課程資訊
課程名稱
工程數學上
Engineering Mathematics (1) 
開課學期
108-1 
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
502E20001 
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215工綜B01 
備註
本課程以英語授課。
限本系所學生(含輔系、雙修生)
總人數上限:65人 
Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1081ME2001_02 
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課程概述

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: TBA 
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
3. Peter V. O’Neil, Advanced Engineering Mathematics  
指定閱讀
D.G. Zill, Advanced Engineering Mathematics, 6th edn., Jones & Bartlett 
評量方式
(僅供參考)
 
No.
項目
百分比
說明
1. 
Homework 
0% 
Homework problem sets will be assigned for self-practice purposes, they will NOT be graded. 
2. 
Mid-term #1 
25% 
1st, 2nd order ODE. Exam will be held in the evenings (outside of regular schedule). 
3. 
Mid-term #2 
25% 
Laplace transform. Exam will be held in the evenings (outside of regular schedule). 
4. 
Mid-term #3 
25% 
Series solutions, S-L BVP. Exam will be held in the evenings (outside of regular schedule). 
5. 
Final exam 
25% 
Linear algebra all. Held in finals week, follows finals schedule. 
 
課程進度
週次
日期
單元主題
第1週
9/09,9/11  Introduction, 1st order ODE (Ch 1, 2) 
第2週
9/16,9/18  1st order ODE (Ch 2) 
第3週
9/23,9/25  2nd and higher order ODE (Ch 3) 
第4週
9/30,10/02  2nd and higher order ODE (Ch 3) 
第5週
10/07,10/09  Laplace transform (Ch 4) 
第6週
10/14,10/16  Laplace transform (Ch 4) 
第7週
10/21,10/23  Laplace transform (Ch 4) 
第8週
10/28,10/30  Series solutions (Ch 5) 
第9週
11/04,11/06  Series solutions (Ch 5) 
第10週
11/11,11/13  Special functions (Ch 5) 
第11週
11/18,11/20  Sturm-Liouville boundary value problems (Ch 3.9, 12) 
第12週
11/25,11/27  Sturm-Liouville boundary value problems (Ch 3.9, 12) 
第13週
12/02,12/04  Vectors and vector space (Ch 7) 
第14週
12/09,12/11  Matrices and linear algebra (Ch 8) 
第15週
12/16,12/18  Matrices and linear algebra (Ch 8) 
第16週
12/23,12/25  Matrices and linear algebra (Ch 8) 
第17週
12/30,1/01  Systems equations (Ch 10) 
第18週
1/06  Final exam