## Math 414 Fall 2004 (Mike Boyle)

Homework

Prerequisites: MATH 410 and MATH 240 (or equivalent)

Text: The Qualitative Theory of Differential Equations, An Introduction

by Fred Brauer and John A. Nohel

Dover Press

Professor Mike Boyle

Office: MATH 4413

Email: mmb@math.umd.edu

Phone: 301-405-5135

Office hours: Tu11, W9, Th1; also usually available after class

We will cover the text, with some embellishments and omissions.

Grades: There will be 600 possible points:
- 200 Final Exam
- 100 First Midterm
- 100 Second Midterm
- 200 Homework and Quizzes

Curve:
- 85% guarantees
an A,
- 75% guarantees at least a B,
- 65% guarantees at least a C,
- 55% guarantees at least a D.

Cutoffs might be relaxed but this should not be counted on.

E-MAIL: I send course e-mail to
email addresses officially registered with the
University. If your
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### Overview

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).