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 | 4/11 | Introduction: Analytical solution, Numerical solution | |

2nd | 4/18 | MATLAB: vectors and matrices, matrix manipulation, graphs | |

3rd | 4/25 | ODE: canonical forms of ordinary differential equations, Euler/Heun/Runge-Kutta methods | |

4th | 5/ 2 | ODE: Runge-Kutta-Fehlberg method, holonomic constraints, constraint stabilization method (CSM) | |

5th | 5/ 9 | Linear equations: LU decomposition, pivot selection, solving linear equations | |

6th | 5/23 | Linear equations: properties of triangular matrices, determinants and inverse matrices, Cholesky decomposition | |

7th | 5/30 | (1st quiz; One A4 paper is available) | |

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

9th | 6/13 | Interpolation: piecewise linear interpolation, spline interpolation | |

10th | 6/20 | FEM: shape functions, stiffness matrix, static deformation of beam | |

11th | 6/27 | FEM: inertia matrix, dynamic deformation of beam | |

12th | 7/ 2 | Probabilistic algorithm: random numbers, Monte Carlo method | |

13th | 7/ 4 | (2nd quiz; One A4 paper is available) | |

14th | 7/11 | Fourier transform: discrete Fourier transform (DFT), fast Fourier transform (FFT) | |

15th | 7/18 | Fourier transform: matched filter, phase-only correlation method |

1st Introduction (updated 2016/4/8) | reduced copy | |

2nd MATLAB (updated 2016/4/11) | reduced copy | |

3rd,4th ODE (updated 2016/4/18) | reduced copy | |

5,6th Linear equations (updated 2016/5/2) | reduced copy reference | |

8th Projection (updated 2016/6/2) | reduced copy | |

9th Interpolation (updated 2016/6/3) | reduced copy | |

10,11th FEM (updated 2016/6/6) | reduced copy | |

12th Probabilistic algorithm (updated 2016/6/21) | reduced copy | |

14,15th Fourier Transform (updated 2016/6/21) | reduced copy |

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

- 2016 Final Exam. 2016 Quiz #2 2016 Quiz #1
- 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 (3rd print) |

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

errata | |

References: | Linear Algebra and Its Applications |

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

Signal Processing (Robotics Textbook Series 4) | |

ISBN 978-4-339-04515-4 |

VectorMatrix.m | |

InnerProduct.m | |

Cholesky.m | |

qdot.m | |

ode.m |

Ordinary differential equations | |

Linear equations | |

Projection | |

Interpolation | |

Probabilistic algorithm | |

Fourier transform |

[Education]