Advanced Calculus for
Engineers & Scientists II
- Complex Variable Techniques -
Penn State University Spring 2009MWF 9:05-9:55 AM (Section 2)
MWF 10:10-11:00 AM (Section 1)
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.
Prerequisites: Math 405. For more information, please contact the instructor.Course Text (required):
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).
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)