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 uptodate 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

Firstorder 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 firstorder 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). Firstorder
equations in disguise.

[F, p.43] 
7

Tue 26 Jan

Linear secondorder equations. Basic concepts:
principle of superposition, linear (in)dependence, Wronski determinant.

[F, Sec.3.12] 
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.3.46] 
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 higherorder 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 !! 




