MATH 405
Advanced Calculus for Engineers/Scientists I

Instructor: Professor Andrew Belmonte

Contact info: 322 McAllister Building, telephone: 865-2491, email: belmonte.AT.math.psu.edu

Office hours: Tues 11-12, Wed 10-11 and 2:30-3:30, or by appointment.

Class location:

• Section 2 (12:20 PM): 216 Thomas Bldg.
• Section 1 (1:25 PM): 121 Thomas Bldg.

Prerequisites: Math 250 or 251.

Web Page: http://www.math.psu.edu/belmonte/math405_06.html

Required Textbooks (available in the bookstore):

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

Additional Texts (not required!)

• Mathematical Methods for Physicists, by George B. Arfken (Elsevier, 2005).
• Mathematical Methods in the Physical Sciences by Mary L. Boas (Wiley, 1983).
• Div, Grad, Curl, and All That, by H. M. Schey (Norton, 1973).
• Introduction to Applied Mathematics, by Gilbert Strang (Wellesley, 1986).
• Linear Algebra and its Applications, by Gilbert Strang (Thomson, 2006).

these additional books will be on reserve at the PAMS library in Davey Lab.

You should be reading the text well ahead of where we are in the lecture - this will be my assumption!

•   Transcribed lecture notes on Legendre's equation and Legendre polynomials (partial - added Spr 07)
•   Formula for Roots of a Cubic (E. Schechter, Vanderbilt University)

This class provides an overview of advanced topics which form the basis of the current mathematical approach to nature in the physical sciences and engineering. As you probably know, calculus was invented to solve physical problems - here we delve into how far along things have gotten! This will include the calculus of vectors, ordinary differential equations (ODEs), partial differential equations (PDEs), and linear algebra - including its relation to systems of differential equations. We will discuss the ideas of superposition, inversion, and decomposition, and there will be a strong emphasis on eigenvalues - and the applications of these concepts!

The general structure of the course can be divided into four areas:

I. ODEs and Linear Algebra (*eigenvalues*)

II. Operators and Physical ODEs (*Sturm-Liouville*)

III. Complete Orthonormal Functions - including Fourier series

IV. Div, Grad, Curl, and Green's Theorems

We will also see how the separation of variables technique, and other techniques which converts PDEs into ODEs (such as the method of characteristics) allows us to apply many of the above results for more general, spatiotemporal physical systems.

Midterm I:   Friday October 13th (in class).
Midterm II:   Friday November 17th (in class).
Final Exam:   Monday December 18th (6:50 PM, 209 S Henderson).