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 #
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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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Tue 5 Jan
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Introduction - What is a differential equation (DE)? What
is a solution of a DE? First examples: growth/decay of a single species; free fall.
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[F, Ch.1]
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2
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Thu 7 Jan
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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).
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[F, Ch.1] |
3
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Tue 12 Jan
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First-order ODE: some aspects of
Picard's Theorem. Examples of separable equations. Logistic growth.
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[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. |
4
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Thu 14 Jan
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Linear first-order equations.
Examples.
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[F, Sec.2.1] |
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Please review/refresh
your integration skills as needed. |
5
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Tue 19 Jan
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Exact equations. Examples. Homogeneous equations.
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[F, p.83] |
6
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Thu 21 Jan
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Equations of the form y'=f(ax+by +c). First-order
equations in disguise.
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[F, p.43] |
7
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Tue 26 Jan
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Linear second-order equations. Basic concepts:
principle of superposition, linear (in)dependence, Wronski determinant.
|
[F, Sec.3.1-2] |
8
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Thu 28 Jan
|
Why are linearly independent solutions important?
Reduction of order.
QUIZ 1 - please see eClass for details.
|
[F, Sec 3.3]
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9
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Tue 2 Feb
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How to solve an inhomogeneous equation.
Homogeneous equations with constant coefficients.
|
[F, Sec.3.4-6] |
10
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Thu 4 Feb
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Inhomogeneous equations: The Undetermined Coefficients
method.
|
[F, Sec.3.7] |
11
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Tue 9 Feb
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Inhomogeneous equations: The Variation of Parameters
method. Free vibrations.
|
[F, Sec.3.8/10] |
12
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Thu 11 Feb
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Forced vibrations. Resonance.
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[F, Sec.3.11]
Tacoma Bridge Collapse (YouTube).
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Have a great Reading
Week. |
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Want to be a mentor ... ? If yes, please see here.
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13
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Tue 23 Feb
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Linear higher-order equations.
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[F, Sec.3.12.] |
14
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Thu 25 Feb
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Laplace Transform. Basic properties and examples.
|
[F, Sec.5.1, 5.2]
|
15
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Tue 1 Mar
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Further properties of Laplace Transform.
Review of Partial Fraction Expansion.
|
[F, Sec. 5.2, 5.3] |
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Thu 3 Mar
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Do not
forget: Midterm test. |
16
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Tue 8 Mar
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Using Laplace Transform to solve IVP.
|
[F, Sec. 5.4] |
17
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Thu 10 Mar
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Discontinuous, delayed, and periodic signals.
|
[F, Sec. 5.5, 5.6] |
18
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Tue 15 Mar
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Examples. Convolution and its properties.
|
[F, Sec. 5.8] |
19
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Thu 17 Mar
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Implusive forces. The Dirac delta function.
|
[F, Sec. 5.7] |
20
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Tue 22 Mar
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Solving linear systems by means of Laplace transform.
|
[F, Sec. 6.7] |
21
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Thu 24 Mar
|
A quick reminder of power series.
QUIZ 2 - please see eClass for details.
|
[F, Sec.4.1] |
22
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Tue 29 Mar
|
Solving linear ODE near ordinary points.
|
[F, Sec. 4.2] |
23
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Thu 31 Mar
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Modified power series solutions near a regular singular point.
|
[F, Sec.4.4] |
24
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Tue 5 Apr
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Method of Frobenius. Example.
|
[F, Sec.4.4] |
25
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Thu 7 Apr
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Another example: Bessel's equation. Some final housekeeping.
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[F, Sec.4.5] |
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Good bye and good luck !! |
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Wed 13 Apr
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Special MATH 334 office hours:
11am - 3pm in CAB 683. |
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Thu 14 Apr
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Special MATH 334 office hours:
11am - 3pm in CAB 683. |
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Fri 15 Apr
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Final exam !
Please see box on the left for details.
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Good luck !! |
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