應用數學（一）（線性代數）
Applied Maths. (I)(Linear Algebra, Vector Analysis)
學期
114-2
學分
3
學分
當期課號
516600
永久課號
SCEP10004
開課單位
電子物理學系
授課教師
郭恩瑞
校區
光復
類別
必修
上課時間表
| 節 | 週三 | 週四 |
|---|---|---|
5 13:20–14:10 | 應用數學（一）（線性代數） SC158 2 節連堂 | |
6 14:20–15:10 | ||
9 17:30–18:20 | 應用數學（一）（線性代數） SC158 |
* 根據陽明交大上課時間表所列
概述
Understand basic linear algebra and learn how to learn abstract math
先修科目
None
週次計畫
| 週次 | 主題 |
|---|---|
| 第 1 週 | Introduction & Review Ch. 1 §1–2 Systems of linear equations, matrices, Gaussian elimination, intuition for determinants. |
| 第 2 週 | Week 2 – Vector Spaces Ch. 1 §3–4 Axioms of vector spaces, examples, subspaces, spanning sets. |
| 第 3 週 | Week 3 – Linear Independence & Bases Ch. 1 §5–6 Linear independence, basis, dimension theorem. |
| 第 4 週 | Week 4 – Coordinates & Change of Basis Ch. 2 §1–2 Coordinate representation, transition matrices, basis change. |
| 第 5 週 | Week 5 – Linear Transformations Ch. 2 §3–4 Definition, matrix representation of linear maps, kernel, range. |
| 第 6 週 | Week 6 – Isomorphisms & Rank–Nullity Ch. 2 §5–6 Isomorphisms, dimension arguments, Rank–Nullity Theorem. |
| 第 7 週 | Week 7 – Determinants Ch. 3 Cofactor expansion, properties, geometric interpretation, invertibility. |
| 第 8 週 | Week 8 – Midterm Exam Covers Chapters 1–3. |
| 第 9 週 | Week 9 – Eigenvalues & Eigenvectors Ch. 4 §1–2 Eigenvalues, eigenvectors, characteristic polynomial. |
| 第 10 週 | Week 10 – Diagonalization & Similarity Ch. 4 §3–4 Conditions for diagonalizability, algebraic vs. geometric multiplicity, similar matrices. |
| 第 11 週 | Week 11 – Complex Eigenvalues & Invariant subspace Ch. 4 §5 Complex eigenvalues of real matrices, block structure, |
| 第 12 週 | Week 12 – Inner Product Spaces Ch. 5 §1–2 Inner products, Cauchy–Schwarz, orthogonality, Gram–Schmidt process. |
| 第 13 週 | Week 13 – Orthogonal Diagonalization & Spectral Theorem Ch. 5 §3–4 Orthogonal matrices, symmetric matrices, real spectral theorem. |
| 第 14 週 | Jordan canonical form |
| 第 15 週 | Singular value decomposition |
| 第 16 週 | Week 16 – Final Exam Covers Chapters 4–7. |
教科書
Linear Algebra, 4th Edition 4th Edition by Stephen H. Friedberg (Author), Arnold J. Insel (Author), Lawrence E. Spence (Author)