工程數學(一)
Engineering Mathematics (I)
| 節 | 週一 | 週三 |
|---|---|---|
2 09:00–09:50 | 工程數學(一) EE130（光復） | |
3 10:10–11:00 | 工程數學(一) EE130（光復） 2 節連堂 | |
4 11:10–12:00 |
* 根據陽明交大上課時間表所列
This is the first half of Engineering Mathematics designed to be a full academic year course. This course is to establish the fundamental mathematical knowledge for sophomore mechanical engineering students. Ordinary differential equations and Laplace transforms will be covered in this course.
Calculus
無備註
All of the course material will be available on new e3 including lecture notes and homework solutions. All the material covered in class will be repeated again in mandarin.
Homework: 20% Midterm 1 & 2: 25% each Final: 30%
Second-Order ODEs
Homogeneous linear ODEs with constant coefficients, Euler-Cauchy equations, Existence and uniqueness of solutions, Wronskian, Nonhomogeneous ODEs, Solution by variation of parameters
Higher Order Linear ODEs
Homogeneous linear ODEs, Homogeneous linear ODEs with constant coefficients, Nonhomogeneous linear ODEs
System of ODEs
Basics of matrices and vectors, System of ODEs in engineering applications, Basic theory of systems of ODEs
Series Solutions of ODEs
Power series method, Legendre's equation, Legendre polynomials, Frobenius method, Bessel equation
Laplace Transforms
Laplace transform, First shifting theorem, Transforms of derivatives and integrals, Unit Step function, Second shifting method, Dirac's delta function, Convolution, Integral equations
First-Order ODEs
Basic concepts, Separable ODEs, Exact ODEs, Linear ODEs
| 週次 | 主題 |
|---|---|
| 第 1 週 | Basic concepts, Separable ODEs 9/9 9/11 |
| 第 2 週 | Exact ODEs, Linear ODEs 9/16 9/18 |
| 第 3 週 | Homogeneous linear ODEs with constant coefficients 9/23 9/25 |
| 第 4 週 | Euler-Cauchy equations 9/30 10/2 |
| 第 5 週 | Nonhomogeneous equations 10/7 10/9 |
| 第 6 週 | Review, 10/16: 1st Midterm 10/14 10/16 |
| 第 7 週 | Homogeneous linear ODEs with constant coefficients 10/21 10/23 |
| 第 8 週 | Nonhomogeneous linear ODEs 10/28 10/30 |
| 第 9 週 | Solution by Variation of Parameter 11/4 11/6 |
| 第 10 週 | Basics of matrices and vectors, system of ODEs in engineering applications, Power series method 11/11 11/13 |
| 第 11 週 | Power series method, Legendre's equation 11/18 11/20 |
| 第 12 週 | Review, 11/27: 2nd Midterm 11/25 11/27 |
| 第 13 週 | Legendre polynomials, Basic theory of systems of ODEs 12/2 12/4 |
| 第 14 週 | Frobenius method, Bessel equation 12/9 12/11 |
| 第 15 週 | Laplace transforms, First shifting theorem 12/16 12/18 |
| 第 16 週 | Transforms of derivatives and integrals, unit Step function, second shifting method 12/23 12/25 |
| 第 17 週 | Dirac's delta function, convolution, integral equations, review 1/1: Holiday 12/30 1/1 |
| 第 18 週 | 1/8: Final Exam 1/6 1/8 |
No specific textbook is appointed, but you may refer to the references below: "Advanced Engineering Mathematics" by Erwin Kreyszig, 10th Ed., John Wiley & Sons, 2011. "Advanced Engineering Mathematics" by Dennis Zill and Warren Wright, 5th Ed., Jones & Bartlett Learning. "Advanced Engineering Mathematics" by Peter V. O'neil, 8th Ed., CENGAGE Learning. ※ Please don't make copies in any form.
- 地點
- EE453
- 時間
- By appointment
- 聯絡方式
- Ext: 55134 Mail: jchang40@nctu.edu.tw