Dr. Neil Balmforth
COURSES
Applied PDEs
This course provides an introduction to practical analytical solution
methods for PDEs.
Anouncements:
Assignments:
I with solution
II with solution
III with solution
IV (due March 31)
V (due April 12)
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.
Provisional breakdown (to be discussed): Coursework: 25%; Midterm: 25%; Final: 50%
Provisional office hours: Tu at 11am, Th at 1pm
Recommended text:
R. Haberman, ``Applied PDEs''
The TA:
Peilin Wu (peilinwu - at - math.ubc.ca)
Office hours: Wed 2pm-4pm, AUDX 125.
In addition, Peilin will be in the MLC Monday 12:00 - 15:00 and 16:00 - 17:00
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
Midterm: March 3rd, Actual exam and solution
Sample 80min exams:
1,
2,
3
Older 50min midterm
Another midterm and its solution
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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