Prerequisites: MATH 410 and MATH 240 (or equivalent)
Text: The Qualitative Theory of Differential Equations, An Introduction
by Fred Brauer and John A. Nohel
Professor Mike Boyle
Office: MATH 4413
Office hours: Tu11, W9, Th1; also usually available after class
Differential equations are at the heart of applications of mathematics to the real world, and at the development of mathematics itself. Efforts to solve and understand differential equations led to calculus, Fourier series, set theory, algebraic topology ...
Differential equations were born with Isaac Newton. He described various physical systems as satisfying certain differential equations. He solved some of these equations to find descriptions of motion and so on. As I recall, Albert Einstein said that in human history Newton's introduction of this viewpoint was perhaps the greatest single intellectual contribution anyone had been privileged to make.
Differential equations is a many-faceted subject. As in Math 246, procedures (recipes) for various special problems are useful. On the other hand, one easily writes down differential equations whose possible solutions are mysterious. Even for practical purposes, it is very useful to have an idea of the theory which constrains or guarantees solutions.
This course will be a introduction to the theory of Ordinary Differential Equations. ("Ordinary" means no partial derivatives.) We'll work at an honest level, proving (i.e. understanding) our results (such as existence and uniqueness results). In contrast with Math 246, we won't run through a large menu of procedures for solving specific types of equations, although we will certainly study some important classes and examples.
The text is an old classic, and very inexpensive ($15 at the moment).