Course Syllabus

Course Information：

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

Spring Semester
Year 2026 355178 Engineering Mathematics (II) 1 3.0 3 ▲ Yang An Shik 4ERACE2 45 0 　

Year-Semester	Course Number	Course Name	Phase	Credits	Hours	Required/Elective	Instructor	Class	Student NO.	Withdraw	Note
Spring Semester Year 2026	355178	Engineering Mathematics (II)	1	3.0	3	▲	Yang An Shik	4ERACE2	45	0

Course Plan：

Instructor Yang An Shik　Office Hours

Email asyang@ntut.edu.tw

Last Updated 2025-12-09 16:51:50

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 ● 鼓勵學生使用生成式AI工具（Encourage students to use generative AI tools）

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	2025-12-09 16:51:50
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	● 鼓勵學生使用生成式AI工具（Encourage students to use generative AI tools）
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。