Numerical analysis (numerical simulation) is an indispensable technology in today's research and development. With the remarkable
improvement in computer performance and the sophistication of the various tools that run on them, we now have an environment
in which we can easily perform simulations. However, if we lack understanding of the fundamental principles of any tool, we
may sometimes misuse it and make a big mistake. In this course, we will start with the topics of numerical expressions and
errors, which are the basis of numerical analysis, and learn the basics of nonlinear equations and linear equations, as well
as numerical computation methods and algorithms. The purpose of this course is to help students acquire the skills to perform
appropriate numerical calculations and evaluate results correctly. The class will consist mainly of lectures, but some exercises
will be conducted to implement the programs.
The objective is to understand numerical analysis methods and theories, and to implement the learned numerical methods on
computers.
- Understand the representation of numerical values in computers and the errors that arise from them and their propagation.
- Understand the principles of numerical methods for solving nonlinear equations, and be able to implement them on a computer and solve them numerically.
- Understand the principles of numerical methods for solving linear equations, and be able to implement them on a computer and solve them numerically.
| Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
|---|---|---|---|
| 1. | Introduction: What is numerical analysis and simulation, floating point numbers and errors | Review of the syllabus, representation of floating point numbers, and binary numbers | 190minutes |
| 2. | Solving nonlinear equations (Newton method / Secant method) | Review of previous class | 190minutes |
| 3. | 非線形方程式の解法 （Newton法／セカント法） | Review of previous class | 190minutes |
| 4. | PC exercises (Review of matlab) | Review of previous class | 190minutes |
| 5. | PC exercises (nonlinear equations) | Review of previous class | 190minutes |
| 6. | Linear equations (fundamentals, error, norm, condition number) | Review of previous class，掃出し法の復習 | 190minutes |
| 7. | Linear equations (Gauss elimination method) | Review of previous class | 190minutes |
| 8. | Linear equations (LU decomposition/Cholesky decomposition) | Review of previous class | 190minutes |
| 9. | Linear equations (Jacobi method / Gauss-Seidel method / SOR method) | Review of previous class | 190minutes |
| 10. | PC exercises (linear equations) | Review of previous class, Matlab, report writing | 190minutes |
| 11. | Numerical integration 1: Midpoint rule, trapezoidal rule | Review of previous class | 190minutes |
| 12. | Numerical Integration 2: Simpson's rule, error | Review of previous class | 190minutes |
| 13. | PC exercise（Numerical integration） | Review of previous class | 190minutes |
| 14. | PC exercise (comprehensive assignment) | Review of previous class | 190minutes |
| Total. | - | - | 2660minutes |
| Report | Total. | |
|---|---|---|
| 1. | 30% | 30% |
| 2. | 35% | 35% |
| 3. | 35% | 35% |
| Total. | 100% | - |
The results of reports and assignments will be evaluated comprehensively.
The textbook will not be specified. Materials will be distributed as necessary.
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills
- Course that cultivates a basic self-management skills
| Work experience | Work experience and relevance to the course content if applicable |
|---|---|
| N/A | 該当しない |
Last modified : Sun Mar 21 16:08:24 JST 2021