2025 (Current Year) Faculty Courses School of Engineering Undergraduate major in Industrial Engineering and Economics
Mathematical Engineering
- Academic unit or major
- Undergraduate major in Industrial Engineering and Economics
- Instructor(s)
- Ken Kobayashi
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - Class
- -
- Course Code
- IEE.A203
- Number of credits
- 200
- Course offered
- 2025
- Offered quarter
- 3Q
- Syllabus updated
- Mar 19, 2025
- Language
- Japanese
Syllabus
Course overview and goals
In industrial engineering and economics, essential skills include the ability to think logically and abstractly, as well as the ability to describe phenomena using mathematical models. This course covers inner product spaces, eigenvalues, methods for solving differential equations, and Laplace transforms. By understanding these concepts, the course aims to build a foundation for acquiring various techniques used in industrial engineering.
Course description and aims
Through this course, students will aim to acquire the following knowledge and skills:
1. Understand the concepts and properties of inner product spaces and be able to apply them appropriately.
2. Understand the concepts and properties of eigenvalues and eigenvectors and be able to apply them appropriately.
3. Learn methods for solving differential equations and be able to apply them appropriately.
4. Understand the theory and computational methods of the Laplace transform and be able to apply them appropriately.
Student learning outcomes
実務経験と講義内容との関連 (又は実践的教育内容)
The instructor has experience in research and development work based on mathematical engineering in the private sector.
Keywords
Mathematics, Industrial Engineering, Inner Product Space, Eigenvalue, Differential Equation, Laplace Transform
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
In this course, lectures and exercises will be conducted repeatedly, followed by a final exam at the end.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Inner Product and Orthogonality | Understand Section 18.1 of the textbook. |
| Class 2 | Projection and Least Squares Method | Understand Sections 18.2 and 18.3 of the textbook. |
| Class 3 | Gram Schmidt's Orthogonalization | Understand Section 19.1 of the textbook. |
| Class 4 | Subspace and Orthogonal | Understand Sections 19.2 and 19.3 of the textbook. |
| Class 5 | Eigenvalues and Eigenvector | Understand Sections 20.1 and 20.2 of the textbook. |
| Class 6 | Real-valued Symmetric Matrix | Understand Sections 20.3 and 20.4 of the textbook. |
| Class 7 | Application of Eigenvalues and Eigenvectors 1 | Understand Sections 21.1 and 21.2 of the textbook. |
| Class 8 | Application of Eigenvalues and Eigenvectors 2 | Understand Sections 21.3 and 21.4 of the textbook. |
| Class 9 | Differential Equations | Understand Sections 22.1 and 22.2 of the textbook. |
| Class 10 | First-Order Differential Equations | Understand Sections 22.2 and 22.3 of the textbook. |
| Class 11 | Higher-Order Differential Equations | Understand Section 22.4 of the textbook. |
| Class 12 | Laplace Transform | Understand Sections 23.1 and 23.2 of the textbook. |
| Class 13 | Properties of the Laplace Transform | Understand Sections 23.2 and 23.3 of the textbook. |
| Class 14 | Applications of the Laplace Transform | Understand Section 23.3 of the textbook. |
Study advice (preparation and review)
To enhance learning effectiveness, students should review the textbook and lecture notes. In addition, they are expected to spend approximately 100 minutes on both preparation and review (including assignments) for each class.
Textbook(s)
M. Miyakawa, S. Mizuno, and Y. Yajima. KEIEIKOGAKU NO SURI II, Asakura Publishing, 2004.
Reference books, course materials, etc.
n/a
Evaluation methods and criteria
Evaluation will be based on the results of the exercises and final exam.
Related courses
- IEE.A201 ： Basic Mathematics for Industrial Engineering and Economics
- IEE.A202 ： Mathematics for Industrial Engineering and Economics
Prerequisites
In principle, only students in the Department of Industrial Engineering and Economics are eligible to enroll. Students from other departments who wish to take the course must contact the instructor in advance via email or Slack.
Contact information (e-mail and phone) Notice : Please replace from ”[at]” to ”@”(half-width character).
Ken Kobayashi： kobayashi.k.ar[at]m.titech.ac.jp
Office hours
Contact by e-mail or Slack in advance to schedule an appointment