工程數學(1)
Engineering Mathematics(1)
| 節 | 週三 |
|---|---|
1 08:00–08:50 | 工程數學(1) 3 節連堂 |
2 09:00–09:50 | |
3 10:10–11:00 |
* 根據陽明交大上課時間表所列
This is the first part of the two-semester course designed for sophomore mechanical engineering students. The materials covered during the semester include ordinary differential equations as well as Laplace transform.
Calculus
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Homework: 40% Midterm #1: 20% Midterm #2: 20% Final exam: 20% **學期總成績58分以下(含58分)恕不調分,請勿前來要求給分** **每次作業成績在更改後公佈於e3本課程網頁,如有誤,請於每次成績公布後兩星期內聯絡助教更改,逾期恕不接受任何更改**
First-Order ODEs
Basic concepts, Separable ODEs, Exact ODEs, Linear ODEs
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 finction, Convolution, Integral equations
| 週次 | 主題 |
|---|---|
| 第 1 週 | Basic concepts, Separable ODEs 1/20 |
| 第 2 週 | Exact ODEs, Linear ODEs 1/27 |
| 第 3 週 | Homogeneous linear ODEs with constant coefficients 2/3 |
| 第 4 週 | Euler-Cauchy equations 2/24 |
| 第 5 週 | Nonohomogeneous euqations 3/3 |
| 第 6 週 | 1st Midterm 3/10 |
| 第 7 週 | Homogeneous linear ODEs with constant coefficients 3/17 |
| 第 8 週 | Nonhomogeneous linear ODEs 3/24 |
| 第 9 週 | Solution by Variation of Parameter 3/31 |
| 第 10 週 | Basics of matrices and vectors, system of ODEs in engineering applications, Power series method, Legendre's equation, Legendre polynomials 4/7 |
| 第 11 週 | Basic theory of systems of ODEs 4/14 |
| 第 12 週 | 2nd Midterm 4/21 |
| 第 13 週 | Power series method, Legendre's equation, Legendre polynomials 4/28 |
| 第 14 週 | Frobenius method, Bessel equation 5/5 |
| 第 15 週 | Laplace transform, First shifting theorem 5/12 |
| 第 16 週 | Transforms of derivatives and integrals, unit Step function, second shifting method 5/19 |
| 第 17 週 | Dirac's delta finction, convolution, integral equations 5/26 |
| 第 18 週 | Final Exam 6/2 |
No specific textbook is appointed, but you may refer to the reference below: "Advanced Engineering Mathematics" by Erwin Kreyszig, 10th Ed., John Wiley & Sons, 2011. "Advanced Engineering Mathematics" by Dennis G. Zill, 6th Ed., Jones & Bartlett Learning. ※ 請同學遵守智慧財產權觀念及勿使用非法影印教科書。
- 地點
- EE473
- 時間
- By appointment
- 聯絡方式
- Email: liaoyh@nctu.edu.tw