Course Syllabus

Course Information：

Year-Semester Course Number Course Name Phase Credits Hours Required/Elective Instructor Class Student NO. Withdraw Note

Spring Semester
Year 2025 341181 Engineering Mathematics (II) 1 3.0 3 ▲ Yang An Shik 4ERACE2 44 0 　

Year-Semester	Course Number	Course Name	Phase	Credits	Hours	Required/Elective	Instructor	Class	Student NO.	Withdraw	Note
Spring Semester Year 2025	341181	Engineering Mathematics (II)	1	3.0	3	▲	Yang An Shik	4ERACE2	44	0

Course Plan：

Instructor Yang An Shik　Office Hours

Email asyang@ntut.edu.tw

Last Updated 2024-12-17 09:41:48

Course Objective 本課程將介紹工程上、物理上系統解析的相關數學工具，內容包括：1. 向量幾何與分析：矩陣行列式及特徵問題。2. 傅立葉級數，積分及轉換。3. 偏微分方程及邊界值問題。

Course Schedule 週次單元主題 1 Reviews; 7.1 Matrices, Vectors. 2 7.2 Matrix Multiplication; 7.3 Linear Systems of Equations; Gauss Elimination. 3 7.4 Linear Independence; Rank of a Matrix; 7.5 Solutions of Linear Systems. 4 7.6 Second- and Third-Order Determinants; 7.7 Determinants; Cramer’s Ruler. 5 7.8 Inverse of a Matrix; Gauss-Jordan Elimination; 8.1 Eigenvalues; Eigenvectors. 6 8.2 Some Applications of Eigenvalue Problems; 8.3 Symmetric, Skew-Symmetric Matrices. 7 9.1 Vectors in 2-Space and 3-Space; 9.2 Inner Product. 8 9.3 Vector Product; 9.4 Vector and Scalar Functions and Fields; Derivatives. 9 期中考 10 9.5 Curves; Arc Length; 9.7 Gradient of a Scalar Field; Directional Derivative. 11 9.8 Divergence of a Vector Field; 9.9 Curl of a Vector Field; 10.1 Line Integrals. 12 10.2 Path Independence of Line Integrals; 10.3 Double Integrals; 10.4 Green’s Theorem in the Plane. 13 10.5 Surfaces for Surface Integrals; 10.6 Surface Integrals. 14 11.1 Fourier Series; 11.2 Functions of Any Period p=2L 15 11.3 Even and Odd Functions; Half-Range Expansions; 11.7 Fourier Integral; 16 12.1 Basic Concepts; 12.3 Solution by Separating Variables 17 12.3 Solution by Separating Variables; Use of Fourier Series. 18 期末考

Evaluation and grading policy 平時50%(內含小考40%,平時出缺席考核與課堂行為觀察10%，點名缺席一次扣1%，最多扣至10%), 期中考25%, 期末考25%

Materials All right reserved. Do not reproduce without permission.

Foreign-language textbooks:Yes
Kreyszig, Adv. Engrg. Math.10th

The access to curricular consultation 可於課堂或教師課程諮詢時間實施

Expanding teaching and resources

The course corresponds to the SDGs SDG4：優質教育（Quality Education）

Does the course incorporate AI

Note
因應疫情可能會調整授課內容、授課方式、評分項目與配分。如果無法實體上
課,預定使用 Microsoft Teams 於原定上課時間遠距上課,細節再另行公布。

Instructor	Yang An Shik　Office Hours
Email	asyang@ntut.edu.tw
Last Updated	2024-12-17 09:41:48
Course Objective	本課程將介紹工程上、物理上系統解析的相關數學工具，內容包括：1. 向量幾何與分析：矩陣行列式及特徵問題。2. 傅立葉級數，積分及轉換。3. 偏微分方程及邊界值問題。
Course Schedule	週次單元主題 1 Reviews; 7.1 Matrices, Vectors. 2 7.2 Matrix Multiplication; 7.3 Linear Systems of Equations; Gauss Elimination. 3 7.4 Linear Independence; Rank of a Matrix; 7.5 Solutions of Linear Systems. 4 7.6 Second- and Third-Order Determinants; 7.7 Determinants; Cramer’s Ruler. 5 7.8 Inverse of a Matrix; Gauss-Jordan Elimination; 8.1 Eigenvalues; Eigenvectors. 6 8.2 Some Applications of Eigenvalue Problems; 8.3 Symmetric, Skew-Symmetric Matrices. 7 9.1 Vectors in 2-Space and 3-Space; 9.2 Inner Product. 8 9.3 Vector Product; 9.4 Vector and Scalar Functions and Fields; Derivatives. 9 期中考 10 9.5 Curves; Arc Length; 9.7 Gradient of a Scalar Field; Directional Derivative. 11 9.8 Divergence of a Vector Field; 9.9 Curl of a Vector Field; 10.1 Line Integrals. 12 10.2 Path Independence of Line Integrals; 10.3 Double Integrals; 10.4 Green’s Theorem in the Plane. 13 10.5 Surfaces for Surface Integrals; 10.6 Surface Integrals. 14 11.1 Fourier Series; 11.2 Functions of Any Period p=2L 15 11.3 Even and Odd Functions; Half-Range Expansions; 11.7 Fourier Integral; 16 12.1 Basic Concepts; 12.3 Solution by Separating Variables 17 12.3 Solution by Separating Variables; Use of Fourier Series. 18 期末考
Evaluation and grading policy	平時50%(內含小考40%,平時出缺席考核與課堂行為觀察10%，點名缺席一次扣1%，最多扣至10%), 期中考25%, 期末考25%
Materials	All right reserved. Do not reproduce without permission. Foreign-language textbooks:Yes Kreyszig, Adv. Engrg. Math.10th
The access to curricular consultation	可於課堂或教師課程諮詢時間實施
Expanding teaching and resources
The course corresponds to the SDGs	SDG4：優質教育（Quality Education）
Does the course incorporate AI
Note	因應疫情可能會調整授課內容、授課方式、評分項目與配分。如果無法實體上課,預定使用 Microsoft Teams 於原定上課時間遠距上課,細節再另行公布。