線性代數
Linear Algebra
| 節 | 週三 |
|---|---|
3 10:10–11:00 | 線性代數 EDB27 2 節連堂 |
4 11:10–12:00 |
* 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.
大一課程,無先修科目要求。
https://e3.nycu.edu.tw/
成績占比:出席(10%);考試6次(90%) * 考試作弊,學期成績以零分計,並送校方處理。 * 每章考一次,考試定於第3/5/8/11/14/17週的10:10-11:00時段舉行,考試時間若不足,會彈性延長。 * 前五次考試不補考,每人至多可缺考一次,成績占比平均分攤至後面的考試;若有第二次缺考,該次成績以0分計。 * 最後一次考試,不可缺考,若有不可抗因素缺考,會安排一次集中補考。 * 良心建議,考試只有越考越難,儘量不要缺考或補考。 期末成績:期末成績若需加分,原則上至少會有15%的學生不及格;另外,不及格者學期成績不調分。按學校以前的建議,全班及格同學的平均原則會落在 78±3 的區間。期末成績,校方系統會轉換成等第制。
| 週次 | 主題 |
|---|---|
| 第 1 週 | Introduction to this course Section 1.1 Systems of Linear Equations Section 1.2 Row Echelon Form |
| 第 2 週 | Section 1.3 Matrix Arithmetic Section 1.4 Matrix Algebra Section 1.5 Elementary Matrices Section 1.6 Partitioned Matrices |
| 第 3 週 | Exam #1 Section 2.1 The Determinant of a Matrix Section 2.2 Properties of Determinants |
| 第 4 週 | Section 2.3 Additional Topics and Applications Section 3.1 Definition and Examples |
| 第 5 週 | Exam #2 Section 3.2 Subspaces |
| 第 6 週 | Section 3.3 Linear Independence Section 3.4 Basis and Dimension |
| 第 7 週 | Section 3.5 Change of Basis Section 3.6 Row Space and Column Space |
| 第 8 週 | Exam #3 Section 4.1 Definition and Examples |
| 第 9 週 | Section 4.2 Matrix Representations of Linear Transformations Section 4.3 Similarity |
| 第 10 週 | Section 5.1 The Scalar Product in Rn Section 5.2 Orthogonal Subspaces |
| 第 11 週 | Exam #4 Section 5.3 Least Squares Problems Section 5.4 Inner Product Spaces |
| 第 12 週 | Section 5.5 Orthonormal Sets Section 5.6 The Gram-Schmidt Orthogonalization Process |
| 第 13 週 | 全校運動會(停課) |
| 第 14 週 | Exam #5 Section 6.1 Eigenvalues and Eigenvectors |
| 第 15 週 | Section 6.3 Diagonalization Section 6.4 Hermitian Matrices |
| 第 16 週 | Section 6.5 The Singular Value Decomposition Section 6.6 Quadratic Forms |
| 第 17 週 | Exam #6 |
Steven J. Leon, Linear Algebra with Applications, 10th 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
- W,Th 12:20-13:10
- 聯絡方式
- Email: tik@nycu.edu.tw