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.

- 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.

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 |

Examination | Reports | Total. | |
---|---|---|---|

1. | 25% | 10% | 35% |

2. | 25% | 10% | 35% |

3. | 20% | 10% | 30% |

Total. | 70% | 30% | - |

Calculus, Linear Algebra, Ordinary differential equation, C programming or Matlab Programming

- Ishiwata: Thr 12:35-13:05

Ozaki: 12:30 -- 13:00

Fukuda: Tue. 15:00 -- 16:40

- Course that cultivates an ability for utilizing knowledge

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