Math 555: Complex Variables

Time:

Tuesday and Thursday, 10:00 - 11:30 p.m.

Place:

East Hall B239 (seats 35)

Instructor:

Jeffrey Lagarias, 3086 East Hall, 763-1186, lagarias@umich.edu

Office hours:

Monday 5-6pm in office, 3086 East Hall
Wednesday 5--6pm in office, 3086 East Hall
Thursday 11:30am-12:30pm in office, 3086 East Hall
(Or by appointment: call or email me)

Prerequisite:

Three term calculus sequence. A course in advanced calculus is essential; the material in Math 555 is a prerequisite to many advanced courses in science and engineering. (Math 450 or 451 equivalent.)

Background:

This course is an introduction to the theory of complex valued functions of a complex variable. Functions of a complex variable were one of the great discoveries of the nineteenth century, first in connection with differential equations, then found of great utility in acoustics, electromagnetic theory and hydrodynamics.

Course description:

Differentiation and integration of complex valued functions of a complex variable, series, mappings, residues. Applications to fourier and Laplace transforms and inversions. Evaluations of improper real integrals. Conformal mapping. If time permits, applications to electrostatics and fluid dynamics.

Text:

James Ward Brown and Ruel V. Churchill,
Complex Variables and Applications. Seventh Edition.
McGraw-Hill, Inc. New York 2004.

Grading:

There will be graded homeworks, two midterm exams and final exam. There will be approximately 10 problem sets. The lowest homework score will be dropped. Current schedule: first midterm Tues. Oct. 11; second midterm Tues. Nov. 22; final exam (date set by registrar) Tues. Dec. 20, 10:30am--12:30pm.

The grading will be total points, weighted so that problem sets 20%, midterms 20% each, final 40%.
(Current plan)

Homeworks are due at the beginning of class of date due. Current policy: late homeworks will be penalized; possibly not accepted. (This will depend on grading arrangements.) Collaboration on the homework is permitted, but each person is responsible for writing up her/his own solutions.

Exams are closed book, closed notebook.

The two midterm exams will be held in class. No makeups will be given.

Schedule:

Here is a current

  • Syllabus

    • This syllabus is incomplete and tentative, and will be superseded by later versions as the course evolves.

    <\h3> Graded Homework Assignments:

  • Graded Homework Assignment 1 Due Tuesday September 13.

  • Graded Homework Assignment 2 Due Tuesday September 20.

  • Graded Homework Assignment 3 Due Tuesday September 27.

  • Graded Homework Assignment 4 Due Tuesday October 4.

  • Graded Homework Assignment 5 Due Tuesday October 25.

  • Graded Homework Assignment 6 Due Tuesday November 1.

  • Graded Homework Assignment 7 Due Tuesday November 8.

  • Graded Homework Assignment 8 Due Tuesday November 15.

  • Graded Homework Assignment 9 Due Tuesday December 6.

  • Graded Homework Assignment 10 Due Tuesday December 13; extension till 5pm Thursday Dec. 15.