# MATH 334 - Introduction to Differential Equations (Winter 2016)

## Time and Location

Time: TR 11:00 - 12:20 pm
Room: CAB 243

## Instructor

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

## Office hours

TWR 1:30 - 3:00 pm or by appointment

## Textbook

Stanley J. Farlow, An Introduction to Differential Equations and their Applications, Dover 2006.

You can obtain a copy of this inexpensive textbook from the University bookstore, the Dover website and many online bookstores. Despite being a great text, Farlow's book does contain a number of typos and misprints; if you spot one that is not listed here, you may want to report it (to your instructor, the errata website, or both).

## Syllabus

Please see this PDF document for all relevant details concerning MATH 334.

## 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, S. Farlow An Introduction to Differential Equations and their Applications, henceforth referred to as [F].

Lecture # Date Material covered / special events Remarks/ additional material
WELCOME TO
MATH 334 !!

1 Tue
5
Jan
Introduction - What is a differential equation (DE)? What is a solution of a DE? First examples: growth/decay of a single species; free fall. [F, Ch.1]
2 Thu
7 Jan
More examples: crossing a river by boat; vibrations of a long elastic string.
Ordering principles: ODE vs. PDE; order; linear vs. nonlinear.
Making solutions unique: Initial value problems (IVP) and Boundary value problems (BVP).
[F, Ch.1]
3 Tue
12 Jan
First-order ODE: some aspects of Picard's Theorem.
Examples of separable equations. Logistic growth.
[F, Sec.2.2]
Your first assignment of MATH 334 homework is waiting for you, see the box on the left for details.
4 Thu
14 Jan
Linear first-order equations.
Examples.
[F, Sec.2.1]
Please review/refresh your integration skills as needed.
5 Tue
19 Jan
Exact equations. Examples. Homogeneous equations. [F, p.83]
6 Thu
21 Jan
Equations of the form y'=f(ax+by +c).
First-order equations in disguise.
[F, p.43]
7 Tue
26 Jan
Linear second-order equations.
Basic concepts: principle of superposition, linear (in)dependence, Wronski determinant.
[F, Sec.3.1-2]
8 Thu
28 Jan
Why are linearly independent solutions important?
Reduction of order.

QUIZ 1 - please see eClass for details.
[F, Sec 3.3]
9 Tue
2 Feb
How to solve an inhomogeneous equation.
Homogeneous equations with constant coefficients.
[F, Sec.3.4-6]
10 Thu
4 Feb
Inhomogeneous equations:
The Undetermined Coefficients method.
[F, Sec.3.7]
11 Tue
9 Feb
Inhomogeneous equations:
The Variation of Parameters method.
Free vibrations.
[F, Sec.3.8/10]
12 Thu
11 Feb
Forced vibrations. Resonance. [F, Sec.3.11]

Tacoma Bridge Collapse (YouTube).
Have a great Reading Week.
Want to be a mentor ... ?
If yes, please see here.

13 Tue
23 Feb
Linear higher-order equations. [F, Sec.3.12.]
14 Thu
25 Feb
Laplace Transform. Basic properties and examples. [F, Sec.5.1, 5.2]
15 Tue
1 Mar
Further properties of Laplace Transform.
Review of Partial Fraction Expansion.
[F, Sec. 5.2, 5.3]
Thu
3 Mar
Do not forget:
Midterm test.
16 Tue
8 Mar
Using Laplace Transform to solve IVP. [F, Sec. 5.4]
17 Thu
10 Mar
Discontinuous, delayed, and periodic signals. [F, Sec. 5.5, 5.6]
18 Tue
15 Mar
Examples. Convolution and its properties. [F, Sec. 5.8]
19 Thu
17 Mar
Implusive forces. The Dirac delta function. [F, Sec. 5.7]
20 Tue
22 Mar
Solving linear systems by means of Laplace transform. [F, Sec. 6.7]
21 Thu
24 Mar
A quick reminder of power series.

QUIZ 2 - please see eClass for details.
[F, Sec.4.1]
22 Tue
29 Mar
Solving linear ODE near ordinary points. [F, Sec. 4.2]
23 Thu
31 Mar
Modified power series solutions near a regular singular point. [F, Sec.4.4]
24 Tue
5 Apr
Method of Frobenius.
Example.
[F, Sec.4.4]
25 Thu
7 Apr
Another example: Bessel's equation.
Some final housekeeping.
[F, Sec.4.5]
Good bye and good luck !!
Wed
13 Apr
Special MATH 334 office hours:
11am - 3pm in CAB 683.
Thu
14 Apr
Special MATH 334 office hours:
11am - 3pm in CAB 683.
Fri
15 Apr
Final exam !

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

#### Homework

Weekly homework assignments will be posted on eClass. Unless stated otherwise, the deadline for homework submission is 4:00 pm on Thursday. Please submit your solutions into the designated MATH 334 assignment box on the third floor of CAB.

While eClass is down ...

#### Quizzes and Midterm test

There will be two quizzes during the semester. These will be multiple-choice quizzes of about 40 minutes duration, held in class, on Thursday, January 28, 2016, and on Thursday, March 24, 2016. In addition, one midterm test will be held in class, on Thursday, March 3, 2016. More details concerning these examinations will be announced in class and on this website.

Some details about the midterm:

• Duration: 80 minutes.
• Material covered: up to, and including linear higher-order ODE (i.e., all of chapter III).
• NO textbooks, notes, calculators, formula sheets etc.!
• NO cell-phones, i-pods, or other electronics!
• Please bring a valid ID with you.
• Good luck!

To help you prepare for the midterm test, a practice version has been posted on eClass. The real test will be very similar.

#### Midterm test average: 32.39 (of 50), i.e. about 64.8%

The results have been posted on eClass.

#### Final exam

The final exam will be held on Friday, April 15, 2016 at 9:00 am, in ETLC E1-013.

Some details concerning the final:

• Duration: 120 minutes.
• Material covered: Everything after the midterm, i.e., Laplace transform and series methods
(chapters IV and V).
• NO calculators!
• NO cell-phones, i-pods, or other electronics!
• A table of Laplace transforms will be provided.
• Please bring a valid ID with you.
• Good luck!

To help you prepare for the final exam, a practice version has been posted on eClass. The real exam will be very similar.