A Mathmatics Course in Scientific Simulation

科学模拟中的数学课程

• 批准号: 9952625
• 负责人: Mike O'Leary
• 金额: $ 6.9万
• 依托单位: Towson University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-04-01 至 2003-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9952625&HistoricalAwards=false
• 关键词: Mathmatics; Course; Scientific; Simulation

Mathematical Sciences (21)This project is developing, implementing, evaluating, and disseminating a two course sequence in scientific simulation. This sequence involves modeling, numerical analysis, and computer programming. The first purpose of the course is to teach students how to solve extended problems that require them to learn how to formulate the problem; decide on the appropriate mathematical tool; implement the method; obtain, interpret, and communicate the results; and use that information to refine the model. The second purpose is for students to learn how to implement modern technology in their problem solving techniques. The overall motivation for the course is that most real world problems are solved with the aid of technology and require these types of problem solving methodologies.In this course students are learning the basics of numerical analysis, including Simpson's rule, Runge-Kutta methods, and finite difference models. The course also includes a discussion of object-oriented C++ programming and shows how computer objects can be used to simplify scientific programming. The primary focus of this multidisciplinary course is on simulations such as a swinging pendulum and catalyzed chemical reactions which can be taken from the sciences. The course is being adapted from the course "Experimental Mathematics" at Northwestern University.

数学科学（21）该项目正在开发，实施，评估和传播科学模拟的两门课程。这个序列包括建模、数值分析和计算机编程。该课程的第一个目的是教学生如何解决扩展问题，这要求他们学习如何制定问题;决定适当的数学工具;实施方法;获得，解释和交流结果;并使用这些信息来完善模型。第二个目的是让学生学习如何在解决问题的技巧中应用现代技术。本课程的总体动机是，大多数真实的世界的问题都是在技术的帮助下解决的，需要这些类型的问题解决方法。在这门课程中，学生将学习数值分析的基础知识，包括辛普森规则，龙格库塔方法和有限差分模型。该课程还包括面向对象的C++编程的讨论，并展示了如何使用计算机对象来简化科学编程。这个多学科课程的主要重点是模拟，如摆动摆和催化化学反应，可以从科学。该课程改编自西北大学的“实验数学”课程。