Ed Bueler: ffelb@uaf.edu, x7693
Office: Chapman 301C ( Hours)
Class times and rooms:
MWF 9:15--10:15 GRUE 202
Tu
9:45--10:45 GRUE 409
Texts:
- Schey, Div, Grad, Curl and
All That, 4th edition
Norton 2005
- Farlow, Partial
Differential Equations for Scientists and Engineers, Dover 1993
Link to Syllabus Here
Parts of course
- Vector calculus (Div,
Grad, Curl, and
Laplacian)
- Boundary value
problems for partial differential equations, separation of variables,
and Fourier series
ON RESERVE IN RASMUSSEN (24 hour checkout):
- Brown and Churchill, Fourier
Series
and Boundary Value Problems
LINKS:
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Schedule: (final, version 12/22/07; mods 8/30/11)
Day
|
Text Chapter
|
Topic
|
Assigned or Due
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F 9/7
|
I
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introduction,
syllabus, electric fields (as example)
|
Assignment #1:
I (pp 8--9):
1aefh, 2, 3ac, 4, 5
II (pp 52--53):
1abe, 2, 4ac, 5ac
|
M 9/10
|
I |
vector
fields, overview of calc III |
|
T 9/11
|
II |
surfaces,
normal vectors
|
|
W 9/12
|
II |
surface
integrals |
Assignment #2:
II (pp 53--58): 7, 8, 10ab, 11,
13ab, 14abeg, 16b, 17, 19, 20, 22
|
F 9/14
|
II |
surface
integrals, cont. |
A #1 Due
|
M 9/17
|
II |
flux,
Gauss' law
|
|
T 9/18
|
II |
cont
|
|
W 9/19
|
II |
divergence, and
in other coordinates
|
|
F 9/21
|
II |
cont. |
A #2 Due |
M 9/24
|
II
|
divergence
theorem |
A #2 Due
(revised date)
|
T 9/25
|
II
|
cont.
|
Assignment
#3:
II (pp 58--62): 23ac, 24, 25, 28ab
III (pp 104--105):
2, 3abch, 4ab, 6 |
W 9/26
|
III
|
line
integrals, path
independence
|
|
F 9/28
|
III
|
cont
|
|
M 10/1
|
III
|
curl and
curl
in other coords |
A #3 Due |
T 10/2
|
III
|
cont. |
A #3 Due (revised date)
|
W 10/3
|
III
|
Stoke's
theorem |
Assignment
#4:
III (pp 105--112): 8, 10a, 12, 14,
15ab, 17, 19, 20, 22, 26 |
F 10/5
|
III |
cont.
|
|
M 10/8
|
III |
Ampere's
law |
|
T 10/9
|
III
|
path
independence
|
|
W 10/10
|
III
|
cont
|
Assignment
#5: not due! (but
covered on exam)
IV (pp 144--149): 1, 2acdg, 3, 4a,
5, 9, 10, 11, 12, 14, 15 |
F 10/12
|
IV |
gradients
and
potentials |
A #4 Due
|
M 10/15
|
IV |
Laplace
eqn,
finding potentials |
|
T 10/16
|
IV |
directional
derivatives,
gradients in coordinates |
|
W 10/17
|
Review
|
review
and
problems from IV |
|
F 10/19
|
Exam
|
DivGradCurl
Exam
|
|
M 10/22
|
Lessons
1,2
|
types
of
PDEs; a
easy PDE; Newton's law of cooling
|
|
T 10/23
|
Lesson
2
|
heat
equation
|
|
W 10/24
|
Lesson
3
|
cont
|
Assignment
#6:
Lesson 1 (p 8): 2, 3, 4, 5
Lesson 2 (p
17): 1, 2, 3
Lesson 3 (p
26): 1
|
F 10/26
|
Lesson
4
|
cont
|
|
M 10/29
|
L
5
|
separation
of
variables and Fourier sine series
|
Assignment
#7:
Lesson 3 (p 26): 4
Lesson 5 (p
41-42): 1, 2, 3, 4, 5
Lesson 6 (p
47-48): 1, 2
[note L6 #1 moved to
A#8]
|
T 10/30
|
L
5
cont
|
|
plotheat.m
(a
Matlab program to graph solutions of Lesson 5 exercises 3,4,6)
|
W 10/31
|
review
|
review
of
series and ODEs |
A #6 Due
|
F 11/2
|
L
6
|
transform
nonhomogeneous
BCs
|
|
M 11/5
|
L6,
L7
|
cont
|
A #7 Due
Assignment
#8:
Lesson
6 (p
47-48): 1 (not graded!)
Lesson 7 (p
56-57): 4, 3, 2
Lesson 8 (p
61-62): 1, 2
|
T 11/6
|
L
7
|
harder
eigenfunction
problems
|
A #7 Due [REVISED
DATE]
|
W 11/7
|
L
8
|
more
transformations
|
xEQtanx.m
(a
Matlab program to solve -x = tan x) |
F 11/9
|
L9
|
cont;
eigenfunction
expansions
|
|
M 11/12
|
L
9
|
cont
|
A #8 Due
|
T 11/13
|
L
20
|
vibrating
string
|
|
W 11/14
|
|
cont;
review
for
exam
|
|
F 11/16
|
Exam
|
Midterm
Exam
(on PDEs)
|
|
M 11/19
|
lecture
|
orthogonal series and classical
Fourier series
|
Assignment
#9:
A#9 (PDF)
also: plotabssin.m
(Matlab to plot |sin(x)| and Fourier approximations)
|
T 11/20
|
lecture
|
cont.
|
|
W 11/21
|
lecture
|
cont.
|
|
F 11/23
|
no class
|
no class
|
|
M 11/26
|
HANDOUT
|
convergence
of
Fourier series |
|
T 11/27
|
HANDOUT
|
proof
of
Dirichlet's Theorem |
Assignment
#10:
A#10 (PDF)
and
notes on the
Riemann-Lebesque lemma
|
W 11/28
|
L
11
|
Fourier
series
vs. transforms; spectrum
|
A #9 Due
Regarding the Dirichlet kernel:
plotDN.m, corrected
plot
of D10(u), corrected plot of D50(u)
|
F 11/30
|
L
11
|
F.
transforms
|
|
M 12/3
|
|
|
how
to
get the Fourier Transform by rescaling Fourier series |
T 12/4
|
L
11,
L 12
|
F.
transforms,
cont.
|
|
W 12/5
|
L
12
|
solution
to
heat equation by F. transforms and convolution
|
A #10 Due
|
F 12/7
|
L
12
|
crustal
deformation
by F. transform
|
FINAL (PDF) |
M 12/10
|
L
17
|
D'Alembert's
solution
|
|
T 12/11
|
L
18
|
cont
|
|
W 12/12
|
L
30
|
vibrating
drum
head
|
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F 12/14
|
|
cont
|
|
WED 12/19
|
FINAL
|
TAKE
HOME
FINAL
DUE NOON
|
FINAL (PDF)
included Matlab codes:
beameig.m,
membraneNo3.m, ageEarth.m
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