Course Syllabus |
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Course Content:
Required Text:
Theory of Functions of a Complex Variable, Second Edition A. I.
Markushevich. This course is an advanced study of complex–valued functions. Holomorphic and harmonic functions, Cauchy’s Integral Theorem, Poisson’s kernel and the Dirichlet problem, conformality, the Riemann Mapping Theorem, analytic continuation. Additional topics may be chosen from univalent, entire, meromorphic functions; Riemann surfaces; asymptotic methods; Mittag–Leffler, Runge and Weierstrass factorization theorems.
We will do a quick review of the first course in complex
variables with some emphasis on the Riemann sphere, linear fractional
transformations, series, and the calculus of complex functions from Part I and
the first chapters of Part II. We will then explore the solution of the
Dirichlet problem, conformal mapping, fluid flow in 2D, infinite products,
and asymptotic integrals. There is a connection between meromorphic functions on
a torus and doubly periodic functions on a 2D lattice. This will lead us
to exploring elliptic integrals, elliptic functions, theta functions, and the
topology of Riemann surfaces. If there is time, we will discuss additional
topics, such as analytic continuation, zeta functions, the Riemann hypothesis,
prime number theorem, the Riemann-Hilbert problem, or differential equations in
the complex domain. Homework: Homework assignments will be collected on a regular basis and you will be told when the work is due. As doing homework is very important for learning the material in this course, it will count as 30% of your grade.
Attendance: YOU ARE EXPECTED TO ATTEND ALL OF THE CLASSES! After
three excused absences there will be a penalty of 1% for each absence from your total grade.
Exams and Grades: There will be
a midterm and a final for this course. The exams will cover the material up to the date of the exam. The tentative dates for the exams are below.
Your final grade will be based on the following:
Borderline grades may be modified by a plus, or a minus, if the instructor determines that such grades are earned. Advice for Success: In order to learn the material in this course and earn a good grade, you need to put in some effort. Do not put off assignments or reading. If you do not understand something, ask the instructor. Come to office hours, use the email, ask knowledgeable students, or go to the library/internet and find supplementary material. This will help you to keep in touch with the physics and not get lost in the details of the mathematics. Additional material will be placed at the course website. The instructor can only cover the basics in class. You are not expected to know the material by only listening to the lectures. You need to work problems and think about what you are doing.
Student Disabilities: UNCW Disability Services supplies information about disability law, documentation procedures and accommodations that can be found at http://uncw.edu/disability/. To obtain accommodations the student should first contact Disability Services and present their documentation to the coordinator for review and verification.Campus Respect Compact. UNCW has recently instituted a Respect Compact to affirm our commitment to a civil community, characterized by mutual respect. That Compact will soon be affixed to the wall of each classroom and can be accessed at: http://uncw.edu/diversity/documents/ApprovedSeahawkRespectCompact8x10.08.09.pdf Learning takes place outside the classroom. __________________________________________________ This syllabus is
subject to change! |
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| E-Mail: Dr. Russell Herman | Last Updated: January 08, 2017 | |||||||||||||||||||||||||