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    题名: 微分轉換於工程問題教學之應用
    The Application of Differential Transformation Method on Engineering Problems Teaching
    作者: 何星輝
    日期: 2007-07-31
    上传时间: 2009-12-30 10:46:55 (UTC+8)
    摘要: 本計劃旨在利用微分轉換理論編撰一套求解工程問題的教材及軟體,幫助技職體系大學部及研究所同學學習三大工程問題---初始值問題、邊界值問題及特徵值問題並提升工程分析能力。本計劃含四個部分:手算例教材的編撰「簡單的用手算,複雜的用電腦算」是本教材及軟體製作之基本理念。透過精心設計之手算例,建立使用微分轉換法求解三大工程問題的整體性基礎概念。手算例之設計包含(1)對工程問題之統御方程式及初值條件或邊界條件取微分轉換(2)求解遞歸型式之代數方程式(3)對上述解答取反微分轉換。教學軟體之編撰利用微分轉換法求解三大工程問題時,處理初始值問題以數值運算為主;處理邊界問題及特徵值問題則以符號運算為主。大學部之教學軟體以線性微分方程為撰寫重點,研究所之教學軟體則以非線性微分方程及偶合微分方程為撰寫重點。輔助教具之製作藉由輔助教具的實際操作,幫助同學學習微分轉換法觀念及內容,並使得理論與實務能結合為一。教學績效評估以問卷調查方式評量教學績效,作為改進之依據。大學部—含日間部四技及二技;夜間部四技。研究所—以產碩班為主。本計劃—’’微分轉換於工程問題教學之應用’’的特色有三: 其一、有別於其他數值方法,微分轉換法具相當簡易性及直觀性,不但適用於線性微分方程而且亦適用於偶合微分方程及非線性微分方程。其二、教材及軟體之研發係手算例與電腦運算並重。其三、教材深入淺出由大學部之基礎訓練至研究所之論文研究均適用。
    The main purpose of this project is to develop a set of teaching materials and software on solving engineering problems using differential transformation method. This software provides the undergraduate and graduate students an easy way to study three major engineering problems —initial value problem, boundary value problem and eigen value problem— and to uplift their engineering analytical ability. There are four parts in this project as follows. Compilation of teaching materials of hand-calculating examples The basic idea to develop this teaching materials is " easy problem by hand, but difficult one by computer ". Through the practice of elaborately designed hand-calculating examples, students can entirely catch the basic concept of solving three major engineering problems by differential transformation. Hand-calculating examples design include the following steps: (i) take differential transformation on governing equations and initial conditions or boundary conditions; (ii) solve the recursive algebraic equation; (iii) take inverse differential transformation on the results solved in the previous step. Compilation of teaching software When solving three major engineering problems, we usually apply numeric computation to initial value problem, while apply symbolic computation to boundary value problem and eigen value problem. In compiling the software we lay stress on linear system for undergraduate students but lay stress on non-linear system and time-varying system for graduate students. Auxiliary teaching tools manufacturing Using those auxiliary teaching tools, students can overcome some difficulties in learning Differential Transform and combine theory with practice together. Teaching and learning estimation Using question paper investigation, we can estimate teaching and learning effect and have some improvement. The estimation includes both undergraduate and graduate students. This project —The Application of Differential Transformation Method on Engineering Problems Teaching— has three distinguishing features: (i) compared with other numeric method, differential transformation provides an easy and intuitive way to study linear, non-linear and coupled differential equations; (ii) both handcalculating examples and computercalculating software are considered; (iii) these teaching materials are quite applicable to both undergraduates and graduates.
    显示于类别:[機械工程系所] 研究計畫

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