Ed Bueler
elbueler@alaska.edu
4747693
Office: Chapman 301C ( hours)
Class times and rooms:
MWF 9:1010:10 GRUE 202
note:
starts & ends
5
minutes
early on MWF!
Tu 9:4510:45 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
89): 1aefh, 2, 3ac, 4, 5
II
(pp 5253): 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
5258): 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 REREVISED DATE!
Assignment #3:
II (pp 5862): 22, 23ac, 24, 25,
27ab
III (pp 104105): 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 105112): 9,
10a, 12, 14, 15a,
19, 20, 22a
IV (pp 144149):
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
(inclass exam; covers Schey)


T 10/18

L 1

types of PDEs;
wave equation


W 10/19 

cont.

from inclass 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 inclass 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 inclass session:
tanroots.m

M 11/14


inclass 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; spacetime 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 inclass 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 (takehome) (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 inclass 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

