課程資訊

Engineering Mathematics (1)

111-1

ME2001

502E20001

02

3.0

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

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.

Calculus

6~9 hrs
Office Hours

1. Zill and Cullen, Differential Equations with Boundary-value Problems, 5th edn., Brooks Cole
2. Strang, Introduction to Applied Mathematics, Wellesley-Cambridge Press
3. O'Neil, Advanced Engineering Mathematics, 4th edn., PWS

D.G. Zill, Advanced Engineering Mathematics, 7th edn., Jones & Bartlett (Chap 1-5, 7, 8, 10, 12)

(僅供參考)

 No. 項目 百分比 說明 1. Mid-term exam (I) 33% Closed book, no calculators. Held outside regular hours, usually in the evenings. 2. Mid-term exam (II) 33% Closed book, no calculators. Held outside regular hours, usually in the evenings. 3. Final exam 34% Closed book, no calculators. Held in finals week, follows final exam schedule. 4. Homework problem sets 0% Practice, not graded.

 上課形式 以錄影輔助, 提供學生彈性出席課程方式 作業繳交方式 考試形式 其他 由師生雙方議定
 課程進度
 週次 日期 單元主題 第1週 09/05, 09/07 Introduction, 1st order ODE (Zill Chap 1, 2) 第2週 09/12, 09/14 2nd and higher order ODE (Zill Chap 3) 第3週 09/19, 09/21 2nd and higher order ODE (Zill Chap 3) 第4週 09/26, 09/28 Laplace transform (Zill Chap 4) 第5週 10/03, 10/05 Laplace transform (Zill Chap 4) 第6週 10/10, 10/12 Laplace transform (Zill Chap 4) 第7週 10/17, 10/19 Series solutions and special functions (Zill Chap 5) 第8週 10/24, 10/26 Series solutions and special functions (Zill Chap 5) 第9週 10/31, 11/02 Sturm-Liouville boundary value problems (Ch 12) 第10週 11/07, 11/09 Sturm-Liouville boundary value problems (Ch 12) 第11週 11/14, 11/16 Vectors and vector space (Zill Chap 7) 第12週 11/21, 11/23 Matrices and linear algebra (Zill Chap 8) 第13週 11/28, 11/30 Matrices and linear algebra (Zill Chap 8) 第14週 12/05, 12/07 Matrices and linear algebra (Zill Chap 8) 第15週 12/12, 12/14 Systems differential equations (Zill Chap 8, 10) 第16週 12/19 Final exam