工程數學（一）
Engineering Mathematics(Ⅰ)
| 節 | 週二 | 週三 |
|---|---|---|
2 09:00–09:50 | 工程數學（一） EE106（光復） | |
3 10:10–11:00 | 工程數學（一） EE106（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 aims to establish the fundamental mathematical knowledge of sophomore mechanical engineering students. Ordinary differential equations and Laplace transforms will be covered in this course. By the end of the semester, students are expected to be able to: 1. Analyze engineering problems via mathematical approaches 2. Write governing equations for physical problems, including actual systems 3. Solve the governing equations by mathematical techniques 4. Improve English listening and reading skills and be ready to take more EMI courses 5. Use communication skills and work as a team
Calculus
無備註
A. All of the course materials will be available on e3, including lecture notes and homework solutions. All the materials covered in class will be repeated again in Mandarin right after the English version. B. The derivations of theories will be posted on e3 and won't be included in classes. C. Homework will be graded by effort, not by correctness, while all late submissions receive only half of the total points. Late submissions will not be accepted if they are not for the upcoming exam. D. No specific grade distribution is required for this course. ※ For all quarantined students as well as those who are taking this course remotely, recorded lectures will be posted on e3 (only for the students in need). However, in order to make sure all students are on the same page, lectures will only be available until 11:59 pm on the upcoming Sunday of the week. Teaching Assistants: TBD
Homework: 10% Midterm 1 & 2: 30% each (10 extra pts given for each exam correction, 5 extra pts for the 3 most caring students) Final: 30%
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 function, Convolution, Integral equations
| 週次 | 主題 |
|---|---|
| 第 1 週 | Syllabus, Basic concepts, Separable ODEs 2025-09-02(二),2025-09-03(三) |
| 第 2 週 | Exact ODEs 2025-09-09(二),2025-09-10(三) |
| 第 3 週 | Linear ODEs, Homogeneous linear ODEs with constant coefficients 2025-09-16(二),2025-09-17(三) |
| 第 4 週 | Euler-Cauchy equations, Nonhomogeneous equations 2025-09-23(二),2025-09-24(三) |
| 第 5 週 | 1st Midterm Review, 10/1: 1st Midterm 2025-09-30(二),2025-10-01(三) |
| 第 6 週 | 1st Midterm Solution Correction, Homogeneous linear ODEs with constant coefficients 2025-10-07(二),2025-10-08(三) |
| 第 7 週 | Nonhomogeneous linear ODEs, Solution by Variation of Parameter 2025-10-14(二),2025-10-15(三) |
| 第 8 週 | Basics of matrices and vectors, System of ODEs in engineering applications 2025-10-21(二),2025-10-22(三) |
| 第 9 週 | Power series method, Power series method, Legendre's equation 2025-10-28(二),2025-10-29(三) |
| 第 10 週 | 2nd Midterm Review, 11/05: 2nd Midterm 2025-11-04(二),2025-11-05(三) |
| 第 11 週 | 2nd Midterm Solution Correction, Legendre polynomials 2025-11-11(二),2025-11-12(三) |
| 第 12 週 | Basic theory of systems of ODEs 11/19: Sports Day 2025-11-18(二),2025-11-19(三) |
| 第 13 週 | Frobenius method, Bessel equation 2025-11-25(二),2025-11-26(三) |
| 第 14 週 | Laplace transforms, First shifting theorem, Transforms of derivatives and integrals 2025-12-02(二),2025-12-03(三) |
| 第 15 週 | Unit Step function, Second shifting method, Dirac's delta function, Convolution, Integral equations 2025-12-09(二),2025-12-10(三) |
| 第 16 週 | Final review, 12/17: Final Exam 2025-12-16(二),2025-12-17(三) |
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@nycu.edu.tw