Spring 2006 Course Syllabus
Course: 0347.001.
Course Title: Introduction to Functions of a Complex Variable.
Time: MWF 10:40 - 11:30.
Place: Barton Hall Classrooms, Room 309.
Instructor: Eby, Wayne.
Instructor Office: Wachman Hall, Room 444.
Instructor Email: eby@temple.edu
Instructor Phone: (215) 204-7286.
Course Web Page: http://www.math.temple.edu/~eby/classes/idx347.html
Office Hours: MWF, 11:40 - 12:30, F 3:20 - 4:20, and by appointment.
Prerequisites: Official prerequisites are Math 248, Advanced Calculus II. However, I am amenable to to those who are currently taking Math 248. However, be forewarned that the series which we cover at the end of the class form a fundamental topic which you will also be learning in Math 248. Thus it may be more difficult for those who have not worked with series at this level before.
Textbook: Brown and Churchill, Complex Variables and Applications, 7th ed., McGraw-Hill, 2004.
Course Goals: Goals are to learn the main techniques in analysis of functions of a complex variable. We intend to set a good foundation for continued study in complex analysis and its many interactions with other areas of mathematics.
Topics Covered: Mapping properties of complex functions, Cauchy-Riemann equations, analytic functions and relation to harmonic functions, evaluation of contour integrals, important theorems of contour integrals (Cauchy-Goursat, Cauchy integral formula and derivatives, Morera), Liouville's theorem, Maximum modulus principle, Taylor and Laurent series, residues and beginning of residue calculus.
Course Grading: Grade will be based on homework assignments, three midterm exams, and a cumulative final exam. The points are distributed as follows: Homework 20%, Midterm exams 50% (20% best, 15% each other two), Final exam 30%.
Exam Dates: There will be three midterm exams, one at the end of each unit. The dates for these are not set and depend on the progress of the class through the material. However the target dates are the following. Exam 1 Wednesday, February 15 ; Exam 2 Friday, March 24 ; Exam 3 Monday, April 24. These are subject to change, and the definitive date will be announced in class, at least a week in advance. The final exam will be held on Friday, May 5, from 8:30 - 10:30 a.m. If you cannot be present at an exam, you must make alternative arrangements with me prior to the day of the exam.
Attendance Policy: You are expected to attend all classes and to participate as we go through the material. Excessive absences may lead to a penalization in your grade.
Any student who has a need for accommodation based on the impact of a disability should contact me privately to discuss the specific situation as soon as possible. Contact Disability Resources and Services at (215) 204-1280, 100 Ritter Annex, to coordinate reasonable accommodations for students with documented disabilities.
Freedom to teach and freedom to learn are inseparable facets of academic freedom. The University has adopted a policy on Student and Faculty Academic Rights and Responsibilities (Policy # 03.70.02) which can be accessed here.
Students will be charged for a course unless a withdrawal form is processed by a registration office of the University by the Drop/Add deadline date given below. For this semester, the crucial dates are as follows:
During the first two weeks of the fall or spring semester or summer sessions, students may withdraw from a course with no record of the class appearing on the transcript. In weeks three through nine of the fall or spring semester, or during weeks three and four of summer sessions, the student may withdraw with the advisor's permission. The course will be recorded on the transcript with the instructor's notation of "W," indicating that the student withdrew. After week nine of the fall or spring semester, or week four of summer sessions, students may not withdraw from courses. No student may withdraw from more than five courses during the duration of his/her studies to earn a bachelor's degree. A student may not withdraw from the same course more than once. Students who miss the final exam and do not make alternative arrangements before the grades are turned in will be graded F.
The grade I (an "incomplete") is reserved for extreme circumstances. It is necessary to have completed almost all of the course with a passing average and to file an incomplete contract specifying what is left for you to do. To be eligible for an I grade you need a good reason and you should have missed not more than 25% of the first nine weeks of classes. If approved by the Mathematics Department chair and the CST Dean's office, the incomplete contract must include a default grade that will be used in case the I grade is not resolved within 12 months.