Math 421 Applied Analysis

Fall 2007   (CRN 71517),    Ed Bueler

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:

 Schedule:  (final, version 12/22/07; mods 8/30/11)

Day

Text Chapter
Topic
Assigned or Due
F 9/7
I
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 #5not 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

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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