MAT
129 Fourier Analysis
Syllabus Page (Spring 2008)
Course:
MAT
129-001: Fourier Analysis
CRN: 66646
Time: MWF
11:00am-11:50am, PHYGEO 140
Instructor:
Linh Lieu
Office:
2113 Math. Sci. Bldg.
Email:
llieu@math.ucdavis.edu
Office
Hours: MW 1pm-2:30pm or by appointment
TA : Dueck, Pierre
Office:
3123 Math. Sci. Bldg.
Prerequisite:
* MAT 21D (basic understanding of vector
calculus)
* MAT 22A or 67 (basic understanding of linear
algebra)
* MAT 22B (basic understanding of ordinary
differential equations)
* MAT 25 or formerly 127A or consent of
instructor (basic understanding of introductory analysis)
Textbook:
* Required Text: G. B. Folland:
Fourier Analysis and Its Applications,
Brooks/Cole,
1992. Errata can be downloaded from http://www.math.washington.edu/~folland/Homepage/index.html
(look for the appropriate printings of your textbook).
* Texts that may be used as References:
H. Dym
and H.
P. McKean: Fourier Series and Integrals,
Academic
Press, 1972.
T. W. Körner:
Fourier Analysis, Cambridge Univ. Press,
1988.
E. M.
Stein and R. Shakarchi: Fourier Analysis,
Princeton Univ. Press, 2003.
J. S. Walker: Fourier Analysis,
Oxford Univ. Press, 1988.
Coverage:
* We will cover the following sections of the
textbook: 1st week: Chap.1, Sec.2.1, 2.2: Fourier series of a periodic
function; A convergence theorem
* 2nd week: Sec.2.3, 2.4, 2.6: Derivatives,
integrals, and uniform convergence; Fourier series on intervals;
Remarks
including the Gibbs phenomenon
* 3rd week: Sec.3.1-3.3: Othogonal
sets of functions;Inner products;
Convergence and
completeness
* 4th Week: Sec.3.4, 3.5: L2 spaces; Regular
Sturm-Liouville problems
* 5th Week: Sec.4.1-4.3: Some boundary value
problems; 1D heat flow and wave motion
* 6th Week: Sec.4.4, 4.5: The Dirichlet
problem; Multiple Fourier series;
* 7th Week: Sec.7.1,7.2:
The Fourier transform; Convolution
* 8th Week: Sec.7.3: Applications of Fourier
transforms
* 9th Week: Sec.7.5; Other
applications, The Fourier transform of sevaral
variables; Various applications
* 10th Week: Other applications; will choose
from Sec. 2.5, 6.1-6.2; Sec.6.6; Sec.7.4; Sec.7.6; Sec.8.1-8.3, i.e.,
Fourier
series and boundary value problems; Orthogonal Polynomials; Haar
and Walsh functions; Fourier transforms and Sturm-Liouville
problems; Laplace transform and its inversion, etc.
Attendance:
Formal attendance will
not be
taken. However, this is a small class, and your attendance (or lack
thereof)
will be noted as the quarter progresses. Whether you are able to attend
class
or not, you are responsible for all material presented in class as well
as any
work that may be due. LATE HOMEWORK IS
NEVER ACCEPTED. While I will try to post class announcements via
email or
on the class web pages, it is your responsibility to find out what
happened if
you miss class.
Class Web
Page:
I will maintain the
Web pages
for this course. All homework assignments and important announcements
will be
posted on these pages. Please check these pages regularly.
You can
access the
MAT 129 Home Page at http://www.math.ucdavis.edu/~llieu/courses/MAT129/index.html.
Grading
Scheme:
* 30% Homework
* 30% Midterm Exam (in class, tentatively
scheduled for Wednesday, May 7, 2008)
* 40% Final Exam (10:30am-12:30pm,
Thursday, June 12, 2008)
Final grade will be
assigned
based on the whole class distribution.
Homework:
I will assign homework
problems after each lecture, which can be seen at Homework Page. The
due date
of each homework is on the Wednesdays, beginning on Wednesday April 9.
I will collect the homework in the beginning of
each
lecture. LATE HOMEWORK WILL NOT BE
ACCEPTED. All homework must be accurate, legible, and logical. You
must
show your work. The reader has explicit instructions to penalize you
severely
if your work cannot be followed. Getting the correct answer is only
part of the
problem. Your homeworks
will be graded based on two criteria: completeness and correctness. A
subset of
the assigned problems will be graded for correctness. I will drop one
lowest
homework score when computing your grade.
Note: This is a 4
unit course! In practical terms, that means you are expected to
work 3
hours at home for each hour of lecture. In other words, expect to have
9 to 10
hours of homework each week.
Exams:
* There will be one midterm and a final
examination. The midterm is tentatively scheduled for Wednesday, May 7
in
class. The coverage of the midterm is the sections from Chap.1 to
Chap.4
covered by the lectures. The final exam will be 10:30am-12:30pm,
Thursday, June 12 at PHYGEO 140. The coverage of the final exam is
cumulative.
Also, be sure to note the following policies: All exams are closed
book. You
may not use the textbook, crib sheets, notes, or any other outside
material. Do
not bring your own scratch paper. Do not bring blue books.
* You are not allowed to use calculators/laptop
computers/cell phones in the exam. The exam is to test whether you know
the
material.
* Everyone works on their
own exams. Any suspicions of collaboration, copying, or otherwise
violating the
Student Code of Conduct will be forwarded to the Student Judicial Board.
* The answer is yes: the final exam is
cumulative, i.e., it covers the whole course material.
* There will be NO MAKE-UP MIDTERM EXAM. If you
miss the midterm exam due to
catastrophic events such as serious illness of yourself or death of
your
immediate family, you must provide me with a written proof (e.g., a
report or a
letter written by a medical doctor with signature). Only then I will
readjust
the weight (i.e., Homework 40%; Final 60%).
* If you miss the final exam due to catastrophic
events such as serious illness of yourself or death of your immediate
family,
you will receive "Incomplete" grade, provided that you give me a
written proof (e.g., a report or a letter written by a medical doctor
with
signature). Then you must take a make-up exam in the following quarter
to
receive a letter grade.
NOTE:
If you miss the midterm exam, you must take the final exam. I will not assign "Incomplete"
grade if you miss both exams. In this case, your grade will be computed
solely
from your homeworks
Please email me if you have
any comments or questions!