MATH 406
Advanced Calculus for Engineers/Scientists II

Instructor: Professor Andrew Belmonte

Contact info: 004E Thomas Building, telephone: 865-2491, email: belmonte.AT.math.psu.edu

Office hours: Thurs 1:15-3, Fri 1:30-3, or by appointment.

EXTRA OFFICE HRS: Tues 4/5   1-2:30 and 5:30-6:30.

Class location:

• Section 2 (9:05 AM): 217 Thomas Bldg.
• Section 1 (10:10 AM): 169 Willard Bldg.

Grader:   Jiangtao Duan (jxd949@psu.edu).

Prerequisites: Math 250 or 251, Math 405.

Web Page: http://www.math.psu.edu/belmonte/05math406.html

Required Textbook (available in the bookstore):

• Complex Variables, 2nd edition, by Stephen D. Fisher (Dover, 1999) ISBN: 0-486-40679-2.

Additional Texts (not required!)

• Advanced Engineering Mathematics, 8th edition, by E. Kreyszig (Wiley, 1999).
• Conformal Mapping by Z. Nehari (unfortunately out of print, but available in library).
• or any supplementary text on complex variables

•   Paul Fishback's Complex Variables Resource
•   A Complex Gallery (Harvard University)

In this class we will talk about imaginary numbers, which are multiples of the square root of -1, and more generally about complex numbers, which are combinations of real and imaginary numbers. The number system which results from this abstraction is quite important to many applications, including signal processing, fluid dynamics, electromagnetism, circuit theory, and quantum mechanics - to name a few. This semester we will study the calculus of complex functions - functions of a complex variable, and complex-valued functions. Among the topics we will cover are: analytic functions, contour integration, sequences and series, residues, conformal mappings, and transforms.

The structure of the course will follow Fisher's text, in more or less the same order. You should be reading well ahead of where we are in the lecture - this will be my assumption!

Midterm I:   Friday February 18th (in class).

Midterm II:   Wednesday April 6th (in class).

Final Exam:   Monday May 2nd (12:20 PM, 117 Borland).