MATH 334  Introduction to Differential
Equations (Fall 2014)
Time and Location
Time: MWF 12:00  12:50 pm Room: SAB 325
Instructor
Dr. Arno Berger (CAB 683,
berger@ualberta.ca)
Office hours
MWF 2:30  4:00 pm
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.
(An abbreviated version of this document will be handed out in class.)
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

Wed 3 Sep

Introduction  What is a differential equation (DE)? What
is a solution of a DE? First examples.

[F, Ch.1]

2

Fri 5 Sep

Examples: growth/decay of a single species; free fall;
crossing a river by boat; vibrations of a long elastic string.
Ordering principles: ODE vs. PDE; order; linear vs. nonlinear;
explicit vs. implicit.

[F, Ch.1] 
3

Mon 8 Sep

Making solutions unique: Initial value problems (IVP) and
Boundary value problems (BVP). Firstorder ODE: some aspects of
Picard's Theorem.

[F, Ch.1 and 2] 
4

Wed 10 Sep

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. 
5

Fri 12 Sep

Linear firstorder equations.
Examples.

[F, Sec.2.1] 



Please review/refresh
your integration skills as needed. 
6

Mon 15 Sep

Exact equations. Examples.

[F, p.83] 
7

Wed 17 Sep

Homogeneous equations. Examples.

[F, p.43] 
8

Fri 19 Sep

Equations of the form y'=f(ax+by +c). Firstorder
equations in disguise.

[F, p.43] 
9

Mon 22 Sep

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

[F, Sec.3.12] 
10

Wed 24 Sep

Why are linearly independent solutions important?
Reduction of order.

[F, Sec 3.3]

11

Fri 26 Sep

How to solve an inhomogeneous equation.
Homogeneous equations with constant coefficients.

[F, Sec.3.46] 
12

Mon 29 Sep

Inhomogeneous equations: The Undetermined Coefficients
method.

[F, Sec.3.7] 
13

Wed 1 Oct

Inhomogeneous equations: The Variation of Parameters method.

[F, Sec.3.8] 
14

Fri 3 Oct

An important application:
Free and forced vibrations.

[F, Sec.3.10] 
15

Mon 6 Oct

Forced vibrations. Resonance.

[F, Sec.3.11] 
16

Wed 8 Oct

Linear higherorder equations.

[F, Sec.3.12.] 

Fri 10 Oct


Do not
forget: Midterm test #1. 

Mon 13 Oct

No class.

Happy Thanksgiving ! 
17

Wed 15 Oct

Examples. Euler equations.

[F, Sec.3.12] 
18

Fri 17 Oct

A quick reminder of power series.

[F, Sec.4.1] 
19

Mon 20 Oct

Solving linear ODE near ordinary points.

[F, Sec. 4.2] 
20

Wed 22 Oct

Illustrating the key idea of power series solutions.
Ordinary vs. singular points.

[F, Sec.4.2] 
21

Fri 24 Oct

Theoretical background. An analytic version of Picard's Theorem.

[F, Sec.4.3] 
22

Mon 27 Oct

Power series solutions near an ordinary point.

[F, Sec.4.3] 
23

Wed 29 Oct

Modified power series solutions near a regular singular point.

[F, Sec.4.4] 
24

Fri 31 Oct

Method of Frobenius. Example.

[F, Sec.4.4] 
25

Mon 3 Nov

Special equations and functions: Airy, Hermite, Chebyshev, ...

[F, Ex.4.2.3] 
26

Wed 5 Nov

... and Bessel.
Laplace Transform. Basic properties.

[F, Sec. 4.5, 5.1, 5.2]
An excellent online resource for special funcions.

27

Fri 7 Nov

Further properties of Laplace Transform.
Review of Partial Fraction Expansion.

[F, Sec. 5.2, 5.3] 

Mon 10 Nov

No class. (Remembrance Day Break)


28

Wed 12 Nov

Using Laplace Transform to solve IVP.

[F, Sec. 5.4] 

Fri 14 Nov


Do not
forget: Midterm test #2. 
29

Mon 17 Nov

Discontinuous and delayed signals.

[F, Sec. 5.5] 
30

Wed 19 Nov

Periodic signals.

[F, Sec. 5.6] 
31

Fri 21 Nov

Examples. Convolution and its properties.

[F, Sec. 5.8] 
32

Mon 24 Nov

Implusive forces. The Dirac delta function.

[F, Sec. 5.7] 
33

Wed 26 Nov

An introduction to systems of ODE.

[F, Sec. 6.1] 
34

Fri 28 Nov

Solving linear systems by means of eigenvalues and vectors.

[F, Sec. 6.4, 6.5] 
35

Mon 1 Dec

Solving linear systems by means of Laplace transform.

[F, Sec. 6.7] 
36

Wed 3 Dec

Examples. Final examination details.

[F, Sec. 6.7] 







Good bye and good luck !! 





Fri 12 Dec


Special MATH 334 office hours:
10am  3pm in CAB 683. 

Mon 15 Dec


Special MATH 334 office hours:
10am  3pm in CAB 683. 

Tue 16 Dec

Final exam !
Please see box on the left for details.

Good luck !! 




