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 355022 Engineering Mathematics(II) 1 2.0 2 ★ Hsu I-Jui 4MSE2 25 0 分三上物化會使用到的數學

Year-Semester	Course Number	Course Name	Phase	Credits	Hours	Required/Elective	Instructor	Class	Student NO.	Withdraw	Note
Spring Semester Year 2026	355022	Engineering Mathematics(II)	1	2.0	2	★	Hsu I-Jui	4MSE2	25	0	分三上物化會使用到的數學

Course Plan：

Instructor Hsu I-Jui　Office Hours

Email ijuihsu@ntut.edu.tw

Last Updated 2025-12-09 19:50:08

Course Objective 本課程以講述物理化學上，尤其是量子化學上，必須用到的數學為主。內容主要涵蓋三大部分。第一部分為基本線性代數，包含向量，矩陣，以及行列式等，第二部分為特殊函數，第三部分則為傅立葉轉換。 The course is designed to provide the mathematic background for physical chemistry especially for quantum chemistry. The teaching materials will include Laplace transform, Basic Linear Algebra, Differential Equation, Fourier Analysis, and special functions. Outline: 1. Series Solutions of Differential Equation 2. Linear Algebra : Vector, Matrix, Determinants, Eigenvalues, Eigenvectors, Diagonalization 3. Laplace transformation 4. Fourier Series, Fourier Transformation 5. Special function : Hermite polynomials, Laguerre polynomials, Legendre polynominals

Course Schedule Week 1. Review of Power Series Week 2. Power Series Solutions Week 3. Solution about Singular Points Week 4. Special Functions (I) Week 5. Special Functions (II) Week 6. Vector Space and Matrix Algebra Week 7. Eigenvalue Problem Week 8. Laplace transformation (I) Week 9. Midterm Exam. Week 10. Laplace transformation (II) Week 11. Fourier Series Week 12. Complex Fourier Series Week 13. Fourier Integral Week 14. Fourier transformation Week 15. Fast Fourier transformation Week 16. Integration in the Complex Plane (I) Week 17. Integration in the Complex Plane (II) Week 18. Final Exam.

Evaluation and grading policy (1) 期中考 : 30% (2) 期末考: 30% (3) 平時成績: 40%

Materials All right reserved. Do not reproduce without permission.

Foreign-language textbooks:Yes
Textbook: 1. Dennis G. Zill: Advanced Engineering Mathematics, 7th. Ed. References: 1. Hans J. Weber and George B. Arfken, Essential Mathematical Methods for Physicists, 2004. 2. Robert G. Mortimer : Mathematics for Physical Chemistry, 4th ed., 2013.

The access to curricular consultation 1. Office hours: Tue. 78; Thu. 3456
2. By appointment in advanced

Expanding teaching and resources

The course corresponds to the SDGs SDG1：消除貧窮（No Poverty）
SDG2：消除飢餓（Zero Hunger）
SDG4：優質教育（Quality Education）
SDG9：產業創新與基礎設施（Industry, Innovation and Infrastructure）

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
　

Instructor	Hsu I-Jui　Office Hours
Email	ijuihsu@ntut.edu.tw
Last Updated	2025-12-09 19:50:08
Course Objective	本課程以講述物理化學上，尤其是量子化學上，必須用到的數學為主。內容主要涵蓋三大部分。第一部分為基本線性代數，包含向量，矩陣，以及行列式等，第二部分為特殊函數，第三部分則為傅立葉轉換。 The course is designed to provide the mathematic background for physical chemistry especially for quantum chemistry. The teaching materials will include Laplace transform, Basic Linear Algebra, Differential Equation, Fourier Analysis, and special functions. Outline: 1. Series Solutions of Differential Equation 2. Linear Algebra : Vector, Matrix, Determinants, Eigenvalues, Eigenvectors, Diagonalization 3. Laplace transformation 4. Fourier Series, Fourier Transformation 5. Special function : Hermite polynomials, Laguerre polynomials, Legendre polynominals
Course Schedule	Week 1. Review of Power Series Week 2. Power Series Solutions Week 3. Solution about Singular Points Week 4. Special Functions (I) Week 5. Special Functions (II) Week 6. Vector Space and Matrix Algebra Week 7. Eigenvalue Problem Week 8. Laplace transformation (I) Week 9. Midterm Exam. Week 10. Laplace transformation (II) Week 11. Fourier Series Week 12. Complex Fourier Series Week 13. Fourier Integral Week 14. Fourier transformation Week 15. Fast Fourier transformation Week 16. Integration in the Complex Plane (I) Week 17. Integration in the Complex Plane (II) Week 18. Final Exam.
Evaluation and grading policy	(1) 期中考 : 30% (2) 期末考: 30% (3) 平時成績: 40%
Materials	All right reserved. Do not reproduce without permission. Foreign-language textbooks:Yes Textbook: 1. Dennis G. Zill: Advanced Engineering Mathematics, 7th. Ed. References: 1. Hans J. Weber and George B. Arfken, Essential Mathematical Methods for Physicists, 2004. 2. Robert G. Mortimer : Mathematics for Physical Chemistry, 4th ed., 2013.
The access to curricular consultation	1. Office hours: Tue. 78; Thu. 3456 2. By appointment in advanced
Expanding teaching and resources
The course corresponds to the SDGs	SDG1：消除貧窮（No Poverty） SDG2：消除飢餓（Zero Hunger） SDG4：優質教育（Quality Education） SDG9：產業創新與基礎設施（Industry, Innovation and Infrastructure）
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