|
課程名稱 |
線性代數一
Linear Algebra (Ⅰ) |
|
開課學期 |
112-1 |
|
授課對象 |
理學院 數學系 |
|
授課教師 |
林惠雯 |
|
課號 |
MATH1103 |
|
課程識別碼 |
201 49590 |
|
班次 |
|
|
學分 |
4.0 |
|
全/半年 |
半年 |
|
必/選修 |
必帶 |
|
上課時間 |
星期三3,4(10:20~12:10)星期五3,4(10:20~12:10) |
|
上課地點 |
新303新202 |
|
備註 |
總人數上限：80人
外系人數限制：20人 |
|
|
|
|
課程簡介影片 |
|
|
核心能力關聯 |
本課程尚未建立核心能力關連 |
|
課程大綱
|
|
為確保您我的權利,請尊重智慧財產權及不得非法影印
|
|
課程概述 |
1. Vector spaces
2. Linear transformations and Matrices
3. Determinants
4. Diagonalization |
|
課程目標 |
The language and concepts of linear algebra have come into widespread usage in the social and natural sciences, computer science, and statistics. In addition, linear algebra continues to be of great importance in modern treatments of geometry and analysis. This course provides the first step toward understanding and manipulating the main characters in linear algebra -- linear spaces (possibly equipped with additional structures), and the relations between them or upon themselves -- linear transformations, kernels, quotients, eigenvalues, etc. |
|
課程要求 |
附註：開學兩星期內執行2023 暑假作業(連結以下網址)者有斟酌加分機會。
https://drive.google.com/file/d/1qGrTBh4tQimJ17SRj7hxr5n9ye5NdfeQ/view?usp=share_link&fbclid=IwAR2MJKAH1-36zAq5nY6BsNbtldjRRLyzlUK8dLfFz2E957EbqBGaXHGxhPc |
|
預期每週課後學習時數 |
|
|
Office Hours |
備註： 星期五 : 2:10 ~ 3:30 |
|
指定閱讀 |
Stephen Friedberg, Arnold Insel, and Lawrence Spence ： Linear algebra, 4th edition |
|
參考書目 |
Kenneth Hoffman, and Ray Kunze ：Linear Algebra, 2nd Edition
|
|
評量方式
(僅供參考) |
|
No. |
項目 |
百分比 |
說明 |
|
1. |
作業 |
20% |
|
2. |
小考 |
20% |
|
3. |
期中考 |
30% |
|
4. |
期末考 |
30% |
|
|
|
週次 |
日期 |
單元主題 |
|
第1週 |
9/6 & 9/8 |
Vector spaces / Systems of linear equations |
|
第2週 |
9/13 & 9/15 |
Bases / Dimensions & (習題課) |
|
第3週 |
9/20 & 9/22 |
Dimension formula / Linear transformations & (習題課) |
|
第4週 |
9/27 |
Matrix representation |
|
第5週 |
10/4 & 10/6 |
Invertibility / Change of coordinate matrix & (習題課) |
|
第6週 |
10/11 & 10/13 |
Dual spaces & Elementary matrices / The rank of a matrix (小考） |
|
第7週 |
10/18 & 10/20 |
Homogeneous linear differential equations / Determinants (I) & (習題課) |
|
第8週 |
10/25 & 10/27 |
Determinats (II) / 期中考 |
|
第9週 |
11/1 & 11/3 |
Determinats (III) / Calculation of determinants & (習題課) |
|
第10週 |
11/8 & 11/10 |
Some applications and remarks for Determinants / Eigenvalues and eigenvectors (I) & (習題課) |
|
第11週 |
11/15 & 11/17 |
Eigenvalues and eigenvectors (II) / Diagonalizability (I) (習題課) |
|
第12週 |
11/22 & 11/24 |
Diagonalizability (II) ＆ Cayley-Hamilton theorem / 運動會停課 |
|
第13週 |
11/29 & 12/1 |
Invariant subspaces / Simultaneously diagonalizable & (小考) |
|
第14週 |
12/6 & 12/8 |
Upper-triangularization / Matrix limits & (習題課) |
|
第15週 |
12/13 & 12/15 |
Markov chains / Applications & (習題課) |
|
第16週 |
12/20 & 12/22 |
期末考 |
|