MAT 121 Syllabus Page (Fall 2002)
Course: MAT 121-001: Advanced Analysis for the Sciences
CRN: 41341
Class: MWF 9:00am-9:50am, Wellman 233 (new room!)
Instructor: Naoki Saito
Office: 675 Kerr
Email: saito@math.ucdavis.edu
Office Hours: MW 1:40pm-3:40pm or by appointment
TA: Chris Algieri
Office: 479 Kerr
Email: algieri@math.ucdavis.edu
Office Hours: T 10:00am-11:00am, Th 2:00pm-3:00pm or by appointment
Audience:
Students in science and engineering departments, who want to understand and
learn the Fourier techniques and the basic partial differential equations
(PDEs), e.g., Laplace, Poisson, heat, and wave equations.
Course Objectives:
- To learn and appreciate the importance and beauty of Fourier series, Fourier
transforms, and their relatives, and how these tools help solving certain
types of PDEs; We will learn the power of representing functions and solutions
of certain basic PDEs as a linear combination of some basic building blocks.
- To understand the sine and cosine functions of the Fourier series are the special
case of the Sturm-Liouville problem with periodic boundary condition, and to learn
what kind of functions emerge by changing the boundary condition and geometry of
the problem, such as rectangular, cylindrical, and spherical coordinates.
- To have an experience of applying the Fourier techniques to simple yet practical
problems in science and engineering. I will give some unexpected examples of
applications of these techniques such as data compression, where the boundary
conditions and geometry are also very important.
Topics:
- Fourier Series and Fourier Transforms
- Basics of certain PDEs
- Basic PDEs on cylindrical and spherical coordinates
- Sturm-Liouville problem and eigenfunction expansion
- Special functions such as Bessel functions and Legendre polynomials
- Green's functions and introduction to generalized functions and distributions
Textbook:
- Mary L. Boas: Mathematical Methods in the Physical Sciences, 2nd Edition,
John Wiley & Sons, 1983, ISBN: 0-471-004409-1.
This is a required textbook. We will cover Chap. 7, 12, 13, and 15
of this book.
Prerequisite:
- MAT 22A (basic understanding of linear algebra)
- MAT 21D (basic understanding of vector calculus)
- MAT 22B (basic understanding of ordinary differential equations)
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:
Class Mailing List:
The MAT 121 Mailing List was created. I will use this list to announce some
important information. You can also submit your emails (must be related
to the class) to this mailing list. If you send your email to this list,
then everyone will receive it. So, please use this wisely and politely.
Once I had two students in the class who started discussing certain aspects
of the exercise problem and sent back and forth about 10 emails to the
mailing list in a few hours, and everyone else got fed up...
The mailing list name is: mat121-f02@ucdavis.edu
.
Grading Scheme:
- 25% Homework
- 25% Midterm Exam (in class, Wednesday, November 6, 2002)
- 50% Final Exam (8:00am-10:00am, Wednesday, December 11, 2002)
Generally speaking, I have found that a total score of 85% or above will get
an A (+ or -), 65% or above will get a B (+ or -), and 50% will get a C (+ or -).
The exact breakdown of letter grades will be determined at the end of the course.
Borderline cases: When determining your grade at the end of the course,
some of you may lie on a border (should this student get a B+ or an A-?).
For those cases, I will look at the following factors:
- Did this student hand in all the homework assignments and show an honest
effort on every one?
- Did this student show improvement over the quarter by increasing
homework scores?
- Was the student an active participant in class (asking questions,
coming to office hours, etc.)?
It is at my discretion alone whether these factors merit an increase in your
letter grade.
Homework:
I will assign homework problems every Friday, which can be seen at
Homework Page.
The due date is the following Friday at the beginning of class.
LATE HOMEWORK WILL NOT BE ACCEPTED.
All homework must be neat, accurate, and legible. You must show your work, and you are
encouraged to write in complete sentences. 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. You must show work that is legible and logical.
A subset of these problems will be graded, and returned on the following Friday
at the end of class.
I will not include the score of the worst performed homework 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 currently scheduled
for Wednesday, November 6 in class.
The final exam will be 8:00am-10:00am, Wednesday, December 11 at Wellman 233 (note
this room number).
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.
- There will be no calculators/laptop computers for the exam.
The exam is to test whether you know the material.
- If I feel that there are tables or formulas needed for the test that
you should not memorize (e.g., the table of Laplace transforms), then I will
provide a copy of the needed information. Refer again to the first point above.
- 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.
Please email me
if you have any comments or questions!
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