Fall 2014 Course Syllabus - Mathematics 8051.001
Course: Mathematics 8051.001.
Course Title: Functions of a Complex Variable.
Time: TR 12:30-1:50.
Place: Wachman Hall 618.
Instructor: Mendoza, Gerardo A.
Instructor Office: Wachman 617.
Instructor Email: gerardo.mendoza@temple.edu
Instructor Phone: 1-5053.
Course Web Page: http://math.temple.edu/~gmendoza/
Office Hours: 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 gaining a deep working understanding of the subject, the student is expected to be able to write clear complete proofs in the subject.
Topics Covered: For the two-semester sequence: Elementary properties and examples of holomorphic functions; differentiability 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. Topics for the second semester include Harmonic functions, the Poisson integral formula, maximum and minimum principles, the mean value property, the Dirichlet problem, Harnack's inequality; spaces of holomorphic and meromorphic functions, the Riemann Mapping Theorem; analytic continuation. Weierstrass and Hadamard's Factorization Theorems; Picard's Theorems; introduction to Riemann Surfaces.
Course Grading: Homework will be given frequently. The final grade will be based on the homework, the tests and a final examination.
Exam Dates: Tentative dates for partial exams: October 2 and November 20. 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 dropped by the Drop/Add deadline date given below.
- Fall Begins: Monday August 25, 2014
- Classes Begin: Monday August 25, 2014
- Labor Day: Monday September 1, 2014
- Course Add/Drop Deadline: Monday September 8, 2014
- Course Withdraw Deadline: Friday October 24, 2014
- Fall Break: Monday-Friday November 24 - November 28, 2014
- Classes End: Monday December 8, 2014
- Study Days: Tuesday-Wednesday December 9 - December 10, 2014
- Exam Week: Thursday-Wednesday December 11 - December 17, 2014
- Diploma Date: Thursday December 18, 2014
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.