MATH 300 - Advanced Boundary Value
Problems I (Winter 2020)
Time and Location
Time: TR 12:30 - 1:50 pm Room: SAB 325
Instructor
Dr. Arno Berger (CAB 683,
berger@ualberta.ca)
Office hours
TR 3:00 pm - 5:00 pm, or by appointment
Syllabus
Please see this PDF document for all relevant
details concerning MATH 300.
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,
T. Hillen, I.E. Leonhard, H. van Roessel, Partial Differential Equations,
henceforth abbreviated as [HLvR].
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 300 !!
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1
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Tue 7 Jan
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Introduction to Partial Differential Equations (PDE). Linear and quasi-linear equations.
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[HLvR] Ch. 1.
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2
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Thu 9 Jan
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Classification of linear second-order PDE: elliptic,
hyperbolic, parabolic.
Deriving the heat equation.
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[HLvR] Sec. 1.2, 1.8. |
3
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Tue 14 Jan
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Deriving the wave equation.
Side conditions and steady-state solutions.
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[HLvR] Sec. 1.3, 1.5, 1.9.
Homework 1 posted - due 28 Jan. |
4
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Thu 16 Jan
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Separation of variables - a (p)review.
Piecewise continuous and piecewise smooth functions.
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[HLvR] Sec. 1.6, 2.1. |
5
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Tue 21 Jan
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Orthogonal and orthonormal systems. Abstract Fourier series.
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[HLvR] Sec. 2.3. |
6
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Thu 23 Jan
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Properties of classical Fourier series. Example.
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[HLvR] Sec. 2.4, 2.5, 2.7. |
7
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Tue 28 Jan
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Integrating and differentiating Fourier series.
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[HLvR] Sec. 2.6.
Homework 2 posted - due 11 Feb. |
8
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Thu 30 Jan
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Fourier cosine and sine series. Gibbs phenomenon. Complex
Fourier series.
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[HLvR] Sec. 2.4, 2.8. |
9
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Tue 4 Feb
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Complex Fourier series.
Quiz #1.
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[HLvR] Sec. 2.8.
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10
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Thu 6 Feb
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Separation of variables. First examples.
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[HLvR] Sec. 3.1. |
11
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Tue 11 Feb
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Eigenfunction expansions. Outline of method. First examples.
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[HLvR] Sec. 3.1, 3.2.
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12
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Thu 13 Feb
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Eigenfunction expansions. Example and modification.
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[HLvR] Sec. 3.2. |
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Have a great Reading
Week.
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Homework 3 posted - due 10 Mar. |
13
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Tue 25 Feb
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Simplified eigenfunction expansion.
Midterm information.
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[HLvR] Sec. 3.2. Practice Midterm
posted - please have a look. |
14
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Thu 27 Feb
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Difficulties with eigenvalue problems ...
Regular Sturm-Liouville (SL) problems.
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[HLvR] Sec. 4.1. |
15
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Tue 3 Mar
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More on SL problems. The magnificent SL theorem. Examples.
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[HLvR] Sec. 4.2, 4.3. |
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Wed 4 Mar
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Special office hours:
3pm - 5pm in CAB 683.
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Thu 5 Mar
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MIDTERM TEST.
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Good luck!!
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16
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Tue 10 Mar
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Rayleigh quotient. Examples. A singular SL problem.
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[HLvR] Sec. 4.4.
Homework 4 posted - due 24 Mar. |
17
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Thu 12 Mar
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Basic definitions of Fourier Transform (FT). Examples.
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[HLvR] Sec. 8.1. |
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Remote classes start. |
18
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Tue 17 Mar
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Fourier integral (or inversion) theorem. Fourier cosine and
sine transforms.
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[HLvR] Sec. 8.1. |
19
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Thu 19 Mar
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Elementary properties of Fourier transform. Examples.
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[HLvR] Sec. 8.2. |
20
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Tue 24 Mar
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Convolution.
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[HLvR] Sec. 8.2.
Homework 5 posted - due 7 Apr.
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21
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Thu 26 Mar
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Applications of FT to (linear) PDE.
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[HLvR] Sec. 9.1. |
22
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Tue 31 Mar
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Revisiting the wave and heat equations.
Quiz #2.
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[HLvR] Sec. 9.1, 9.2.
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23
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Thu 2 Apr
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One-sided heat equation. Poisson and Laplace equations.
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[HLvR] Sec. 9.2, 9.3. |
24
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Tue 7 Apr
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Laplace equation in the upper half plane.
Final housekeeping and exam information.
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[HLvR] Sec. 9.3.
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Good bye and good luck !! |
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Thu 16 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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