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 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 #
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Date
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Material covered / special events
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Remarks/ additional material
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WELCOME TO MATH 334 !!
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1
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Wed 3 Sep
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Introduction - What is a differential equation (DE)? What
is a solution of a DE? First examples.
|
[F, Ch.1]
|
2
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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
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Mon 8 Sep
|
Making solutions unique: Initial value problems (IVP) and
Boundary value problems (BVP). First-order ODE: some aspects of
Picard's Theorem.
|
[F, Ch.1 and 2] |
4
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Wed 10 Sep
|
Examples of separable equations. Logistic growth.
|
[F, Sec.2.2] |
|
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Your first assignment of MATH 334 homework is waiting for you, see the box on
the left for details. |
5
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Fri 12 Sep
|
Linear first-order 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
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Wed 17 Sep
|
Homogeneous equations. Examples.
|
[F, p.43] |
8
|
Fri 19 Sep
|
Equations of the form y'=f(ax+by +c). First-order
equations in disguise.
|
[F, p.43] |
9
|
Mon 22 Sep
|
Linear second-order equations. Basic concepts:
principle of superposition, linear (in)dependence, Wronski determinant.
|
[F, Sec.3.1-2] |
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.3.4-6] |
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 higher-order 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] |
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Good bye and good luck !! |
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Fri 12 Dec
|
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Special MATH 334 office hours:
10am - 3pm in CAB 683. |
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Mon 15 Dec
|
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Special MATH 334 office hours:
10am - 3pm in CAB 683. |
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Tue 16 Dec
|
Final exam !
Please see box on the left for details.
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Good luck !! |
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