Differential Equations with Linear Algebra:
Vocabulary and Concepts

robert t jantzen

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]

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)

Preliminaries: Parameters and Linearity

Differential Equations I

Linear Algebra I: Matrices

Linear Algebra II: Matrices and Linear Systems

Linear Algebra III: Linearity, Independence, Dependence

Linear Algebra IV: Linear (Vector) Spaces, Bases

Linear Algebra V: Linear Transformations and the Eigenvalue Problem;
Differential Equations II: Decoupling Homogeneous Linear Systems of 1st Order DEQ's

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

Differential Equations IV: Linear Differential Equation Systems