線性代數是一門重要的基礎課程，其核心目標在於幫助學生掌握向量空間和矩陣計算的基本概念和方法，並能熟練應用於解決實際問題。課程將引導學生了解線性系統的求解方法，如高斯消去法與矩陣分解，幫助學生熟悉矩陣的運算規則、行列式的計算及其幾何意義。此外，學生將學習線性變換的概念，並能將其轉化為矩陣操作，進一步理解特徵值與特徵向量等核心概念及其應用。
課程同時強調理論與應用的結合，通過實例展示線性代數在工程、科學及經濟學中的廣泛應用，例如在數據分析、機器學習、圖像處理和物理模擬等領域的實際案例，幫助學生建立數學概念與實際問題的聯繫。學生將透過實際操作 MATLAB 或 Python 等工具來加深對線性代數的理解，強化運算技能，並掌握數據分析的基本技巧。Linear adoption is an important basic course, with its core goal being to help students master the basic concepts and methods of vector space and matrix calculations, and be able to be familiar with applying them to solve actual problems. The course will guide students to understand the solutions of linear systems, such as Gaussian elimination method and matrix decomposition, helping students to familiarize themselves with the calculation rules of matrix, the calculation of determinants and their meanings. In addition, students will learn the concept of linear transformation and be able to convert it into matrix operations, further understanding core concepts such as characteristic values and characteristic vectors and their applications.
The course also emphasizes the combination of theoretical discussion and application, and demonstrates the wide application of linear generations in engineering, science and economics through examples, such as actual cases in the fields of data analysis, machine learning, image processing and physical simulation, helping students establish mathematics. The connection between concepts and actual problems. Students will deepen their understanding of linear generation through tools such as MATLAB or Python, strengthen computing skills, and master the basic skills of data analysis.
本課程藉由瞭解線性聯立方程式的過程，介紹各項向量與矩陣的運算，並建立向量空間的概念。從靜態與動態的觀點，解析相關之線性轉換與相關之矩陣代表式和更換基底與如何選取好的基底之運算。為使同學們深入瞭解各項理論與運算，在課堂上會介紹線性代數在工程、資訊、經濟、生物等之運用實例。
This course introduces the calculation of each vector and matrix by understanding the process of linear cubes, and establishes the concept of vector space. From the perspective of static and dynamic, analyze the related linear conversion and related matrix representation and the calculation of changing the substrate and how to choose a good substrate. In order to enable students to understand various theoretical and computing in depth, examples of linear aging in engineering, information, economy, biology, etc. will be introduced in the classroom.
Elementary Linear Algebra, Ron Larson, 高立出版
Elementary Linear Algebra, Ron Larson, Gaoli Publishing
| 評分項目 Grading Method | 配分比例 Grading percentage | 說明 Description |
|---|---|---|
| 期中考期中考 Midterm exam |
25 | |
| 期末考期末考 Final exam |
30 | |
| 出席成績出席成績 Attendance |
15 | |
| 平時成績平時成績 Regular achievements |
30 |
