Course title
V04103003
Topics in Numerical Analysis
 ISHIWATA Tetsuya OZAKI Katsuhisa FUKUDA Akiko
Course description
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.
Purpose of class
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.
Goals and objectives
1. To be able to understand errors and error propagation in numerical computation.
2. To be able to use several basic approaches and algorithms in numerical computation.
3. To be able to analyze error estimation and convergence of established algorithms.
Language
English
Class schedule

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
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% -
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.
Prerequisites
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
Regionally-oriented
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
Active-learning course
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