Topic Maps Used to Present Interrelationships in Dynamic Linear Systems

The study of linear physical systems is one of the topics in engineering with a rich interplay among the topics and no natural order in which to present the material. In this paper, we describe a system that uses topic maps to emphasize these interrelationships without imposing an arbitrary hierarchy on the material presented. For example, in terms of types of systems, mechanical systems can be taught first, or electrical. In terms of transforms, Laplace can be taught first, or Fourier, or even the Z-transform. There are also many relationships between topics. Examples include the transforms mentioned previously, the different types of physical system (electrical, mechanical, thermal...), and different solution methods such as state-space and transfer functions. By their very nature, textbooks must present and follow a linear path through the material, and any two textbooks are likely to follow very different paths. Web-based presentation of the material removes part of this problem because the material need not be presented linearly, but raises the prospect of a chaotic portrayal of the subjects because HTML links are merely from text to text and have no inherent meaning. Another way to present such interrelated ideas is through the use of topic maps. Topic maps are used to represent these interrelationships using topics (concepts), associations (the relationships between topics) and occurrences (information, e.g., web pages, relating to the topics). This is distinct from concept maps and other commonly used visual methods for organizing information in that the ideas need not be hierarchical; for example Fourier Transforms are not a subset of Laplace transforms (or vice-versa) as is presented in most textbooks. In addition the topics have certain roles in the association that give the link meaning, a clear advantage over traditional HTML hyperlinks and other methods. We have developed a system using HTML, PHP, JavaScript and XML that enables a user to author a topic map, as well as to present a graphical visualization of that map. When visualizing a map, a topic is selected (by clicking on it), and all related topics are displayed around it. Included in the display are the associations and roles played by each topic in that association. Topics can also have other information (occurrences in the form of HTML links, simulations...) that give explanatory detail about the topic, including descriptions of how it is related to other, associated, topics. While many textbooks (and even web-based presentations) have only short sections describing the interrelationships between topics, this system puts the relationship at the core of the presentation of the material to make it more clear why a particular topic is being learned and how it fits into the larger context of linear systems.