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課程名稱 |
工程數學一
Engineering Mathematics (Ⅰ) |
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開課學期 |
112-1 |
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授課對象 |
生物資源暨農學院 生物環境系統工程學系 |
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授課教師 |
許少瑜 |
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課號 |
BSE2003 |
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課程識別碼 |
602 20310 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
必帶 |
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上課時間 |
星期三2,3,4(9:10~12:10) |
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上課地點 |
農工繪圖室 |
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備註 |
英語授課
限生農學院學生(含輔系、雙修生)
總人數上限：57人 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
This course is an introduction to the methods of mathematical physics used in the environmental and hydrologic sciences. It is presented in the context of basic mathematical methods and their application in the environmental and hydrologic contexts. The lecture introduces ordinary differential equations (ODEs) and vectors. Both analytical and numerical methods of solution of differential equations are introduced.
Analytical solutions
1. First-order ODEs
2. Second-order Linear ODEs
3. Higher Order Linear ODEs
4. System of ODEs (Eigenvalue Problems for Systems of ODEs)
Series Solutions
5. Series Solutions of ODEs (Special Functions)
Transforms
6. Laplace Transforms
Some of the contents in the below chapters are merged into chapters 1 to 6
Linear algebra
7. Matrices, Vectors, Determinants, Linear system
8. Eigenvalue and Eigenvectors
9. Vector differential and integral calculus (Optinal)
Numerical methods
20. Numeric Linear Algebra (20.6 – 20.8)
21. Numerics for ODEs (21.1 – 21.3) |
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課程目標 |
Primarily introduces analytical methods for solving commonly used mathematical equations in the fields of physics and engineering.
Cultivates students' abilities to interpret and handle mathematical equations in their professional fields. |
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課程要求 |
Calculus |
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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指定閱讀 |
Erwin Kreyszig, Advanced Engineering Mathematics, Tenth Edition, Wiley |
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參考書目 |
Erwin Kreyszig, Advanced Engineering Mathematics, Tenth Edition, Wiley |
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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. |
Midterm |
55% |
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2. |
Homework |
20% |
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3. |
Final |
25% |
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針對學生困難提供學生調整方式 |
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上課形式 |
以錄影輔助 |
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作業繳交方式 |
延長作業繳交期限 |
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考試形式 |
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其他 |
由師生雙方議定 |
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週次 |
日期 |
單元主題 |
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第1週 |
9/6 |
Introduction
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第2週 |
9/13 |
Linear 1st order ODEs (modeling, separation variables, Euler’s method) |
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第3週 |
9/20 |
Linear 1st order ODEs (Linear Equ., Exact Equ., Bernoulli Equ.) |
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第4週 |
9/27 |
Linear 2nd ODEs with constant coefficients (homogeneous ODE, non-homogeneous ODE, Mass-Spring System) |
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第5週 |
10/4 |
Linear 2nd ODEs with constant coefficients (non-homogeneous ODE, Resonance) |
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第6週 |
10/11 |
Midterm |
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第7週 |
10/18 |
System of Linear ODEs （Eigenvalue, Eigenvector, system ODEs with constant coefficients） |
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第8週 |
10/25 |
System of Linear ODEs (homogeneous and nonlinear) |
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第9週 |
11/1 |
Linear 2nd ODEs with variable coefficients and serious solutions (special functions) I |
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第10週 |
11/8 |
Linear 2nd ODEs with variable coefficients and serious solutions (special functions) II |
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第11週 |
11/15 |
No class 校慶停課 |
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第12週 |
11/22 |
Midterm |
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第13週 |
11/29 |
Laplace transform （Linearity, first shifting theory, derivatives and integrals) |
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第14週 |
12/6 |
Laplace transform (Unit step function, Heaviside function, second shifting theory) |
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第15週 |
12/13 |
Laplace transform (convolution, solve ODEs) |
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第16週 |
12/20 |
Final |
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