Fall 2008 Course Syllabus
Course: 8051.001.
Course Title: Functions of a Complex Variable I.
Time: 2:40 pm - 4:00 pm.
Place: Wachman 527.
Instructor: Mendoza, Gerardo A.
Instructor Office: Wachman 538.
Instructor Email: gerardo.mendoza@temple.edu
Instructor Phone: 1-5053.
Office Hours: Monday, Wednesday 10-11:30 am, or by appointment.
Prerequisites: Permission of instructor.
Textbook: John B. Conway, Functions of One Complex Variable I, Graduate Texts in Mathematics , Vol. 11. 2nd ed. 1978. Corr. 7th printing, 1995, Hardcover, ISBN: 978-0-387-90328-6.
Course Goals: This is a two semester course. In addition to gain a deep working understanding of the subject, the stuent is expected to be able to write clear complete proofs in the subject.
Topics Covered: Elementary properties and examples of holomorphic functions; diff erentiability and analyticity, the Cauchy-Riemann equations; power series; conformality; complex line integrals, the Cauchy Integral Formula and Cauchy's Theorem; applications of the Cauchy Integral Formula- power series expansion for a holomorphic function, the Maximum Modulus principle, the Cauchy estimates, Liouville's Theorem; Singularities of holomorphic functions, Laurent expansions, the calculus of residues and applications to the calculation of definite integrals and sums; zeros of a holomorphic function, the Argument Principle, Rouche's Theorem, Hurwitz's Theorem; conformal mappings.
Course Grading: Homework will be given frequently and the final grade will be based on the homework, two tests and a final examination.
Exam Dates: Partial exams on October 7 and November 25. Final exam date to be determined.
Attendance Policy: Attendance is required. Missing four classes implies a failing 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:
- The first day of classes is Tuesday, September 2.
- The last day to drop/add (tuition refund available) is Monday, September 15.
- Thanksgiving is Thursday, November 27.
- The last day to withdraw (no refund) is Monday, November 3.
- The last day of classes is Wednesday, December 10.
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.