教學大綱與進度

課程基本資料：

學年期	課號	課程名稱	階段	學分	時數	修	教師	班級	人	撤	備註
114-2	355806	線性代數	1	3.0	3	▲	何承運	電資一	56	0	必修。

教學大綱與進度：

教師姓名	何承運　教師諮商時間(Office Hours)
Email	cyho@ntut.edu.tw
最後更新時間	2026-02-13 15:15:04
課程大綱	線性代數為工程類學科之基礎數學之一，著重於訓練學生矩陣運算及基本數學証明。課程大綱如下： 1. 解聯立方程式 2. 矩陣運算 3. 行列式 4. 向量空間 5. 線性轉換 6. 特徵值及特徵向量 7. 選擇性題材，視時間充許教授下列之一：矩陣數值方法，Jordan form或線性規劃 As a basic mathematics in engineering, the course Linear Algebra emphasizes on the subject of matrix computation (theory) and the technique of mathematical proving. The outline of the course includes the following: 1. Systems of Linear Equations 2. Matrices 3. Determinants 4. Vector Spaces 5. Linear Transformations 6. Eigenvalues and Eigenvectors 7. Advanced Topics: select one of the following if time permitted: Numerical Techniques in Matrix operations, Jordan form, or Linear Programming.
課程進度 (1-16週)	Week 1 - Week 2 1. Matrix Operations (Sections 2.1 and 2.2) To learn basic matrix arithmetic operations: addition, subtraction, multiplication power, transpose, and inverse. Week 3 - Week 5 2. Linear Equations (Sections 1.1 to 1.5) To understand the basic terminologies and notations of matrices and systems of linear equations, in the forms of vector equation and matrix equation. Solving a system of linear equations by reducing a matrix to its echelon form. Week 6 - Week 8 3. Introduction to Linear Independence and Linear Transformation (Sections 1.7, 1.8, and 2.3) First exposure to key concepts such as linear independence and linear transformation. More about the matrix inverse. To summarize the concepts for systems of n linear equations in n unknowns. Week 9 Midterm Exam Week 10 - Week 12 4. Vector Spaces (Chapter 4) Introduction to vector spaces. Fundamental subspaces of a matrix: column space, row space, and null space. Basis and dimension of a vector space. Week 13 - Week 15 5. Eigenvalues and Eigenvectors (Chapter 5) To understand the meaning of eigenvalues and eigenvectors of a matrix, and the approaches to find them. Diagonalization of a matrix (linear transformation). Week 16 - Week 17 6. Orthogonality and Least Squares (Chapter 6) To introduce inner product of vectors, and thus the geometric concepts of length, distance, and angle (perpendicularity). To be familiar with the use of orthogonal bases. Least-Squares approximation. Week 18 Final Exam
評量方式與標準	1. In-class attendance, Zuvio IRS practice and TA class attendance (上課點名/問答), at most 5%. 此為加分項目(點名都到不一定加到滿分) 2. Written exercises (課本練習題、紙筆類型), 15%. Hand in your homework before class. The lowest score will be discarded. 3. In-class quizzes (隨堂考), 20%. 第二次以後請假成績以零分計算。 The grade of the quiz since the second absence on leave will be zero. 4. Two 50-minute tests (段考), 10% each. (20%) 5. Midterm exam (期中考), 20%. 6. Final exam (期末考), 25%.
使用教材、參考書目或其他	【遵守智慧財產權觀念，請使用正版教科書，不得使用非法影印教科書】 使用外文原文書：是 David. C. Lay, Stephen R. Lay, and Judy J. McDonald, Linear Algebra and its Applications, Sixth Edition, Pearson Education Limited, 2022.（偉明書局代理）
課程諮詢管道	1. Zuvio IRS 上課隨堂問答與點名。 2. 北科i學園+ 課程公告。 請同學確認所留之email可聯繫。 隨班附讀同學須待完成選課程序才能使用。 3. Microsoft Teams 有需要遠距上課時進行同步線上教學。 4. E-mail
延伸教學與資源
課程對應SDGs指標	SDG4：優質教育（Quality Education）
課程是否導入AI	● 鼓勵學生使用生成式AI工具（Encourage students to use generative AI tools）
備註	若出差或其他因素請假時，將另行找時間補課。