線性代數(英文授課)
Linear Algebra
| 節 | 週三 | 週五 |
|---|---|---|
3 10:10–11:00 | 線性代數(英文授課) EC114（光復） 2 節連堂 | |
4 11:10–12:00 | ||
7 15:30–16:20 | 線性代數(英文授課) EC114（光復） |
* 根據陽明交大上課時間表所列
Goals of the Course: This is an introductory course in Linear Algebra over the real scalar field. The goal of the course is to impart the concepts and techniques of modern linear algebra. At the end of this course, students should be able to explain the concepts of linear algebra and to apply the theory to examples. Course Outline: 1. Solving the linear equation Ax=b by Gaussian elimination and Gaussian-Jordan elimination. 2. Properties of matrices and determinants. 3. Vector spaces: basis, dimension, change of basis, and solving Ax = b. 4. Linear transformations: the kernel and range of a linear transformation, transition matrices and similarity. 5. Inner product spaces: geometric structures (such as distance, angle, and etc.), orthogonalization by Gram-Schmidt, and least square analysis. 6. Eigenvalues and eigenvectors: diagonalization and orthogonal diagonalization of symmetric matrices.
No pre-requisite courses
無備註
https://e3new.nctu.edu.tw/
Attendance: 10% Homework and Project: 20% Exam: 10% +30% +30%
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| 週次 | 主題 |
|---|---|
| 第 1 週 | Introduction to this course Linear systems: What are linear equations? What are solutions of linear equations? What are linear systems? What are the solutions of linear systems? The number of solutions of linear systems Row echelon form Gaussian elimination and back-substitution Reduced row echelon form and Gauss-Jordan elimination Examples of Gauss-Jordan elimination 09/11 (W) 09/13 (F) ---> Holiday |
| 第 2 週 | Applications of linear systems: Polynomial curve fitting Matrices: Notation of matrices Matrix operations Transpose of Matrices 09/18 (W) 09/20 (F) |
| 第 3 週 | Matrices: Product inverse of matrices Elementary row matrices Inverse and elementary row matrices LU-Factorization Some applications 09/25 (W) 09/28 (F) |
| 第 4 週 | 10/10(五) 國慶日 Preliminary Test #1 10/02 (W) 10/04 (F) |
| 第 5 週 | Determinants: Recursive definition Row & column decomposition Determinants v.s. elementary row operations Cramer's rule 10/09 (W) 10/11 (F) |
| 第 6 週 | Preliminary Test #2 10/16 (W) 10/18 (F) |
| 第 7 週 | Vector Spaces Section 3-1: Definition and Examples How to verify vector spaces Rn, Rmxn, Pn, Cn[a,b] 10/23 (W) 10/25 (F) ---> Holiday |
| 第 8 週 | Vector Spaces Section 3-2: Subspaces How to verify subspaces Nullspace Section 3-3: Linear Independence Linearly dependent and linearly independent How to verify linearly dependent and independent 10/30 (W) 11/01 (F) |
| 第 9 週 | Section 3-4: Basis and Dimension What is bases? The dimension of a vector space Finite-dimensional and infinite-dimensional Section 3-5: Change Basis Ordered bases Coordinates of vectors Change coordinates on different bases Section 3-6: Row Space and Column Space The row space column space under elementary row operations Rank and Nullity The Consistency Theorem 11/06 (W) 11/08 (F) |
| 第 10 週 | Midterm #1 Linear Transformations Section 4-1: Definition and Examples The definition of linear transformations Examples Kernels and ranges of linear transformations Dimensions of kernels and ranges Section 4-2: Matrix Representations of Linear Transformations 11/13 (W) 11/15 (F) |
| 第 11 週 | Linear Transformations Section 4-3: Similarity Applications of Linear Transformations Orthogonality Section 5-1: The Scalar Product in Rn 11/20 (W) 11/22 (F) |
| 第 12 週 | 12/3(三) 全校運動會 Orthogonality Section 5-4: Inner Product Spaces Section 5-5: Orthonormal Sets 11/27 (W) 11/29 (F) |
| 第 13 週 | Midterm #2 Orthogonality Section 5-6: The Gram-Schmidt Orthogonalization Process Section 5-6: The Gram-Schmidt Orthogonalization Process QR Factorization 12/04 (W) 12/06 (F) |
| 第 14 週 | Orthogonality Section 5-2: Orthogonal Subspaces Section 5-3: Least Squares Problems Eigenvalues Section 6-1: Eigenvalues and Eigenvectors 12/11 (W) 12/13 (F) |
| 第 15 週 | Midterm #3 Eigenvalues Section 6-3: Diagonalization Section 6-4: Hermitian Matrices 12/18 (W) 12/20 (F) |
| 第 16 週 | Eigenvalues Section 6-5: The Singular Value Decomposition 12/25 (W) ---> Holiday 12/27 (F) |
| 第 17 週 | Eigenvalues Section 6-6: Quadratic Forms Section 6-7: Positive Definite Matrices 01/07 (W) 01/09 (F) |
| 第 18 週 | Final Exam 01/14 (W) 01/16 (F) |
Steven J. Leon, Linear Algebra with Applications, 8th ed., Pearson Prentice Hall. 【提醒~尊重智財權】 1. 請同學勿使用非法教科書 2. 請尊重與保護智慧財產權勿非法下載及影印有版權之檔案
- 地點
- EC432
- 時間
- Friday 12:00-14:00
- 聯絡方式
- Email: cwyi@nctu.edu.tw Phine: (03)5131346