MAT401 Mathematics Seminar

 Kevin J. CarlinOffice:  Fo 113 M-F 2:30-4:00 Telephone: 7563E-mail: kcarlin@assumption.edu

Text

Brown and Churchill, Complex Variables and Applications, eighth edition, McGraw-Hill, 2009.

Electronic Devices

Calculators may not be used in this course. A cell phone or other electronic communication device may not be used as a watch, a calculator, or for any other purpose. They must be put away and completely deactivated during class.

Topics

Complex numbers: arithmetic, complex conjugates, modulus, polar form, de Moivre’s formula, complex roots, neighborhoods, open and closed sets.

Complex functions: limits and continuity, derivatives, Cauchy-Riemann equations, analytic functions, harmonic functions, exponential and logarithmic functions, general exponents.

Integrals: arcs and contours, contour integrals, Cauchy’s theorem, simply and multiply connected domains, Cauchy’s integral formula, Morera’s theorem, Liouville’s theorem, the fundamental theorem of algebra.

There will be a midterm exam (October 16) and a final exam. Homework will be collected weekly. Your final grade will be based on 500 points:

 Presentations 200 Homework 100 Midterm exam 100 Final exam 100 500

Exam grades are based on partial credit and will be scaled. Typically, the scale is A- = 75%, B- = 60%, C- = 50%, D- = 35%.

Make-up of any graded work due to serious illness or other emergency is possible only with prior or immediate notice and will be granted at my discretion. Unexcused absence from any exam will result in a failing grade for the course.

Learning Objectives

• Students should be able to prepare lecture notes by reading and analyzing a topic from a text. Students should be able to deliver effective oral presentations.

• Students should know the definitions and properties of complex numbers and their polar representations. They should be able to use these to find complex roots. They should understand the elementary geometry and topology of the complex plane.

• Students should understand the concepts of limits, continuity, and the derivative of functions of a complex variable. They should know the relationship between the complex derivative and partial derivatives. They should understand the properties of analytic and harmonic functions.

• Students should know the definition of a complex contour integral. They should know the properties of integrals of analytic functions on various contours. They should be able to apply these in a variety of situations.

Course Description

MAT 401 Mathematics Seminar
The topic is determined by the instructor. Emphasis is placed on student oral presentations. Required course for senior mathematics majors.