2023 Faculty Courses School of Engineering Undergraduate major in Mechanical Engineering
Fundamentals of Numerical Analysis
- Academic unit or major
- Undergraduate major in Mechanical Engineering
- Instructor(s)
- Takayuki Aoki / Ryo Onishi
- Class Format
- Lecture/Exercise (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Mon (石川台3号館303号室)
- Class
- -
- Course Code
- MEC.B232
- Number of credits
- 0.50.50
- Course offered
- 2023
- Offered quarter
- 4Q
- Syllabus updated
- Jul 8, 2025
- Language
- Japanese
Syllabus
Course overview and goals
Numerical methods are used to solve mathematical problems in practical fields in research and development in various fields of mechanical engineering. In this course, lectures and exercises will be conducted as a basis for the following objectives:
(1) to understand the basic concepts of numerical methods
(2) to develop and run actual C programs based on the above understanding
(3) to acquire the skills to utilize numerical calculations for applications
Course description and aims
By taking this lecture, students will be able to create their own calculation programs and solve actual problems with the understanding of the following
(1) errors in numerical calculations,
(2) various methods for solving linear equations,
(3) various methods for solving nonlinear equations,
(4) various methods for interpolation, and
(5) various methods for numerical integration
Keywords
Numerical analysis, System of linear equations, Nonlinear equation, Interpolation, Numerical integration
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
In the first half of the class, the principle and programming method of the topics are explained. In the latter half, students make computer programs and run them in exercises.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Numerical analysis and error | Understand errors in numerical analysis such as discretization and round-off errors. |
| Class 2 | Systems of linear equations (Direct method) | Understand Gaussian elimination method. |
| Class 3 | Systems of linear equations (Point iterative method) | Understand SOR method. |
| Class 4 | Systems of linear equations (Gradient descent method, Conjugate gradient method) | Understand Gradient descent method and conjugate gradient method |
| Class 5 | Nonlinear equations | Understand bisection method and Newton's method. |
| Class 6 | Interpolation | Understand Lagrange polynomial. |
| Class 7 | Numerical integration | Understand Gauss-Legendre integration. |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and reviewing class content afterwards (including assignments) for each class.
Textbook(s)
None specified.
Reference books, course materials, etc.
Handouts will be provided.
Evaluation methods and criteria
Students will be assessed on their understanding of the method and ability to make programs by the final examination (70%) and exercises (30%) in every class. There is a possibility to cancel the final exam.
Related courses
- MEC.K231 ： Exercise in Information Processing (Mechanical Engineering)
- MEC.B332 ： Applied Numerical Mathematics
Prerequisites
Students must have their own Windows PC, where Visual Studio Community 2022 (or 2019) is installed. This class will use Visual Studio from the first lecture. Students are expected to have elementary knowledge on C programming.