Amath 567A/B MWF 1:30-2:20 pm Denny(DEN) 212 SLN 10254
Instructor: Prof. Chris Bretherton
Office Hours: Tu 1-2 pm or by appointment, Atmospheric Science Geophysics Bldg. (ATG) 704
TA: Benjamin Liu
Office Hours: We 2:30pm, Applied Mathematics Bldg. (LEW) 129
Instructor travel (Ben Liu will teach; no Bretherton office hours):
We Sep. 27, Tu-Th Oct. 10-12, Tu-Th Oct. 24-26
Complex variable and associated topics. Branch cuts, series and product expansions. Contour integration, numerical implications. Harmonic functions. Complex potential (and singularities) in physical problems. Conformal mapping; applications and examples. Fourier and Laplace transforms and applications.
Prerequisite: Either AMATH 401or equivalent, or permission of instructor
This is an introductory graduate class, meaning that we will move fast through the basics and we will not avoid more challenging concepts and problems, with an emphasis on technique (practiced in the homework) and just enough rigor to be convincing. My goal is that students appreciate both the beauty of complex variables methods and understand the fundamentals behind their many applications to integrals, ordinary and partial differential equations.
Ablowitz, M. J., and A. S. Fokas, Complex Variables, Introduction and Applications (Second Edition, paperback), Cambridge Univ. Press, ISBN: 9780521534291. Available at UW bookstore or Amazon.
50% homework, 20% in-class midterm (We Nov 1), 30% comprehensive in-class final (Mo Dec 11, 2:30-4:20 pm), both open book/note. Homework, assigned quasi-weekly, should be submitted using Canvas, and is due by 5 pm. You are encouraged to collaborate with your classmates on homework, but each of you is expected to write out solutions in your own words, to reinforce the learning process. Late homework must be handed in using Canvas by 5 pm of the next day of lecture following the due date. After the first late assignment, there will be a 25% penalty for subsequent late homeworks.