Provides fundamental numerical algorithms including linear computations, Fourier transform, ordinary differential equations, finite element method, random numbers, digital filtering, and digital image processing. Students will write programs on these topics to understand and to use practically the alogorithms. (Dept. Mechanical Eng. / Robotics / Micro System Tech., B3)

1st | 4/ 8 | Introduction: Analytical solution, Numerical solution | |

2nd | 4/15 | ODE: Canonical forms of ordinary differential equations, Euler/Heun/Runge-Kutta methods | |

3rd | 4/22 | ODE: Runge-Kutta-Fehlberg method, Holonomic constraints, Constraint stabilization method (CSM) | |

4th | 4/29 | Linear equations: Gaussian elimination, LU decomposition, Triangular matrices, Cholesky decomposition | |

5th | 5/11 | Projection: Minimum error solution, Projection matrix, Gram-Schmidt orthogonalization, QR decomposition | |

6th | 5/13 | (1st quiz) ODE, Linear equations | |

7th | 5/20 | Interpolation: Piecewise linear interpolation, Spline interpolation | |

8th | 5/27 | Variational principles: Lagrangian, Lagrangian under constraints, Lagrange eqs. of motion | |

9th | 6/ 3 | Variational principles: Open link mechanism, Closed link mechanism | |

10th | 6/ 8 | Variational principles: Rigid body rotation, Quaternions | |

11th | 6/10 | (2nd quiz) Projection, Interpolation, Variational principles | |

12th | 6/17 | FEM: Shape functions, Stiffness matrix, Static deformation of beam | |

13th | 7/ 1 | FEM: Inertia matrix, Dynamic deformation of beam | |

14th | 7/ 8 | Fourier Transform: Discrete fourier transform(DFT), Fast fourier transform (FFT) | |

15th | 7/20 | Fourier Transform: Matched filter, Phase-only correlation method |

1st Introduction (updated 2013/4/2) | reduced copy | ||

2nd,3rd ODE (updated 2013/4/16) (updated 2013/4/14) | reduced copy | ||

4th Linear equations (updated 2013/4/16) | reduced copy | ||

5,6th Projection (updated 2013/4/29) | reduced copy | ||

7th Interpolation (updated 2013/5/15) | reduced copy | ||

8,9,10th Variational principles (updated 2013/5/27) (updated 2013/5/26) | reduced copy | ||

11,12,13th FEM (updated 2013/5/27) | reduced copy | ||

14,15th Fourier Transform (updated 2013/5/27) | reduced copy | ||

Numerical Methods for Mechanical Systems (2nd print) errata (updated 2013/5/27) (updated 2013/4/2) |

Evaluation: | Final Exam. 60% and Quiz 40% |

Textbook: | Numerical Methods for Mechanical Systems (2nd print) |

ISBN 978-4-339-06094-2 | |

errata | |

References: | Linear Algebra and Its Applications |

Gilbert Strang Thomson Learning ISBN 0-15-551005-3 |

Ordinary differential equations | |

Linear equations | |

Projection | |

Interpolation | |

Fourier transform |

[Education]