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課程名稱 |
常微分方程導論
Introduction to Ordinary Differential Equations |
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開課學期 |
105-1 |
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授課對象 |
理學院 數學系 |
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授課教師 |
陳俊全 |
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課號 |
MATH2217 |
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課程識別碼 |
201 49690 |
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班次 |
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學分 |
4 |
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全/半年 |
半年 |
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必/選修 |
必修 |
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上課時間 |
星期二8,9(15:30~17:20)星期五1,2(8:10~10:00) |
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上課地點 |
新102新102 |
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備註 |
教學改善計畫課程，有教學助理實施小班輔導。
MATH2205常微分方程導論得用此課替代。
總人數上限：100人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1051MATH2217_ODE |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
The course will cover the following topics.
1. Introduction.
2. First Order Differential Equations.
3. Second Order Linear Equations.
4. Higher Order Liner Equations.
5. Series Solutions of Second Order Linear Equations.
6. The Laplace Transform.
7. Systems of First Order Linear Equations.
8. Numerical Methods.
9. Nonlinear Differential Equations and Stability. |
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課程目標 |
This course introduces basic theory and applications of ordinary differential equations. |
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課程要求 |
Linear Algebra and Calculus |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
Textbook: R.K. Nagle, E.B. Saff and A.D. Snider, Fundamentals of Differential Equations and Boundary Value Problems |
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參考書目 |
I-Liang Chern, lecture notes.
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
homework |
25% |
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2. |
midterm exam |
35% |
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3. |
final exam |
40% |
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週次 |
日期 |
單元主題 |
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第1週 |
9/13,9/16 |
1. Introduction: 一點歷史,ODE 的動態觀點, ODE 可揭露自然科學之定律及事務間關係,Tacoma Narrows Bridge
2. Linear 1st-order equation |
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第2週 |
9/20,9/23 |
1. Metric space, open set, closed set
2. Compact and sequential compact
3. Continuity and uniform continuity
4. Linear 1st order equation |
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第3週 |
9/27,9/30 |
1. Separable equation, method of separation of variables
2. Exact equation |
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第4週 |
10/04,10/07 |
1. Exact equation, three proofs for "Test for Exactness" |
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第5週 |
10/11,10/14 |
1.Special integrating factor
2.Substitution and transformation |
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第6週 |
10/18,10/21 |
Existence and uniqueness of 1st order equations |
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第7週 |
10/25,10/28 |
Chapter 3 Math modeling and numerical methods
1. Population models
2.Braschistochrone problem and calculus of variations
3.Heating and cooling of buildings
4.Euler method |
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第8週 |
11/01,11/04 |
Chapter 4 Linear 2nd-order equations
1. Operator method
2. Linear independence of functions, Wronskian
3. Uniqueness of initial value problems for linear 2nd-order equations
4. Homogeneous equations with constant coefficients, general solution |
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第9週 |
11/08,11/11 |
1.Auxiliary equation (characteristic equation): distinct real roots; repeated root; complex roots and complex exponential function
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第10週 |
11/15,11/18 |
Uniqueness Theorem for initial value problems, Wronskian, linear independence of functions |
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第11週 |
11/22,11/25 |
Method of undetermined coefficients, method of variation of parameters, method of reduction of order, Cauchy-Euler equations |
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第12週 |
11/29,12/02 |
Mechanical vibrations: damping and resonance, beats |
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第13週 |
12/06,12/09 |
Chapter 6 Higher-Oorder linear equations: uniqueness theorem, Wronskian, fundamental solution set, general form of the solutions, solutions for equation with constant coefficients |
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第14週 |
12/13,12/16 |
Chapter 9 First-order linear systems and matrix methods:
uniqueness theorem, Wronskian, fundamental solution set, general solution |
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第15週 |
12/20,12/23 |
system with constant coefficients, characteristic equation, distinct eigenvalue, repeated eigenvalue, complex eigenvalue, matrix exponential function |
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第16週 |
12/27,12/30 |
Matrix exponential function, non-homogeneous systems;
Chapter 12, Stability of autonomous systems:
critical points for linear system |
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第17週 |
1/03,1/06 |
Competition system, Lyaponuv's method, energy method;
Chapter 7, Laplace transform |
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第18週 |
1/10 |
Almost linear system |
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