The Sheet That Should Be Handed Out
The First Day Of Class
Fourier Analysis ~ Fall 2011
(revised 8/18/2011)
General Stuff
The Course(s): Introduction to Fourier Analysis, MA 460 and MA 561
Prerequisites: Reasonable performance in elementary courses on lin
ErratA
for
Principles of Fourier Analysis
( October 3 2011)
Notes:
text from the book is printed using this font (Times Roman)
Comments are printed using this font (Univers Condensed)
text to be added is underlined and in italics like this
text to be dele
Preparing for the Second Exam
The test covers everything weve done concerning the Fourier transforms, up through the
material on Gaussian functions in 23.1. For details on what we covered over that period,
look at the assigned homework from Friday 9/23 to
Preparing for the In-Class Part of the First Exam
The test covers everything weve covered up through the material on the convergence of
Fourier series in chapter 13. Reviewing the homework given up through Wednesday,
Sept. 21 may be a good idea.
Know the
Take Home Part of Test I
The Answers (Using Mathcad)
Problems I & II (combined):
The period:
p
3
The function :
First define f0(t) to be the given function for t between 0 and p, and
zero elsewhere.
f 0( t )
t if 0 t< 1
1 if 1 t< 2
3
t if 2 t< 3
0 otherwi
MA 460/561
9/21/2011
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Take Home Portion of
Test I
GENERAL NOTES:
Due at the beginning of class on Wednesday, September 28, 2011.
This is NOT to be a team effort. Do your own work! (You may, of course, consult
with the instructor.)
Combine parts A an
Table 1: A Short Table of Transforms
f (t )
F () = F [ f (t )]|
restrictions
pulse (t )
2 sinc(2 )
0<
e t step(t )
1
+ i 2
0<
e t step(t )
1
i 2
0<
e |t |
2
2 + 4 2 2
0<
2
exp 2
0<
1
()
none
e i 2 t
()
none
(t )
ei 2
none
comb (t )
1
comb 1 ()
0<
Table 1: A Very Short Table of Transforms
f (t )
F () = F [ f (t )]|
restrictions
pulse (t )
2 sinc(2 )
0<
et step(t )
1
+ i 2
0<
e |t |
et
2
2
+ 4 2 2
2
exp 2
2
0<
0<
Table 2: A Basic Table of Identities
Near-equivalance:
F 1 [(x )]| y = F [(x )]| y =
MA 460/561
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Random Notes on Using Maple
in the Homework
First of all, review how to define functions and how to graph them using the plot
command. To plot two are more functions together, enclose the functions by square
brackets [ ] when you input t
MA 460/561
Howell
Notes on Constructing Periodic Functions
in Maple and Mathcad
(With Addendums)
First of all, read any introductory tutorials that come with the product. In both
Maple and Mathcad, introductory tutorials are easily found under Help (also,
Mathcad Intro
page 1
Intro. to Mathcad
This is a very brief intro to using Mathcad (originally written in Mathcad IV) by
someone who is not an expert.
The following assumes that you have successfully opened Mathcad. Read the
commentary and see if you can
Your Maple Discount
A recommendation for this course is Maple 15 Student Edition. Because we are part of the Maple
Adoption Program, you are entitled to purchase this product at a significantly discounted price.
To purchase Maple 15
Visit the Maplesoft We
MA 460/561
9/2/2011
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Homework Very Much Like
the Take Home Portion of
Test I
GENERAL NOTES:
Due at the beginning of class on Wednesday, September 14, 2011
This is NOT to be a team effort. Do your own work! (You may, of course, consult
with the instr
MA 460/561
10/17/2011
Howell
Homework Set II
Note: All use of tables is to be limited to the tables handed out in class (available
online). Be sure that I can tell how you got your answers using those tables.
At the beginning of class on Wednesday, Octobe
MA 460/561
9/12/2011
Howell
Homework Set I
At the beginning of class on Wednesday, September 14, 2011.
Hand in your work on the Homework Very Much Like the Take Home Portion of
Test I (for 40 pts.)
At the beginning of class on Friday, September 16, 2011.
MA 460/561
9/21/2011
Howell
Bonus Points 1
On Friday, September 30, at the start of class (or earlier), turn in a list of as many
certifiable errors or typos as you can find in the text1, excluding, of course, those
already listed in the on-line Errata sh
Notes About the First Test
and Software
A Special Note about the First Test: The first test will include a take home portion in
which you will write and use a computer program to compute and graph partial
sums of Fourier series. The word program is mislea