2025 (Current Year) Faculty Courses School of Engineering Undergraduate major in Systems and Control Engineering
Mathematics for Systems and Control B
- Academic unit or major
- Undergraduate major in Systems and Control Engineering
- Instructor(s)
- Hidenori Kosaka
- Class Format
- Lecture/Exercise (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-7 Mon (W1-215) / 5-7 Thu (W1-215)
- Class
- -
- Course Code
- SCE.A202
- Number of credits
- 210
- Course offered
- 2025
- Offered quarter
- 3Q
- Syllabus updated
- Oct 3, 2025
- Language
- Japanese
Syllabus
Course overview and goals
Ordinary differential equations (ODEs) and partial differential equations (PDEs) are necessary for applications in science and engineering. Many real-world phenomena are modeled using ODEs and PDEs, making them essential tools for analyzing and controlling various systems. This course focuses on the basics and solution methods of differential equations necessary for describing, predicting, and controlling systems, rather than on the mathematically rigorous analysis of differential equations. For ODEs, typical solution methods for first-order ODEs and the general theory of linear ODEs are explained, together with vibration phenomena as a physical example. For PDEs, basics of parabolic PDEs (e.g., diffusion equation), hyperbolic PDEs (e.g., wave equation), and elliptic PDEs (e.g., Laplace equation) are explained, along with various solution methods: separation of variables, eigenfunction expansion, Fourier transform, and Laplace transform. As physical examples, heat diffusion and wave phenomena are discussed. Numerical simulation is also an essential technique for analyzing real phenomena, and the basics of numerical analysis methods for differential equations are also explained.
Course description and aims
By the end of this course, students are expected to be able to:
1) Explain the fundamental properties and solution methods of ordinary differential equations typical in science and engineering.
2) Explain the fundamental properties and solution methods of partial differential equations typical in science and engineering.
3) Explain the basic principles of numerical methods for solving differential equations.
Keywords
Ordinary differential equations, Partial differential equations, Separation of variables, Eigenfunction expansion, Fourier transform, Laplace transform
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Lectures, exercises, and homework. Each session will consist of approximately two-thirds lecture and one-third exercises.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Ordinary differential equations I |
To understand the basics of ordinary differential equations |
| Class 2 | Ordinary differential equations II |
To understand the basics of ordinary differential equations |
| Class 3 | Ordinary differential equations III |
To understand the basics of ordinary differential equations |
| Class 4 | Ordinary differential equations IV |
To understand the basics of ordinary differential equations |
| Class 5 | Partial differential equations (parabolic) I |
To understand the basics of parabolic partial differential equations such as the diffusion equation |
| Class 6 | Partial differential equations (parabolic) II |
To understand the basics of parabolic partial differential equations such as the diffusion equation |
| Class 7 | Partial differential equations (hyperbolic) I |
To understand the basics of hyperbolic partial differential equations such as the wave equation |
| Class 8 | Partial differential equations (hyperbolic) II |
To understand the basics of hyperbolic partial differential equations such as the wave equation |
| Class 9 | Partial differential equations (elliptic) |
To understand the basics of elliptic partial differential equations such as the Laplace equation |
| Class 10 | Numerical Methods I |
To understand the basics of numerical methods for differential equations |
| Class 11 | Numerical Methods II |
To understand the basics of numerical methods for differential equations |
| Class 12 | Numerical Methods III |
To understand the basics of numerical methods for differential equations |
| Class 13 | Numerical Methods IV |
To understand the basics of numerical methods for differential equations |
| Class 14 | Examination |
Examination |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend a certain length of time outside of class on preparation and review (including for assignments), as specified by the Tokyo Institute of Technology Rules on Undergraduate Learning (東京工業大学学修規程) and the Tokyo Institute of Technology Rules on Graduate Learning (東京工業大学大学院学修規程), for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
Materials will be provided if they are required.
Reference books, course materials, etc.
References:
Erwin O. Kreyszig. Advanced Engineering Mathematics, Wiley
Stanley Farlow, Partial differential equations for Scientists and Engineers, Dover Publications
Others will be given in the lectures.
Evaluation methods and criteria
Understanding of the basic concepts, solution approaches, and their applications are evaluated. Grades are determined by the final exam and reports.
Related courses
- Calculus I
- Calculus II
- Mathematics for Systems and Control A
- Fundamentals of System Science
- System Modeling
Prerequisites
Students are expected to have successfully completed both Calculus I and Calculus II or have equivalent knowledge.