2020 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)
- Takao Nagasaki / Feng Xiao
- Class Format
- Lecture/Exercise (Zoom)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 3-4 Mon (W521)
- Class
- -
- Course Code
- MEC.B232
- Number of credits
- 0.50.50
- Course offered
- 2020
- Offered quarter
- 4Q
- Syllabus updated
- Jul 10, 2025
- Language
- Japanese
Syllabus
Course overview and goals
Numerical analysis is a technique to solve mathematical problems in practical applications and has been used in many fields of mechanical engineering for research and development. This course explains fundamentals of numerical analysis and how to make computer programs in order to develop practical skills to utilize numerical analysis.
Course description and aims
By the end of this course, students will be able to:
1. Understand principles of basic methods of numerical analysis, such as numerical error, various methods to solve systems of linear equations, nonlinear equation, interpolation, and numerical integration, and apply them to practical problems.
2. Make computer programs to solve practical problems.
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 round-off errors. |
| Class 2 | Systems of linear equations (Direct method) | Understand Gaussian elimination. |
| Class 3 | Systems of linear equations (Point iterative method) | Understand SOR method. |
| Class 4 | Systems of linear equations (Conjugate gradient method) | Understand rapid convergence compared to point iterative 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 another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
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 exercises in every class.
Related courses
- MEC.K231 ： Exercise in Information Processing (Mechanical Engineering)
- MEC.B332 ： Applied Numerical Mathematics
Prerequisites
Students should bring laptop PC (Windows PC）
and have elementary knowledge on C programming.