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, B3)

1st | 4/13 | Introduction: Analytical solution, Numerical solution | |

2nd | 4/20 | MATLAB: vectors and matrices, matrix manipulation, graphs | |

3rd | 4/27 | ODE: canonical forms of ordinary differential equations, Euler/Heun/Runge-Kutta methods | |

4th | 5/ 9 | ODE: Runge-Kutta-Fehlberg method, holonomic constraints, constraint stabilization method (CSM) | |

5th | 5/11 | Linear equations: LU decomposition, pivot selection, solving linear equations | |

6th | 5/18 | Linear equations: properties of triangular matrices, determinants and inverse matrices, Cholesky decomposition | |

7th | 5/25 | (1st quiz) ODE, Linear equations | |

8th | 6/ 6 | Projection: least square meth, projection matrix, Gram-Schmidt orthogonalization, QR decomposition | |

9th | 6/ 8 | Interpolation: piecewise linear interpolation, spline interpolation | |

10th | 6/15 | FEM: shape functions, stiffness matrix, static deformation of beam | |

11th | 6/22 | FEM: inertia matrix, dynamic deformation of beam | |

12th | 6/29 | (2nd quiz) Projection, Interpolation, FEM | |

13th | 7/ 6 | Probabilistic algorithm: random numbers, Monte Carlo method | |

14th | 7/13 | Fourier transform: discrete Fourier transform (DFT), fast Fourier transform (FFT) | |

15th | 7/20 | Fourier transform: matched filter, phase-only correlation method |

1st Introduction (updated 2015/4/9) | reduced copy | ||

2nd MATLAB (updated 2015/4/9) | reduced copy | ||

3rd,4th ODE (updated 2015/4/20) | reduced copy | ||

5,6th Linear equations (updated 2015/4/22) | reduced copy | ||

8th Projection (updated 2015/4/27) | reduced copy | ||

9th Interpolation (updated 2015/4/28) | reduced copy | ||

11,12th FEM (updated 2015/6/8) | reduced copy | ||

13th Probabilistic algorithm (updated 2015/7/2) | reduced copy | ||

14,15th Fourier Transform (updated 2015/7/2) | reduced copy | ||

Numerical Methods for Mechanical Systems (2nd print) errata (updated 2015/4/27) |

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

- 2015 Final Exam. 2015 Quiz #2 2015 Quiz #1
- 2014 Final Exam. 2014 Quiz #2 2014 Quiz #1
- 2013 Final Exam. 2013 Quiz #2 2013 Quiz #1
- 2012 Final Exam. 2012 Quiz #2 2012 Quiz #1

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 |

VectorMatrix.m | |

InnerProduct.m | |

Cholesky.m | |

qdot.m | |

ode.m |

Ordinary differential equations | |

Linear equations | |

Projection | |

Interpolation | |

Probabilistic algorithm | |

Fourier transform |

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