Department of Mathematics Generic Syllabus
Boise State University Updated Fall 1998

Math 326
Complex Analysis
3 semester credits

Catalog Description

M 326 Complex Analysis (3-0-3)(S)(Offered on demand even numbered years) Complex numbers, functions of a complex variable, analytic functions, infinite series, integration, the residue theorem and conformal mapping. PREREQ: M275

Prerequisites

Multivariable and vector calculus.

Jurisdiction

This course is not currently controlled by a departmental committee and individual instructors may choose different textbooks. Exams, homework and grading system are left to the instructor.

Learning Objectives

As an upper division mathematics course in an area with applications to non-mathematical areas, this course can vary in its focus toward the general departmental goals. Some faculty will emphasize the aesthetic nature of the subject while others will concentrate on the nontrivial applications to non mathematical fields. In both cases, the course will emphasize the nature of mathematics as a language and as a collection of tools with the understanding of the limitations of those tools.

Upon completion of this course, the students will have made substantial progress in:

extending their skills in elementary calculus to the complex plane.
Finding Taylors and Laurent series for complex functions.
Using the topology of the complex plane to determine limits of sequences and series of complex valued functions
applying complex residue theory to integration of real valued functions over the real line.

1 Assessment of Learning Objectives

Students will be assessed by evaluating their ability to do problems based on the learning objectives. The problems will occur in several contexts;

Periodic problem sets for homework serve both as learning and assessment tools. Classroom activities may vary depending on students' performances on homework assignments.
Problems given on in-class examinations are designed to give students the opportunity to demonstrate their ability to apply rules and formulae to the solution of simpler problems.
Instructor optional take-home examinations designed to evaluate the students ability to solve more complicated and time consuming problems. These problems give students the opportunity to demonstrate their ability to use technology to solve problems that are not amenable to simple analytic techniques.

Topics and Approximate Timeline


	Number of
Topic	Lectures
Geometry and arithmetic of complex numbers	3
Topology of the complex plane	3
Cauchy-Riemann equations and analyticity	6
Exponential and logarithmic functions and analytic branches	5
Complex integration	9
Series representations	9
Residue theory	10

Text

The following texts are appropriate for this course:
R.V. Churchill & J.W. Brown, Complex Variables and Applications, McGraw-Hill, 1984.
I. Stewart & D. Tall, Complex Analysis, Cambridge University Press, 1983.
E. B. Saff & A. D. Snider Fundamentals of Complex Analysis for Mathematics, Science and Engineering Prentice Hall, 1976

Format, Student Activities, and Grades

Class meetings involve a combination of lecture, questions and discussion and sometimes small group activity. The particular mix is determined by the current instructor.

As in all mathematics courses, homework is an important part of the course.

The exams may be given in class or take-home. The students are given a letter grade based on points earned. The points are typically available as:


Homework	100
Two exams	200
Final exam	200
Total	500

Letter grades are based on a scale in which 90% of the 900 possible points guarantees an A, 80% a B, 70% a C, 60% a D, and less an F, with the instructor having the discretion to adjust these cut-offs if warranted.

File translated from T_EX by T_TH, version 1.56.