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AMATH 567 A: Applied Complex Analysis

Meeting Time: 
MWF 1:30pm - 2:20pm
Location: 
DEN 212
SLN: 
10254
Joint Sections: 
AMATH 567 B
Instructor:
Chris Bretherton
Chris Bretherton

Syllabus Description:

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

Lecture schedule and notes

Course Description

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

Learning objectives

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.  

Recommended Text

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.

Grading

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.  

Catalog Description: 
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 . Offered: A.
Credits: 
5.0
Status: 
Active
Last updated: 
August 9, 2017 - 9:20pm
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