Lectures: This one semester course will introduce graduate students to some methods of applied mathematics. We will assume that students have studied undergraduate linear algebra, ordinary differential equations and some aspects of partial differential equations (or, at least, heard about it). The main emphasis of this course will be on selected principles and techniques of applied mathematics.  The introductory lecture prior to the work in selected chapters from the assigned textbooks will provide an overview of the material including goals and objectives. Applications from the engineering sciences will be given.

Topics to be covered from the assigned textbooks are as follows:

(a) Keener: Chapter 3 - Volterra, Fredholm and Singular  equations; Compact Operators; Resolvent Kernels; The Fredholm Alternative; Approximate Solutions; The Hilbert-Schmidt theorem

(b) Bender & Orszag: Chapters 6, 7, 10 & 11 - Asymptotic Expansion of Integrals; Perturbation Methods; WKB Theory; Singular Perturbation Methods, Multiple Scale Analysis

(c) Murray: Chapters 2, 3, 4, 6 & &: Laplace's Method for Integrals; Method of Steepest Descent; Method of Stationary Phase; Perturbation Methods; WKB Theory; Singular Perturbation Methods.

Homework: Homework will be assigned when necessary, except before tests. I might mention that some of the problem sets will be quite extensive, therefore, even if you do not complete all of the problems assigned you should attempt to maintain the turn-in schedule.

Course Expectation & Conduct: The purpose of our class meetings is to help you to obtain the core material that will allow you to learn through your own work outside the classroom. Therefore, an essential part of your {positive} learning process is to look for additional information from the library and other sources.

Students with Special Needs: Students with documented learning disabilities are entitled by law to certain “reasonable accommodations.” If you have a documented reason for special accommodations, you must provide written evidence of this as soon as possible from the appropriate office. No accommodations can or will be given without the documentation. Each time special accommodations are requested, the request must be submitted, in writing, at least one week before the event.