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