Math 331 Syllabus
Spring, 2009
We will cover the following topics. Except as noted, the lectures will
follow the order of presentation of material in the text,
"Elementary Differential Euqations" (9th edition) by W. Boyce and R.
Diprima.
Chapter 1. Introduction
Differential equations
(DE's), initial value problems,
DE's and mathematical
modeling.
classification of
DE's: linear, linear inhomogeneous, and nonlinear equations.
Chapter
2. First order DE's
Analytic versus
geometric (direction field) solutions, existence and uniqueness
theorem; (material is covered in sections 1.1 and 2.8, text).
First order equations:
solution of linear and linear inhomogeneous first order equations.
Nonlinear DE's:
separable and other nonlinear first order equations
Mathematical modeling
and applications
Population models
Exact equations (we
will omit the material on integrating factors).
Chapter 3. Second
and higher order DE's
Remark: We will focus on 2nd
order DE's, but at times, we will llustrate the methods for simple
examples of higher order DE's.
Initial value
problems for 2nd and higher order linear DE's, the superposition
principle, independent solutions and fundamental solution sets; (this
topic includes some material from
section 4.1)
Constant coefficient
DE's and the characteristic equation;
Real, complex, and
repeated roots
Solutions of
nonhomogeneous equations by undetermined coefficients and variation of
parameters.
Applications to
vibrations in spring-mass systems.
Chapter
6. Solution of DE's by Laplace Transformation
Laplace transform
methods: Calculation of Laplace transforms and inverse transforms;
Application to the
solution of constant coefficient linear equations;
Problems with
discontinous and impulsive forcing; convolutions.