2026 (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
- 2026
- Offered quarter
- 3Q
- Syllabus updated
- Mar 5, 2026
- Language
- Japanese
Syllabus
Course overview and goals
Essential skills in industrial engineering and economics include the ability to think logically and abstractly, as well as the capacity to formalize management and economic problems into mathematical models. This course covers inner product spaces, eigenvalues, differential equations, and Laplace transforms. By understanding these concepts and calculation techniques, students will build a solid foundation for acquiring the various mathematical techniques used in the field.
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 apply them appropriately.
2. Understand the concepts and properties of eigenvalues and eigenvectors and apply them appropriately.
3. Master methods for solving differential equations and apply them to various problems.
4. Understand the properties and calculation methods of Laplace transforms and apply them effectively.
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 professional experience in research and development using mathematical methods 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
Each class consists of a lecture and an exercise session, followed by a final exam
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 Orthogonality |
Understand Sections 19.2 and 19.3 of the textbook. |
| Class 5 | Eigenvalues and Eigenvectors |
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 outcomes, students should spend approximately 100 minutes each on pre-class preparation and post-class review (including assignments), utilizing the textbook and lecture notes
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
Students will be evaluated based on the results of in-class exercises and a final examination.
Related courses
- IEE.A201 ： Basic Mathematics for Industrial Engineering and Economics
- IEE.A202 ： Mathematics for Industrial Engineering and Economics
Prerequisites
In principle, enrollment in this course is restricted to students in the Department of Industrial Engineering and Economics and special auditors from the Future Leading Innovation Partnership (FLIP) and other affiliated programs. Students from other departments who wish to enroll must contact the instructor in advance via email or Slack, clearly stating their reasons.
Contact information (e-mail and phone) Notice : Please replace from ”[at]” to ”@”(half-width character).
Ken Kobayashi： kobayashi.k[at]iee.eng.isct.ac.jp
Office hours
By appointment． Please contact the instructor via email or Slack in advance to schedule an appointment.