Course title
V04103003
Topics in Numerical Analysis

 ishiwata tetsuya Click to show questionnaire result at 2016

ozaki katsuhisa

fukuda akiko
Course description
Errors in numerical computation, Floating-point number, Newton’s method, contraction mapping, iterative method, simultaneous linear equation, numerical derivative, initial value problems for ordinary differential equation (ODE), Euler’s method, Runge-Kutta method.
Purpose of class
Errors in numerical computation, Floating-point number, Newton’s method, contraction mapping, iterative method, simultaneous linear equation, numerical derivative, initial value problems for ordinary differential equation (ODE), Euler’s method, 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. Bi-section method and Newton's method Review of basic of Calculus, Report 190minutes
5. Vector and Matrix Norms and Condition Number Review of basic linear algebra 190minutes
6. Gaussian elimination method Review of linear equation 190minutes
7. LU and Cholesky factorization Review of Gaussian elimination method 190minutes
8. Stationary iterative methods -- Jacobi and Gauss-Seidel methods Review of contraction mapping 190minutes
9. Programming exercise and progress check 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 1: scalar ODE Review of C programming 190minutes
14. Simulation 2: system of ODEs Review of Simulation 1. Report. 190minutes
15. Finial examination and its review Review and final check
Total. - - 2480minutes
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 Examination Reports Total.
1. 25% 10% 35%
2. 25% 10% 35%
3. 20% 10% 30%
Total. 70% 30% -
Evaluation method and criteria
Reports: 30%, Final exam: 70%
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: 12:30 -- 13:00
    Fukuda: Tue. 15:00 -- 16:40
Relation to the environment
Non-environment-related course
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
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 applicatable
N/A N/A
Last modified : Thu May 30 04:29:36 JST 2019