## Numerical Computation

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/ 7 Introduction: Analytical solution, Numerical solution 2nd 4/14 MATLAB: vectors and matrices, matrix manipulation, graphs 3rd 4/21 ODE: canonical forms of ordinary differential equations, Euler/Heun/Runge-Kutta methods 4th 4/28 ODE: Runge-Kutta-Fehlberg method, holonomic constraints, constraint stabilization method (CSM) 5th 5/12 Linear equations: LU decomposition, pivot selection, solving linear equations 6th 5/19 Linear equations: properties of triangular matrices, determinants and inverse matrices, Cholesky decomposition 7th 5/26 (1st quiz) ODE, Linear equations 8th 6/ 2 Projection: least square meth, projection matrix, Gram-Schmidt orthogonalization, QR decomposition 9th 6/ 9 Interpolation: piecewise linear interpolation, spline interpolation 10th 6/16 FEM: shape functions, stiffness matrix, static deformation of beam 11th 6/23 FEM: inertia matrix, dynamic deformation of beam 12th 6/30 (2nd quiz) Projection, Interpolation, FEM 13th 7/ 7 Probabilistic algorithm: random numbers, Monte Carlo method 14th 7/14 Fourier transform: discrete Fourier transform (DFT), fast Fourier transform (FFT) 15th 7/21 Fourier transform: matched filter, phase-only correlation method

Handouts
 1st    Introduction (updated 2014/4/2) reduced copy 2nd    MATLAB (updated 2014/4/2) reduced copy 3rd,4th    ODE (updated 2014/4/16) (updated 2014/4/14) reduced copy 5,6th    Linear equations (updated 2014/4/14) reduced copy 8th    Projection (updated 2014/5/14) reduced copy 9th    Interpolation (updated 2014/5/14) reduced copy 11,12th    FEM (updated 2014/6/9) reduced copy 13th    Probabilistic algorithm (updated 2014/7/1) reduced copy 14,15th    Fourier Transform (updated 2014/7/1) 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

Sample programs (MATLAB)

[Education]