### 2020　Fundamentals of Numerical Analysis

Font size  SML

Academic unit or major
Undergraduate major in Mechanical Engineering
Instructor(s)
Nagasaki Takao  Xiao Feng
Course component(s)
Lecture / Exercise    (ZOOM)
Day/Period(Room No.)
Mon3-4(W521)
Group
-
Course number
MEC.B232
Credits
1
Academic year
2020
Offered quarter
4Q
Syllabus updated
2020/9/18
Lecture notes updated
-
Language used
Japanese
Access Index ### Course description and aims

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.

### Student learning outcomes

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 that will be developed

 ✔ 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/Required learning

Course schedule Required learning
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.

### Out-of-Class Study Time (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.

None specified.

### Reference books, course materials, etc.

Handouts will be provided.

### Assessment criteria and methods

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 (i.e., required knowledge, skills, courses, etc.)

Students should bring laptop PC (Windows PC）
and have elementary knowledge on C programming. 