A Dynamic, Interactive Approach to Learning Engineering and Mathematics

The major objectives of this thesis involve the development of both dynamic and interactive applications aimed at complementing traditional engineering and science coursework, laboratory exercises, research, and providing users with easy access by publishing the applications on Wolframs Demonstration website. A number of applications have been carefully designed to meet cognitive demands as well as provide easy-to-use interactivity. Recent technology introduced by Wolfram Mathematica called CDF (Computable Document Format) provides a resource that gives ideas a communication pipeline in which technical content can be presented in an interactive format. This new and exciting technology has the potential to help students enhance depth and quality of understanding as well as provide teachers and researchers with methods to convey concepts at all levels. Our approach in helping students and researchers with teaching and understanding traditionally difficult concepts in science and engineering relies on the ability to use dynamic, interactive learning modules anywhere at any time. The strategy for developing these applications resulted in some excellent outcomes. A variety of different subjects were explored, which included; numerical integration, Green's functions and Duhamel's methods, chaotic maps, one-dimensional diffusion using numerical methods, and two-dimensional wave mechanics using analytical methods. The wide range of topics and fields of study give CDF technology a powerful edge in connecting with all types of learners through interactive learning.