課程資訊

Engineering Mathematics (1)

100-1

ME2001

502 20001

02

Ceiba 課程網頁
http://ceiba.ntu.edu.tw/1001EngMath_1

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

[作業規定]：
1. 請勿抄襲作業。
2. 鼓勵同學間相互討論研究作業內容，但最後繳交之作業必須是由各位同學自己獨力 (用自己的想法及思考邏輯) 所準備與撰寫完成之作業。請同學們使用A4規格淡色紙撰寫作業並且裝訂整齊(釘書針於左上角)以方便助教批改。
3. 作業遲交不收亦不計分。(因為會請助教於作業繳交後公佈解答，所以基於公平性，需要這樣做。)

1. 學習進階數學工具，並懂得如何利用這些數學工具去解決工程上的相關問題。
2. 認識各種常微分方程式，並且知道怎麼找到該方程式的解答。
3. 學習利用矩陣與線性代數方法解系統聯立或是微分方程。

Calculus

Office Hours

1. Zill and Cullen, Differential Equations with Boundary-value Problems, 5th or latest edn., Brooks Cole
2. Strang, Introduction to Applied Mathematics, Wellesley-Cambridge Press

Peter V. O’Neil, Advanced Engineering Mathematics [6th edn.]

(僅供參考)

 No. 項目 百分比 說明 1. Mid-term #1 20% 1st & 2nd order ODE, Laplace (half?) 可能於晚間舉行考試。 2. Mid-term #2 20% Laplace (half?), series solutions, Sturm-Liouville problem 可能於晚間舉行考試。 3. Finals 25% Linear algebra 依照學校期末考時程 4. Homework 35% ~7 or 8 psets

 課程進度
 週次 日期 單元主題 第6週 10/24,10/19 Mid-term #1 第12週 12/05,11/30 Mid-term #2