18.04: Complex Variables with Applications

Announcements

• Prof. Toomre will be away the week of May 15, and Prof. Bazant will cover his recitations. However, Prof. Toomre will be available for extra office hours 11am-3pm on Friday May 19 and Monday May 22 to help students prepare for the final exam on May 23 (in Johnson Ice Rink).

Handouts

• Syllabus
• Problem Set 1 due Fri Feb 17.
• Problem Set 2 due Fri Mar 3.
• Problem Set 3 due Fri Apr 7.
• Problem Set 4 due Fri May 12.

• Practice problems: 2001 Final Exam (with solutions) plus eight old exams (mostly with solutions) of Prof. Toomre handed out in recitations.

Lectures

• MWF 12-1 in 2-190.
• Lecturer: Prof. M. Z. Bazant, bazant@math.mit.edu, Office hours TuWF 1:30-2:30 in 2-363B.

Recitations

• W 2-3 in 2-131, W 3-4 in 2-132, Th 3-4 in 12-142.
• Instructor: Prof. A. Toomre, toomre@math.mit.edu, Office hours MTh 1:30-2:30 in 2-371.

Important Dates

• Problem sets due at lecture on Fridays Feb 17, Mar 3, Apr 7, May 12.
• Midterm exams in Walker Gym on Fridays Mar 17 and Apr 21.
• Final exam Tu May 23, 9-12 in Jonhson Ice Rink.

Topics

1. Complex algebra and functions
2. Contour integration
3. Laurent series and residue calculus
4. Conformal mapping and potential theory
5. Transform methods

Books

• Required: E. Saff and A. Snider, Fundamentals of Complex Analysis, 3rd edition (2001).
• Optional (but highly recommended): T. Needham, Visual Complex Analysis (2000).

Links

• Graphics for Complex Analysis by Douglas Arnold
• Table of Conformal Mappings Using Continuous Coloring by George Abdo and Paul Godfrey
• Complex Function Viewer by Keith Orpen and Djun M. Kim.
• Complex Function Grapher by Andrew Bennett.

A steady fluid vortex structure

Fringe currents of parallel-plate electrodes

bazant@math.mit.edu