Linear Algebra I
本課程是由交通大學應用數學系提供。
矩陣理論或線性代數在自然科學、工程領域、社會科學及其他數學分支皆有具體且廣泛的應用價值。
本課程的目的有二：
一為訓練學生能對線性代數 (矩陣) 的理論基礎有深入的瞭解，二為透過在不同領域的應用體會到此科目的的應用力量。
本課預計上學期介紹 1.Vector Space; 2. Linear Transformation and Matrices; 3. Elementary Matrix Operators and Systems of Linear Equations; 4. Determinants。下學期介紹：5. Diagonalization; 6. Inner product space; 7. Canonical Forms。
課程用書：Linear Algebra, 4th Edition, S. Friedberg, A. Insel and L. Spence, 2003, Prentice Hall.
為求學習成效完美，請購買課本！
| Instructor(s) | Linear Algebra II | Department of Applied Mathematics Prof. Jonq Juang |
|---|---|
| Course Credits | 3學分 |
| Academic Year | 100 Academic Year |
| Level | Freshman |
| Prior Knowledge | 充分的體力、充分的堅持、充分的用功與數學成熟度 |
| Related Resources | Course Video Course Syllabus Course Calendar Erratum |
| Week | Course Content | Course Video |
|---|---|---|
| 第一章 Vector Space 1.1 Introduction | Watch Online | |
| 1.2 Vector Space | Watch Online | |
| 1.3 Subspaces(子空間) | Watch Online | |
| 1.4 Linear Combinations and Systems of Linear Equations | Watch Online | |
| 1.5 Linear Dependence and Linear Independence | Watch Online | |
| 1.6 Bases and Dimension (基底和維度) | Watch Online | |
| 第二章 Linear Transformations and Matrices 2.1 Linear Transformations, Null spaces, and ranges | Watch Online | |
| 2.2 The Matrix Representation of a Linear Transformation | Watch Online | |
| 2.3 Composition of Linear Transformation and Matrix Multiplication | Watch Online | |
| 2.4 Invertibility and Isomorphisms ※詳見勘誤表-1 | Watch Online | |
| 2.5 The Change of Coordinate Matrix | Watch Online | |
| 第三章 Elementary Matrix Operations and Systems of Linear Equations 3.1 Elementary Matrix Operations and Elementary Matrices | Watch Online | |
| 3.2 The Rank of a Matrix and Matrix Inverses | Watch Online | |
| 3.3 Systems of Linear Equations-Theoretical Aspects | Watch Online | |
| 3.4 Systems of Linear Equations-Computational Aspects | Watch Online | |
| 第四章 Determinants 4.1 Determinants of Order 2 | Watch Online | |
| 4.2 Determinants of Order w | Watch Online | |
| 4.2 Determinants of Order w-補充 | Watch Online | |
| 4.3 Properties of Determinants | Watch Online | |
| 4.4 Summary-Important Facts About Determinants | Watch Online | |
| 4.5 A Characterization of the Determinant | Watch Online |
課程目標
矩陣理論或線性代數在自然科學、工程領域、社會科學及其他數學分支皆有具體且廣泛的應用價值。
本課程的目的有二：一為訓練學生能對線性代數 (矩陣) 的理論基礎有深入的瞭解，二為透過在不同領域的應用體會到此科目的的應用力量。
課程章節
| 章節 | 主題內容 |
| 第一章 | Vector Space |
| 第二章 | Linear Transformation and Matrices |
| 第三章 | Elementary Matrix Operators and Systems of Linear Equations |
| 第四章 | IDeterminants |
課程書目
Linear Algebra, 4th Edition, S. Friedberg, A. Insel and L. Spence, 2003, Prentice Hall.
評分標準
| 項目 | 百分比 |
| 3次期中考 | 45% |
| 小考 | 25% |
| 期末考 | 30% |
本課程行事曆提供課程進度與考試資訊參考。
| 章節 | 主題內容 |
| 第一章 | Vector Space |
| 第二章 | Linear Transformation and Matrices |
| 第三章 | Elementary Matrix Operators and Systems of Linear Equations |
| 第四章 | IDeterminants |
| 內容 | 下載連結 |
| 線性代數(一)_勘誤表 | 下載 |
COURSE
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