETLC 1-003. Please make an effort to attend!
The material for this review session can be found here and here.

#### 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.

Your integration skills are a bit rusty? The Math and Applied Sciences Centre is running a Review of Integration Techniques.

The Math and Applied Sciences Centre is offering a Midterm Review.

The Math and Applied Sciences Centre is offering a Final Exam Review.