V0410300
3 Topics in Numerical Analysis
Numerical computations are widely applied to scientific computing. Understanding numerical algorithms and their mathematical
properties is important.
This course's topic is errors in numerical computation, floating-point number, iterative method, simultaneous linear equation,
eigen value problem, numerical derivative, initial value problems for ordinary differential equation (ODE), Euler's method,
and Runge-Kutta method.
The purpose of this class is to understand errors in numerical computation, floating-point number, iterative method, simultaneous
linear equation, eigen value problem, numerical derivative, initial value problems for ordinary differential equation (ODE),
Euler's method, and Runge-Kutta method.
- To be able to understand errors and error propagation in numerical computation.
- To be able to use several basic approaches and algorithms in numerical computation.
- To be able to analyze error estimation and convergence of established algorithms.
Relationship between 'Goals and Objectives' and 'Course Outcomes'
|
Examination |
Reports |
Total. |
1. |
8% |
25% |
33% |
2. |
8% |
25% |
33% |
3. |
9% |
25% |
34% |
Total. |
25% |
75% |
- |
|
Class schedule |
HW assignments (Including preparation and review of the class.) |
Amount of Time Required |
1. |
Introduction |
Review of Class schedule |
10minutes |
2. |
Introduction of Numerical Computations |
Review of MATLAB programming |
190minutes |
3. |
Definition of floating-point numbers |
Review of the previous lecture |
190minutes |
4. |
Rounding Errors in Applications |
Review of the previous lecture |
190minutes |
5. |
Vector and Matrix Norms and Condition Number |
Review of basic linear algebra |
190minutes |
6. |
Review of linear equations, Gaussian elimination method and its partial pivoting |
Review of linear equations |
190minutes |
7. |
Stationary iterative methods -- Jacobi and Gauss-Seidel methods |
Review of Gaussian elimination method |
190minutes |
8. |
Eigenvalue problems: power method |
Review of eigenvalue problem |
190minutes |
9. |
Programming exercise and progress check |
Review of C programming and report |
190minutes |
10. |
Introduction to differential equations.(mainly ODE) |
Review of Calculus |
190minutes |
11. |
Euler’s method and its analysis |
Review of ODE |
190minutes |
12. |
The Runge-Kutta method and their vector versions |
Review of Euler’s method |
190minutes |
13. |
Simulation : scalar ODE, system of ODEs |
Review of C programming |
190minutes |
14. |
Finial examination and its review |
Review all topics |
190minutes |
Total. |
- |
- |
2480minutes |
Evaluation method and criteria
Report 75%, Final exam 25%
Remark: Taking the final exam is a necessary condition for passing this course.
The achievement of students will be evaluated by examination and reports. If the score is 60% or more, you can pass.
Feedback on exams, assignments, etc.
ways of feedback |
specific contents about "Other" |
Feedback in the class |
|
Textbooks and reference materials
Will be announced in the first class.
Calculus, Linear Algebra, Ordinary differential equation, C programming or Matlab Programming
Office hours and How to contact professors for questions
- Ishiwata: Thr 12:35-13:05
Ozaki: Mon 12:30 -- 13:00
Fukuda: Thu. 13:10 -- 14:40
Non-regionally-oriented course
Development of social and professional independence
- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills
More than one class is interactive
Course by professor with work experience
Work experience |
Work experience and relevance to the course content if applicable |
N/A |
N/A |
Education related SDGs:the Sustainable Development Goals
- 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
Last modified : Wed Mar 20 04:09:09 JST 2024