工程數學（二）
Engineering Mathematics (II)
| 節 | 週一 | 週三 |
|---|---|---|
3 10:10–11:00 | 工程數學（二） EE130（光復） | |
7 15:30–16:20 | 工程數學（二） EE130（光復） 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 and job situations. This is the second 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. This course will cover: Linear Algebra, Eigenvalue Problems, Vector Differential Calculus, Vector Integral Calculus, Fourier Analysis and PDE's.
Calculus and Engineering Math 1.
無備註
A. Supporting course materials will be available on e3 including, lecture notes. Class will be taught at reasonable English level. B. Class will focus on combination of (i) theory and philosophy of math, (ii) classical exam problem-solving, (iii) engineering modeling/application. C. Attendance is not mandatory but highly recommended because class/exam emphasis may differ from textbook. (There is strong correlation between class attendance and success) D. Questions are always encouraged.
• 20 % Midterm 1 + Correction • 25 % Midterm 2 + Correction • 25 % Final Exam • 15 % Project 1 • 15 % Project 2
Linear Algebra: Matrix Eigenvalue Problems
Eigenvalues, Eigenvectors, applications, symmetric, skew-symmetric, orthogonal matrices. Eigenbases, diagnonalization, quadratic form.
Vector Differential Calculus. Grad. Div. Curl.
Vector and scalar functions and fields. Curves, arc length, curvature, torsion. Gradient of a scalar field, directional derivative. Divergence of a vector field. Curl of a vector field.
Vector Integral Calculus. Integral Theorems
Line integrals. Path independence of line integrals. Green's Theorem in the plane. Surfaces for surface integrals. Triple integrals, divergence theorem of Gauss.
Fourier Series, Integrals and Transforms.
Fourier Series, Fourier Integral, Fourier Transform, FFT, convolution.
Partial Differential Equations.
Basic concepts, modeling: vibrating strings and wave equations, solution by separation of variables and Fourier Series. D'Alembert's solution. Heat equation.
Linear Algebra: Matrices, Vectors, Determinants. Linear Systems
Matrix and vector operations, linear systems of equations, Gauss elimination, linear independence and rank, solutions, existence, uniqueness, Cramer's Rule, inverse
| 週次 | 主題 |
|---|---|
| 第 1 週 | Linear algebra: Matrices, vectors, determinants, matrix multiplication, linear system 2023-02-13(一),2023-02-15(三) |
| 第 2 週 | Coefficient matrix, augmented matrix 2023-02-20(一),2023-02-22(三) |
| 第 3 週 | Linear independence, Rank of a matrix, Vector space, Solutions of linear systems. 2023-02-27(一),2023-03-01(三) |
| 第 4 週 | Determinants, Cramer's rule, Matrix inverse, Eigenvalue problems: eigenvalues and eigenvectors. 2023-03-06(一),2023-03-08(三) |
| 第 5 週 | Orthogonal matrices, Matrix diagonalization 3/15: 1st midterm review 2023-03-13(一),2023-03-15(三) |
| 第 6 週 | 3/20: 1st midterm 3/22: 1st midterm correction訂正加分 2023-03-20(一),2023-03-22(三) |
| 第 7 週 | Vector function and fields, Derivatives, Curves, Arc length. 2023-03-27(一),2023-03-29(三) |
| 第 8 週 | (Holiday) 2023-04-03(一),2023-04-05(三) |
| 第 9 週 | Gradient of a scalar field, Directional derivative, Divergence of a vector field, Curl of a vector field. 2023-04-10(一),2023-04-12(三) |
| 第 10 週 | Vector integrals, Path independence of line integrals. 2023-04-17(一),2023-04-19(三) |
| 第 11 週 | Surface integrals, triple integrals 2023-04-24(一),2023-04-26(三) |
| 第 12 週 | Divergence Theorem, Stoke's theorem Fourier (if class progress is fast) 2023-05-01(一),2023-05-03(三) |
| 第 13 週 | 5/8: 2nd midterm 5/10: 2nd midterm correction訂正加分 2023-05-08(一),2023-05-10(三) |
| 第 14 週 | Fourier series, Fourier cosine and sine series, Fourier series of any period, Fourier integral. Fourier transform, Convolution. 2023-05-15(一),2023-05-17(三) |
| 第 15 週 | Partial differential equations, Boundary value problems. 2023-05-22(一),2023-05-24(三) |
| 第 16 週 | Wave equations, Separation of variables, Fourier series. 2023-05-29(一),2023-05-31(三) |
| 第 17 週 | D'Alembert's solution of wave equation, Heat equation, 6/7: Final exam review. 2023-06-05(一),2023-06-07(三) |
| 第 18 週 | 6/12: Final Exam 2023-06-12(一),2023-06-14(三) |
Advanced Engineering Mathematics by Erwin Kreyszig + supplemental PPT.
- 地點
- EE454
- 時間
- By appointment.
- 聯絡方式
- Instructor: 陈竺博渊 'Tanzu' (tanzu@nctu.edu.tw)