COURSE SYLLABUS

Course Number: MATH6040
Course Title: COMPLEX VARIABLES WITH APPLICATIONS II
Credit Hours: 3
Prerequisites: MATH6030
Corequisite: 

Objectives: This course is a continuation of MATH 6630. The course will introduce students to the fundamental concepts and techniques of Complex Variables. Major goals will be to develop the student's understanding of the theory of Complex Variables and the corresponding ability to apply the theory to solve problems arising in the physical sciences and engineering.

Schedule and Outline of Course Content:  (Individual instructors may re-arrange the material and use different headings.)

Residue Theory (5 weeks)
The Residue Theorem, Trigonometric integrals, improper integrals, Jordan's Lemma. Indented contours. Integration of
multiple-valued functions. The Principle of the Argument, Rouche's Theorem.

Conformal Mapping (5 weeks)
Invariance of Laplace's equation. Geometric considerations, Mobius Transformations.  The Schwarz-Christoffel transformation.  Applications in Electrostatics, Heat Flow, and Fluid Mechanics.

The Transforms of Applied Mathematics (5 weeks)
Fourier Series (The Finite Fourier Transform), The Fourier Transform, The Laplace Transform, The z-Transform, Cauchy Integrals and the Hilbert Transform.

Possible Textbook:
Fundamentals of Complex Analysis for Mathematics, Science, and Engineering, second edition, Saff, E. B. and Snider, A. D.(1993);
Other texts may be used by individual instructors.

II.     Grading and Evaluation Procedures:
Typically tests, and quizzes, with other methods employed at the discretion of the instructor.

III.    Policies related to the conduct of the class are set by individual instructors.