Interdisciplinary Laboratory Course in Non-Linear Dynamics

在过去的二十年里，几何方法在复杂动力系统分析中的重要性已经被认识到。随着高速计算机的出现，这些方法现在正被应用于各种领域。然而，本科课程中现有的课程并没有利用这些强大的工具，只强调解微分方程的传统方法。该项目将在本科生水平上开发一门创新的、跨学科的、以实验室为基础的非线性动力系统课程。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。这门课程的创新方面将是跨学科的实验练习以及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实验室实验，作为课程讲课的补充。这些实验来自动力系统理论的多个领域，包括在物理、化学、生物学以及电气和土木工程中的应用。这些实验被用来强化课堂上学到的材料，并说明看似不相关的物理系统之间的潜在相似性。本课程将作为其他大学的样板，并将提供经过测试的材料，可用于构建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.