Dr. Neil Balmforth
COURSES
Applied PDEs
This course provides an introduction to practical analytical solution
methods for PDEs.
Anouncements:
The syllabus:
I. PDEs and canonical examples
II. Separation of variables and Fourier series
III. Eigenfunction expansions
IV. Transform methods
V. Characteristics methods
Assessment will involve coursework (homework problems) and examination.
Office hours: Wed at 2pm, Fri at 1pm
Recommended text:
R. Haberman, ``Applied PDEs''
The TA: Merlin Pelz (merlinpelz at math)
Hours in MLC: Mon 2:30-3:30, 6:00-7:00 (online),
Thurs 2:00-3:00, 5:00-6:00 (online)
Lecture notes:
I,
II,
III,
IV,
V,
VI,
VII
(Beware! These are a work in progress and may contain typos
- please let me know if you spot any)
Synopses from a previous year:
1,
2,
3,
4,
5,
6a,
6b,
7a,
7b,
8,
9,
10a,
10b,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
More lecture notes:
Laplace transforms,
Method of characteristics
Laplace transform question
From Michael Ward:
Worked problems
Notes
Assignments:
Assi 1 (due Sep 29).
By popular demand, and because I am a complete push-over, now due October 2nd.
figure (pd23a.png),
MATLAB code (pd23a)
Assi 2 (due ??; preliminary version).
figure (pd23b.png),
MATLAB code (pd23b)
Midterm: Provisional date - Oct 20
Sample 80min exams:
1,
2,
3
Older 50min midterm
Previous finals:
2018,
2019
Additional problems on traffic flow and more sample
final exam problems
Video lectures for the final few weeks of the course,
should I become mysteriously waylaid:
Laplace transforms I
(beware of a slip in this lecture - the Laplace transform of f(t)=t exp(-t) is
1/(s+1)^2)
Laplace transforms II
Method of characteristics I
Method of characteristics II
Method of characteristics III
Method of characteristics IV
Method of characteristics V
Additional relevant problems from Haberman (4th edition):
* Separation of variables and Fourier series -
2.5.3, 2.5.9, 3.4.12, 4.4.3(b)
* Halfway house (requiring Sturm-Louiville theory, but trig functions)
- Worked example of section 5.7 upto eq (5.7.11),
Physical examples of section 5.8
* Separation of variables and Bessel functions - 7.7.1 (assume r is less than
a),
7.7.3 (the frequencies of vibration are the possible values of w
in the cos(wt) and sin(wt) functions of the separation-of-variables
general solution), 7.8.2(d), 7.9.1(b), 7.9.4(a)
*
Separation of variables and Legendre functions - final example in section 7.10,
problem 7.10.2
More relevant problems from Haberman (4th edition):
* Fourier Transforms - example in Sec 10.4.1;
problems 10.4.3, 10.4.6;
example at the end of Sec 10.6.3;
problems 10.6.1(a), 10.6.18
* Laplace transforms - problems 13.4.3, 13.4.4, 13.5.3
* Characteristics - example starting with eq (12.2.13);
problems 12.2.5(b) and (d);
Sec 12.6.5; problems 12.6.3, 12.6.8, 12.6.9
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