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The fundamental research to introduce environment simulation for the mathematical teaching in Technical Colleges

高职数学教学引入环境模拟的基础研究

基本信息

批准号：
10680299
负责人：
TUBOKAWA Takehiro
金额：
$ 2.24万
依托单位：
Fukui National College of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1998
资助国家：
日本
起止时间：
1998 至 1999
项目状态：
已结题

项目摘要

The aims of this research are to investigate mathematics used for the environment simulation and to adopt it in applied mathematics.(1) We picked out actual conditions of the modeling of fundamental phenomena in physics or chemistry after analyzing the mathematical model concerning environment science. We examined the large-scale computer simulation skill in the global atmosphere-ocean circulation model. Our object was CCM3. We extracted mathematical techniques used for it. These techniques were compared with the course of the mathematical teaching. From this process, we found lots of teaching materials of both differential equations and numerical analysis. It is important to made a differential equation from the phenomenon, to solve the equation by numerical method and to examine the result. CCM3 shows the convection and diffusion of the heat through the 3-dimensional model, and besides it consumes computer resources in a large quantity. We tried simplifying this model into the 1 or 0 dimensional model. Stella, a computer language for system dynamics, was adopted for this. A new program is under development now.(2) We took the circulation of carbon dioxide as a simple model that is treated easily. Its global circulation hasn't been made clear completely yet. At present, the proposed model is comparatively simple and, moreover, easy to be handled as a suitable material in the teaching of math.(3) We have tried getting the graph of the simulation result. We are planning to open our new programs to the public in the Net.This research made it clear that there were a lot of teaching materials suitable for applied mathematics in the environment science. We will continue to search for much more materials of applied mathematics.

本研究的目的是探讨数学用于环境模拟，并采用它在应用数学。(1)通过对环境科学数学模型的分析，找出了物理、化学基本现象建模的实际条件。本文探讨了全球海气环流模式中的大尺度计算机模拟技术。我们的目标是CCM3。我们提炼出了用于数学教学的数学技术，并将这些技术与数学教学过程进行了比较。在这个过程中，我们发现了大量的微分方程和数值分析的教材。从这一现象出发，建立微分方程，用数值方法求解微分方程，并对结果进行检验，是十分重要的。CCM3通过三维模型显示热量的对流和扩散，此外，它消耗了大量的计算机资源。我们尝试将这个模型简化为一维或零维模型。Stella是一种用于系统动力学的计算机语言。一个新的计划正在制定中。(2)我们把二氧化碳的循环作为一个简单的模型，很容易处理。它的全球流通还没有完全弄清楚。目前，所提出的模型比较简单，而且，易于处理，作为一个合适的材料在数学教学。(3)我们试着得到了仿真结果的图形。本课题的研究结果表明，在环境科学领域中，适合应用数学的教材有很多。我们将继续寻找更多的应用数学材料。