Interdisciplinary Laboratory Course in Non-Linear Dynamics

在过去的二十年中，几何方法在 的 复杂动力系统的分析 被认可。 随着高速计算机的出现，这些方法现在被应用于各种领域。 然而，现有的课程在本科课程不利用这些强大的工具，只强调传统的方法来解决微分方程。该项目将开发一种创新的， 跨学科 基于实验 当然 非线性动力系统的课程 该课程旨在向物理，数学，生物，化学和工程科学的本科生教授动力系统分析的几何方法，并建立对此类系统行为的直观理解。 该课程的创新方面将是跨学科的，实验室练习和计算机和可视化技术的应用。 开发工作的一个重要部分是创建补充课程讲座的实验室实验。 这些实验是从一些 的 地区 动力系统理论 包括在物理、化学、生物、电气和土木工程中的应用。 这些实验用于强化课堂上所学的材料，并说明看似无关的物理系统之间的潜在相似性。 这门课程将作为其他大学的一个模式，并将产生测试材料，可用于建立类似课程的实验室组成部分。

During the past two decades the importance of geometrical methods in the analysis of complex dynamical systems have been recognized. With the advent of high speed computers, these methods are now being applied in a variety of fields. Houever, existing courses in the undergraduate curriculum do not utilize these powerful tools and only emphasize traditional methods for solving differential equations. This project will develop an innovative, interdisciplinary laboratory-based course on nonlinear dynamical systems at the undergraduate level. The course is designed to teach the geometrical methods of dynamical systems analysis to undergraduates in physics, mathematics, biology, chemistry and the engineering sciences and to build an intuitive understanding of the behavior of such systems. The innovative aspects of the course will be interdisciplinary, experimental laboratory exercises and applications of computers and visualization techniques. A significant portion of the development effort is to create laboratory experiments which complement course lectures. These experiments are drawn from a number of areas of dynamical systems theory, including applications in physics, chemistry, biology and electrical and civil engineering. The experiments are used to reinforce the material learned in class and to illustrate the underlying similarities between seemingly unrelated physical systems. This course will serve as a model for other universities and will produce tested material that can be used to build the laboratory component for similar courses.