MATH 406
Engineers & Scientists II
- Complex Variable Techniques -

## Penn State University      Spring 2009

MWF   9:05-9:55 AM (Section 2)
MWF   10:10-11:00 AM (Section 1)

Instructor:   Andrew Belmonte
Contact info:   322 McAllister Building, telephone: 865-2491, email: belmonte.AT.math.psu.edu
Office hours:   Tues 1--3, Thurs 2--3, or by appointment.

Class location:
• Section 2 (9:05 AM): 009 Life Science Bldg     Registrar Schedule Number: 194665
• Section 1 (10:10 AM):     169 Willard Bldg        Registrar Schedule Number: 194662

Course Text (required):
• Advanced Engineering Mathematics, by E. Kreyszig (Wiley, 2006) - 9th edition
ISBN 0-471-48885-2

Course description:

As you probably already know by now, the square root of a negative number is allowed in mathematics: the so-called imaginary numbers are multiples of the square root of -1, represented as i. More generally, complex variables can take on either real or imaginary values (or both). But is it useful to do this?

This semester we will delve into the properties of complex variables and complex-valued functions, and explore some of the applications that are current in engineering and the fundamental sciences. There are in fact a large number of important results resulting from the abstract idea of including i along with the real numbers: for example signal processing, fluid dynamics, electromagnetism, circuit theory, and quantum mechanics, among others. We will study integral and differential calculus of complex functions. Among the topics we will cover are analytic functions, contour integration, residues, conformal mappings, and transforms (Fourier, Laplace, etc). We will however spend more time on techniques (such as the use of transforms to solve partial differential equations) at the expense of more fundamental aspects of the subject (such as sequences and series).

The general structure of the course will follow Chapters 13-18 (Part D, selected sections) of Kreyszig's text, more or less in the same order, with the addition of parts of Chapter 12 (transforms).

Exam Schedule:

Midterm I:   Wednesday, February 18th (in class).

Midterm II:   Wednesday, April 8th (in class).

Final Exam:   Wednesday, May 6th (2:30-4:20pm, 358 Willard Bldg)