Add to ORKGA new text in any area of mathematics requires an explanation: a new text in linear differential equations may require an apology as well. There may not be a more throughly documented area of natural science, and any new attempt may well be regarded with enough skepticism to ask pointedly what particular merits inhere in this approach which are not to be found in others. The premise underlying this effort is that the demonstration of the strong interconnection between linear algebra and the theory of linear differential equations benefits the student more than even the most complete cataloging of techniques of solutions of these equations. This premise is motivated by the belief that such an approach builds understanding of the underlying t...