Ed Bueler
elbueler@alaska.edu
474-7693
Office: Chapman 301C ( hours)
Class times and rooms:
MWF 9:10--10:10 GRUE 202
note:
starts & ends
5
minutes
early on MWF!
Tu 9:45--10:45 CHAP 106
Texts:
- Schey,
Div, Grad, Curl and All That, 4th edition Norton 2005
- Farlow,
Partial Differential Equations for Scientists and
Engineers, Dover 1993
Syllabus Here
Prior course: Math 421 Fall 2007
Two Parts
of Course:
- from Schey: vector calculus (=
surface integrals, div, line integrals, curl, laplacian,
potentials, grad, directional derivatives)
- from Farlow: boundary value
problems for partial differential equations, separation
of variables, and Fourier series
LINKS:
|
Schedule: (version
12/18/11 FINAL)
Day
|
Text Chapter
|
Topic
|
Assigned or Due
|
F
9/2
|
I
|
introduction
vector functions (fields)
|
Assignment #1:
I (pp
8--9): 1aefh, 2, 3ac, 4, 5
II
(pp 52--53): 1abe, 2
|
M 9/5
|
|
no
class: Labor Day
|
|
T 9/6
|
I |
electric fields (as
example)
|
|
W
9/7
|
II
|
cont; surfaces
|
|
F
9/9
|
II |
unit normal vector
fields
|
A #1 Due
|
M
9/12
|
II |
cont
|
A #1 Due
Assignment #2:
II (pp
52--58): 4ac, 5ac, 8, 10ab,
11,
13ab,
14abeg,
16b,
17,
19, 20
|
T
9/13
|
II |
surface integrals
|
|
W
9/14
|
II |
Gauss' law; flux |
|
F
9/16
|
II |
cont
|
|
M 9/19
|
II
|
divergence |
|
T 9/20
|
II
|
div in other
coordinates |
A #2 Due |
W 9/21
|
II
|
divergence
theorem |
A
#2 Due |
F 9/23
|
III
|
cont.
|
A #2 Due RE-REVISED DATE!
Assignment #3:
II (pp 58--62): 22, 23ac, 24, 25,
27ab
III (pp 104--105): 2, 3abch, 4ab,
6, 7
|
M 9/26
|
III
|
line
integrals
path independence
(Bueler away; subst.)
|
|
T 9/27
|
III
|
curl
curl in other coords
(Bueler away; subst.)
|
|
W 9/28
|
III
|
cont.
(Bueler away; subst.)
|
|
F 9/30
|
II |
divergence
thm cont
|
|
M 10/3
|
II
|
cont.
|
|
T 10/4
|
III
|
line integrals, curl
|
|
W 10/5
|
III
|
cont; curl in cylindrical |
Assignment
#4:
III (pp 105--112): 9,
10a, 12, 14, 15a,
19, 20, 22a
IV (pp 144--149):
1a, 1bc, 2acdg, 3, 4a,
8,
9, 10, 15
|
F 10/7
|
III |
Stoke's theorem |
A
#3 Due |
M 10/10
|
III |
cont
|
|
T 10/11
|
IV |
path independence; gradients;
potentials |
|
W 10/12
|
IV |
Laplace eqn
finding potentials |
A #4 Due |
F 10/14
|
Review |
review;
problems from IV |
A
#4 Due (REVISED DATE)
(make
yourself a copy of what you turn in; I will distribute
solutions immediately)
|
M 10/17
|
Exam
|
Vector calculus Exam
(in-class exam; covers Schey)
|
|
T 10/18
|
L 1
|
types of PDEs;
wave equation
|
|
| W 10/19 |
|
cont.
|
from in-class session:
wavemovie.m
|
| F 10/21 |
|
cont
|
Assignment
#5 (PDF)
|
| M 10/24 |
L 2
|
heat equation
|
|
| T 10/25 |
L 3, L 4
|
derivation of heat eqn
|
|
| W 10/26 |
|
cont
|
|
| F 10/28 |
L 5
|
separation of variables
Fourier sine series |
A #5 Due |
M 10/31
|
|
cont; variation |
A
#5 Due
from in-class session:
showexpheat.m
|
| T 11/1 |
review
|
review of trig integrals |
Assignment
#6:
Lesson 4: 2
Lesson 5: 3, 4, 5
Lesson 6: 2, 3
Lesson 7: 1, 2
|
| W 11/2 |
L 6
|
nonhomogeneous BCs
|
|
| F 11/4 |
L6
|
cont
|
|
| M 11/7 |
review
|
review of ODEs
|
|
| T 11/8 |
L 7 |
new eigenfunction problems |
A #6 Due |
| W 11/9 |
L 7
|
cont
|
|
F 11/11
|
L 8 |
more transformations |
A
#6 Due
Midterm Exam
from in-class session:
tanroots.m
|
M 11/14
|
|
in-class work: start A#7 in public
|
Assignment
#7 (PDF)
|
T 11/15
|
L 9
|
eigenfunction expansions |
|
W 11/16
|
|
cont
review for exam |
A
#7 Due |
F 11/18
|
Exam
|
Midterm Exam (on PDEs; in class exam)
|
Midterm Exam |
| M 11/21 |
L 20 |
vibrating string |
|
| T 11/22 |
L16, L17, L18
|
cont.;
recalling D'Alembert's solution; space-time diagram
|
Assignment
#8 (PDF) |
| W 11/23 |
L11 |
Fourier Series
|
|
| F 11/25 |
|
no class:
Thanksgiving break |
|
| M 11/28 |
|
cont.
|
|
T 11/29
|
|
frequency spectrum and complex Fourier series
|
from in-class session:
showfourier.m
the "applet" I showed in class:
www.falstad.com/fourier/
|
W 11/30
|
|
Fourier transform |
A
#8 Due
Assignment #9 (PDF)
|
F 12/2
|
|
cont
|
|
M 12/5
|
L 12 |
solution to heat equation by F. transforms and
convolution |
|
T 12/6
|
|
cont |
FINAL
EXAM (take-home) (PDF) |
W 12/7
|
L 31
|
Laplacian; in polar coordinates
|
A
#9 Due |
F 12/9
|
L 33
|
Dirichlet problem on a disc
|
|
M 12/12
|
L 30 |
cont; vibrating drum head |
last day of instruction
note on E1(b)&(c) on Final
Exam (PDF)
from in-class session:
bidisc.m
|
Thursday
12/15
(revised)
|
FINAL
|
TAKE HOME FINAL
DUE at 5pm
|
TAKE HOME FINAL
DUE at 5pm in my office
box (Chapman 101)
solutions to Final
Exam (PDF)
from these solns:
compareheat.m
squaredrums.m
|
|