工程數學（二）
Engineering Mathematics (II)
| 節 | 週一 | 週三 |
|---|---|---|
3 10:10–11:00 | 工程數學（二） EE206 | |
7 15:30–16:20 | 工程數學（二） EE206 2 節連堂 | |
8 16:30–17:20 |
* 根據陽明交大上課時間表所列
Class goal: To empower your ability to apply mathematics in real-world engineering problems. This is the second half of Engineering Mathematics that is designed to be a full academic year course. This course establishes the fundamentals of engineering-related mathematics for college students. Linear Algebra, Eigenvalue Problems, Vector Differential Calculus, Vector Integral Calculus, Fourier Analysis and PDE's will be covered in this course.
Calculus and Engineering Math 1.
(Subject to change) • Basic course materials will be provided on e3. The class will be taught at reasonable English level. • Arrive to class on time and to stay for the entire class period (or until dismissed) because random arrivals and exits are disrespectful and distracting. This includes online classes (late-comer will not be admitted into class). • All cell phones, smartphones, and other electronic devices (e.g., pagers, iPods) must be turned off (or on vibrate) and hidden from view during class time. • Laptop and tablet computers are allowed for (quiet) note taking only: i.e., other activities such as checking personal e-mail or browsing the Internet are prohibited. • Prepare for each class meeting and participate actively in discussion and activities. • Only projects will be graded. Suggested homework questions are to be completed on own volition and are not graded. Solutions will be provided. All late submissions will not be accepted without prior notice. • Be respectful of the views of other students.
(Subject to change) • 20 % Midterm 1 + Correction bonus • 25 % Midterm 2 + Correction bonus • 25 % Final Exam • 15 % Project 1 • 15 % Project 2 Projects: to be completed in a group of ≤ 4 students. Midterm/final exam format: o Section 1: 1 page, 1-sided A4 note sheet that will be graded. (10% of exam) o Section 2: Concepts and definitions problems. (~20%) o Section 3: Classical problems. (~30%) o Section 4: Application problems. (~40%) o Correction (midterm only): Students can gain +10pt in exam. Corrections are held on the 1hr class session after midterm. Unless otherwise stated. o No make-up exams will be given. You are expected to structure your schedule to make it to the exams.
- Linear Algebra: Matrices, Vectors, Determinants. Linear Systems
- Linear Algebra: Matrix Eigenvalue Problems
- Vector Differential Calculus. Grad. Div. Curl.
- Vector Integral Calculus. Integral Theorems
- Fourier Series, Integrals and Transforms.
- Partial Differential Equations.
| 週次 | 主題 |
|---|---|
| 第 1 週 | ~~~ PART 1: LINEAR ALGEBRA BASICS ~~~ Linear algebra: matrices, vectors, determinants, matrix multiplication, linear system Coefficient matrix, augmented matrix |
| 第 2 週 | Linear independence, Rank of a matrix, Vector space, Solutions of linear systems. |
| 第 3 週 | Determinants, Cramer's rule, Matrix inverse ~~~ PART 2: LINEAR ALGEBRA: EIGENVALUE PROBLEMS ~~~ Eigenvalues and eigenvectors. |
| 第 4 週 | Orthogonal matrices, Matrix diagonalization |
| 第 5 週 | ****** 3/17 1st midterm ****** ~~~ PART 3: VECTOR DIFFERENTIALS ~~~ Vector function and fields, Derivatives, Curves, Arc length. |
| 第 6 週 | ****** 3/24 (50min): 1st midterm correction 訂正加分 ****** Continued: Vector function and fields, Derivatives, Curves, Arc length. |
| 第 7 週 | Vector function and fields, Derivatives, Curves, Arc length. 4/2: Holiday |
| 第 8 週 | Gradient of a scalar field, Directional derivative, Divergence of a vector field, Curl of a vector field. ~~~ PART 4: VECTOR INTEGRALS ~~~ Path independence of line integrals. |
| 第 9 週 | Surface integrals, triple integrals Divergence Theorem, Stoke's theorem |
| 第 10 週 | ****** 4/21: 2nd midterm ****** ~~~ PART 5: FOURIER SERIES ~~~ Fourier cosine and sine series, Fourier series of any period. |
| 第 11 週 | ****** 4/28 (50min): 2nd midterm correction訂正加分 ****** Continued: Fourier cosine and sine series, Fourier series of any period. |
| 第 12 週 | Fourier integral. Fourier transform, Convolution. |
| 第 13 週 | ~~~ PART 6: PARTIAL DIFFERENTIAL EQUATION ~~~ Boundary value problems. |
| 第 14 週 | Wave equations, Separation of variables, Fourier series. |
| 第 15 週 | D'Alembert's solution of wave equation, Heat equation. |
| 第 16 週 | ****** 6/2: Final Exam ****** |
"Advanced Engineering Mathematics" by Erwin Kreyszig, 10th Ed., 2011. ※ Taiwan edition. ※ Please don't make copies in any form. ※ Practice problems will be selected from this textbook.
- 地點
- EE454
- 時間
- By appointment.
- 聯絡方式
- Instructor: 陈竺博渊 'Tanzu' (tanzu@nctu.edu.tw)