Integrated Physical, Mathematical and Computer Modeling of Simple Dynamical Systems: Constructing an Understanding of the Earth

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Through this project, the laboratory experiences in two classes, an introductory earth systems science course and an upper-level geochemistry course, are redesigned. Both courses emphasize the behavior and interrelationships of natural systems and demonstrate to students the power of a quantitative approach to problem-solving in science. By combining simple physical models with mathematical modeling (for upper-level students) and simple computer modeling (both levels), students not only gain a deeper understanding of the particular system they've studied, but gain insight into an entire class of problems with many practical applications. In the intro-level course, students build identical physical and computer models of a one-box dynamical system. This approach has several advantages: (1) Students gain confidence in computer modeling by working with a system that they already understand well. (2) Computer modeling is creative, students both analyze a situation and design its solution. (3) The one-box model is a flexible system, easily adapted for study of a wide variety of natural phenomena. (4) With appropriate software, model building can be carried out by introductory-level students. (5) The mathematical description of a one-box model is well within the grasp of students with basic calculus skills, and geology majors can gain experience in applying mathematical techniques to problems of practical interest. This exercise is open-ended. Students begin on a firm platform of observation and are armed with theory and computer skills, thus allowing them to explore a range of problems whose solutions require creative and critical thinking. This project provides seven new PowerMacintosh computers, two printers, modeling software, and network hardware.