# Differential Equations with Linear Algebra:

Vocabulary and Concepts

department of mathematical sciences, villanova university, villanova, pa 19087-1699 usa

copyright 1997

Maple files updated in 2007 to Standard Maple worksheets and the package
LinearAlgebra but the conversion of
the input still requires work.

See also at lighter
version at bob's
Maple tips and examples.

This was an ambitious collision with a newly evolving computer algebra system
last century that proved to be inappropriate for daily classroom use as
supplementary material to the textbook in use at the time, but which remains as a
self-contained development of the subject with symbolic calculation incorporated
into the text. It is not complete, since the final chapter was never filled in.

## Table of Contents

### dewla0.mw
[just a Maple worksheet table of contents, works only locally]

Introduction

Students often have trouble with the vocabulary in this course. After several years of
calculus (high school plus college) where a small vocabulary is applied in many different
situations, they are suddenly confronted with a very different kind of mathematics. Even
though it uses the same language as calculus, now there are many new words to describe
many different concepts. Concepts are very important in this course. Computer algebra
systems can do most of the busywork, but to use them effectively and also understand how
to apply the subject in other fields, one must have a basic understanding of its
foundations, including its vocabulary and the interrelationships among the concepts of
both differential equations and linear algebra. This worksheet attempts to list the basic
vocabulary that should be understood by the end of the semester, including definitions,
explanation, and examples.

#### minimal literacy testing (what you need to know)

### dewla1.mw

Preliminaries: Parameters and Linearity

### dewla2.mw

Differential Equations I

### dewla3.mw

Linear Algebra I: Matrices

### dewla4.mw

Linear Algebra II: Matrices and Linear Systems

### dewla5.mw

Linear Algebra III: Linearity, Independence, Dependence

### dewla6.mw

Linear Algebra IV: Linear (Vector) Spaces, Bases

### dewla7.mw

Linear Algebra V: Linear Transformations and the Eigenvalue Problem;

Differential
Equations II: Decoupling Homogeneous Linear Systems of 1st Order DEQ's

### dewla8.mw

Differential Equations III: Higher Order Linear Differential Equations in 1 Dependent
Variable

### dewla9.mw

Differential Equations IV: Linear Differential Equation Systems