MAA4402 - Complex Variables
Department of Mathematics, University of South Florida
SPRING 2003
TR02:00-03:15pm PHY109
Instructor:
- Dr. Wen-Xiu Ma, Office: PHY307, Phone: 974-3140.
Office Hours and Location:
- M3:00-4:00pm and TR3:30-4:30pm (tentative) or by appointment, PHY307.
Prerequisites:
- MAS 3105 - Linear Algebra, MAC 2283 - Eng Calculus III or MAC 2313 -
Calculus III, MAP 2302 - Differential Equations, or equivalent.
Aims and Objectives:
- - The course aims to introduce students to the fundamental concepts, techniques and theories of functions of a complex variable and their applications, especially
the classical Cauchy theory of analytic functions including residue theory and contour integration.
- - When successfully completing the course, the student should be able to express complex numbers in both cartesian and polar forms, identify curves and regions in the complex plane defined by simple formulae, determine whether and where a function is analytic, obtain appropriate series expansions of functions, evaluate residues at pole singularities, and apply the Residue Theorem to the calculation of real integrals.
Course Text:
- - E. B. Saff and A. D. Snider, Fundamentals of Complex Analysis for
Mathematics, Science, and Engineering, 2nd edition, Prentice Hall, 1993
- - Part I. Chapters 1 - 2 (four weeks), Part II. Chapters 3 - 4 (six
weeks), Part III. Chapters 5 - 7 (five weeks)
- - Notes or tapes of class lectures are not permitted for purposes of sale.
Homework Assignments:
- - There will be six homework assignments for the course. All chosen
exercises will help you to develop your skills in calculation, and more
importantly, to develop reasoning skills and your ability to apply the
techniques you have learned to concrete situations.
- - You are required to do all homework exercises. Doing exercises is the
best way to deepen your understanding of the topics and to convince yourself
that you understand them.
- - Keep in mind the following statement by D. Hilbert: ``A mathematical
problem should be difficult to entice us, yet not inaccessible lest it mock
our efforts."
- - Homework assigned in Week 3 and Week 8 will be collected on Thursday,
January 30 and Thursday, March 6 (tentative), respectively.
Examinations:
- There will be three examinations.
- Exam 1. Week 5 - Thursday, February 6 (tentative).
- Exam 2. Week 11 - Thursday, March 27 (tentative).
- Final exam. 1:00pm-3:00pm, Tuesday, April 29 (tentative).
- The contents of three exams will cover Part I, Part II, and Part III,
respectively, and will be announced in more detail in class. No make-up test.
Grading Scheme:
- - Attendance at classes will not be taken. But regular and
punctual attendance is important, since the material of the text
will be embellished and augmented.
- - Each of the three exams counts for 30%. Homework counts for 10% plus 5%
as bonus points. Your final score will be computed by these weights, the
maximum being 105.
- - A plus/minus grading system will be used for the course.
Course letter grades will be decided based on final scores as
follows:
90 for A-, 80 for B-, 65 for C-, 50 for D-, 0-49 for F, and other letter grades will be assigned accordingly.
Major Religious Observance:
- No student shall be compelled to attend class or sit for an examination at
a day or time prohibited by his/her religious belief. In accordance with the
University policy on observance of religious holidays, students are expected
to notify the instructor during the first week of class if they anticipate the
necessity of being absent from a class or announced examination due to the
observation of a major religious observance.
Incomplete Grades:
- An incomplete grade can be awarded to a student only when the student is
passing the course but unable to complete the course because of an unforeseen
dire circumstance such as documented illness or a family death. (See http://www.ugs.usf.edu/catalogs/0203/gradetc.htm
or USF 2002-2003 Undergraduate Catalog - Pages 43 - 45
for
I grade policy.)
S/U Grading:
- An S/U grade will be issued if and only if a contract is completed within
the first three weeks of the semester between the student and the instructor.
An S grade will be awarded only if the student's letter grade would have been
equivalent to C or better. (See http://www.ugs.usf.edu/catalogs/0203/gradetc.htm
or USF 2002-2003 Undergraduate Catalog - Pages 43 - 45
for S/U grade system.)
Academic Dishonesty Policy:
- For the ramifications of academic dishonesty policy, see http://www.ugs.usf.edu/catalogs/0203/adadap.htm
or USF 2003-2004 Undergraduate Catalog - Pages 47 - 49.
Blackboard Website:
- The course Blackboard web site can be reached via the university web single sign-on portal at myUSF Online. All homework assignments,
supplementary material, etc. will be
available for download from the Blackboard course web site.
There is
also a discussion board at the Blackboard course web site,
administrated by the instructor.
Links to Related Sites:
If you have questions or comments, please leave your messages at mawx@math.usf.edu