課程資訊
課程名稱
工程數學上
Engineering Mathematics (1) 
開課學期
110-1 
授課對象
機械工程學系  
授課教師
黃信富 
課號
ME2001 
課程識別碼
502 20001 
班次
02 
學分
3.0 
全/半年
全年 
必/選修
必修 
上課時間
星期一3,4(10:20~12:10)星期三2(9:10~10:00) 
上課地點
工綜211工綜211 
備註
限本系所學生(含輔系、雙修生)
總人數上限:55人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1101ME2001_02 
課程簡介影片
 
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課程概述

NOTE: My lectures will be given in Mandarin this year. NOT English.

If you are interested in enrolling this class, please email me using the following title:
[Eng. Math. Reg.] Student ID BXX502XXX Name XXXXX

Sending me an email does not guarantee that you will definitely be added to the class since we also need to consider the size of this class, student seniority, department priority...etc.

Nonetheless, there are still vacancies in two out of the four classes offered by the Mech. Eng. Dept. You may also want to check out those classes first.

For those still interested in enrolling our class, you MUST attend our first on-line meeting or lecture on Sep 22, 2021 starting 9:10 AM. We will be using on-line meeting software to hold that meeting. Details will be given to you after you email me first. I will be adding people only on Sep 22.

重要(2021/09/14),關於加簽:由於本班已額滿,且還有其他班別可以選擇,因此傾向不積極加簽,請同學們盡量選擇尚未額滿的班別。

如果真的很希望加簽本班,9/17公布二階結果之後,請email來信,主旨標題欄請以下列格式撰寫:
[工數加簽登記] 學號 BXX502XXX 姓名 XXXXX

注意,來信登記不保證一定簽你。但若要加簽,請一定要在 9/22 週三上午 9:10 第一堂課參與線上會議課程。線上會議資訊會另行通知。

9/22 有來的才 **有機會** 加簽(不見得全簽,要參考班級人數、高年級人數、本系外系...等因素),之後不再加簽,以維持本班人數合理,以及各班次人數跟助教工作量穩定。

NOTE: This class may be conducted in-person or on-line. Which form of teaching depends on the development of the COVID-19 pandemic. Form of exam and grading policies may also vary accordingly.

In this course, we shall introduce series of mathematical methods and techniques that are applied in solving mathematical governing equations frequently encountered in modern science and engineering analyses. The lectures and classes will mostly be devoted to solving problems. However, emphasis will also be placed on the connections between mathematics and engineering applications, the modeling of the physical problems using mathematical equations, and finally the physical significances of the mathematical solutions obtained through problem solving.

Topics discussed this semester generally include:
1. First Order Ordinary Differential Equations
Introduction to engineering mathematics and mathematical modeling;
Definitions and concepts of differential equations;
Separable, linear, and exact differential equations;
Integrating factors;
Some special equations;
Applications of 1st order ODE

2. Second Order Linear Ordinary Differential Equations
2nd order linear ODE and the reduction of order;
The constant coefficient homogeneous linear equation and Euler’s equation;
Nonhomogeneous 2nd order linear ODEs and higher order equations;
Applications of 2nd order linear ODEs

3. The Laplace Transform
Fundamentals of Laplace transform;
Solving IVPs with Laplace transform;
1st and 2nd shifting theorems;
Convolution and integral/integro-differential equations;
Heaviside, unit impulse, and the Dirac delta functions;
More solution techniques using Laplace transform

4. Series Solutions
Power series solutions: IVPs and recurrence relations;
The method of Frobenius: singular points, second solutions

5. Orthogonal expansions and BVPs
The Sturm-Liouville problem and orthogonal expansions;
Special functions: Bessel and Legendre functions

6. Fundamentals of Linear Algebra
Vector algebra and vector products;
The vector space: linear independence, spanning sets, and dimension;
Matrices and operations of matrices;
Row and column spaces of a matrix;
Homogeneous systems of linear equations and its solution space;
Nonhomogeneous systems of linear equations;
Inverse and determinant of matrices;
Cramer’s rule;
Eigenvalues, eigenvectors, and diagonalization of matrices;
Orthogonal and symmetric matrices
Solving 1st and 2nd order systems differential equations using diagonalization  

課程目標
To learn advanced mathematical tools as well as how to apply these mathematical tools in solving real life science and engineering problems. Our study will focus on differential equations and linear algebra for this semester. 
課程要求
Calculus 
預期每週課後學習時數
 
Office Hours
另約時間 備註: Please e-mail me to set up an appointment. 
參考書目
1. Zill and Cullen, Differential Equations with Boundary-value Problems, 5th edn., Brooks Cole
2. Strang, Introduction to Applied Mathematics, Wellesley-Cambridge Press 
指定閱讀
D.G. Zill, Advanced Engineering Mathematics, 7th edn., Jones & Bartlett  
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Mid-term exam #1 
33% 
Held outside of regular hours, e.g., in the evenings. 
2. 
Mid-term exam #2 
33% 
Held outside of regular hours, e.g., in the evenings. 
3. 
Final exam 
34% 
Follows final exam schedule. 
4. 
Problem sets 
0% 
Problem sets will be assigned but not graded. The semester grade solely depends on the three exams. 
 
課程進度
週次
日期
單元主題
第1週
9/22  Introduction (WED) 
第2週
9/27,9/29  1st order ODE 
第3週
10/04,10/06  2nd and higher order ODE 
第4週
10/11,10/13  2nd and higher order ODE 
第5週
10/18,10/20  Laplace transform 
第6週
10/25,10/27  Laplace transform 
第7週
11/01,11/03  Laplace transform 
第8週
11/08,11/10  Series solutions and special functions 
第9週
11/15,11/17  Series solutions and special functions 
第10週
11/22,11/24  Sturm-Liouville boundary value problems 
第11週
11/29,12/01  Sturm-Liouville boundary value problems 
第12週
12/06,12/08  Vectors and vector space 
第13週
12/13,12/15  Matrices and linear algebra 
第14週
12/20,12/22  Matrices and linear algebra 
第15週
12/27,12/29  Matrices and linear algebra 
第16週
1/03  Systems equations (MON) 
第17週
1/10  Final exam