Course title |
微分方程與智慧邏輯 Differential Equation and Intelligent Logics |
Semester |
106-2 |
Designated for |
COLLEGE OF ELECTRICAL ENGINEERING AND COMPUTER SCIENCE GRADUATE INSTITUTE OF ELECTRICAL ENGINEERING |
Instructor |
管傑雄 |
Curriculum Number |
EE5185 |
Curriculum Identity Number |
921 U2630 |
Class |
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Credits |
3.0 |
Full/Half Yr. |
Half |
Required/ Elective |
Elective |
Time |
Monday 2,3,4(9:10~12:10) |
Room |
博理114 |
Remarks |
The upper limit of the number of students: 40. |
Ceiba Web Server |
http://ceiba.ntu.edu.tw/1062EE5185_ |
Course introduction video |
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Table of Core Capabilities and Curriculum Planning |
Association has not been established |
Course Syllabus
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Please respect the intellectual property rights of others and do not copy any of the course information without permission
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Course Description |
本課就是微分方程(II),是討論如何應用智慧邏輯來解微分方程式的相關問題。智慧邏輯是指相關的中國哲學思考邏輯,我們活用這些邏輯來求解微分方程的問題,竟然發現可以完全解決微分方程的所有問題;因此,藉這門課來討論智慧邏輯的使用,進而推展出相對於一般性問題的智慧邏輯,期望學習者從此處學習到解決問題的能力。所謂智慧邏輯的解題方法,指的是具有完備性、解題又準又迅速的方法,這個方法如何得到,可以用下列的課程大綱大致說明其中的程序:
1.智慧邏輯的基本概念:包括專一邏輯及多元化邏輯
2.微分方程的分類與一階多次(線性或非線性)常微分方程式:
a.General form and Normal form.
b.Domain of unique analytic solution and singular curve(boundary curve)
c.Singular point and singular solution
d.型的定義分類與二分法邏輯
e.型走意隨與意走型隨
3.高階線性常微分方程式:
a.Solution space and function space
b.Homogeneous solution space and piecewise continuous function space
c.解之排列組合的邏輯概念(看山又是山,看水又是水)
4.Systems of linear differential equations
a.Elimination method and normalization method
b.Degenerate solution(無法normalization 的system)
c.Systems of first order linear equations
d.完整的解空間邏輯概念
5.線性偏微分方程:
a.Taylor expansion and Fourier series expansion.
b.orthogonal base and quasi orthogonal base
c.eigenspace 與 互補的eigenstate的重新組合
d.完備性的邏輯
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Course Objective |
根據線性代數、微分方程的基本概念及向量空間,整合建構一個完整的微分方程之解題模式。 |
Course Requirement |
基本微積分、線性代數、微分方程-I、向量空間、邏輯簡介。
期末的分組報告需要利用電腦求解微分方程。
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Student Workload (expected study time outside of class per week) |
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Office Hours |
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Designated reading |
待補 |
References |
教科書: 自編講義
參考書目: Differential Equations with Boundary-Value Problems, 8th Edition 8th Edition by Dennis G. Zill (Author), Warren S. Wright (Author)
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Grading |
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