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)

1st4/ 7Introduction: Analytical solution, Numerical solution
2nd4/14MATLAB: vectors and matrices, matrix manipulation, graphs
3rd4/21ODE: canonical forms of ordinary differential equations, Euler/Heun/Runge-Kutta methods
4th4/28ODE: Runge-Kutta-Fehlberg method, holonomic constraints, constraint stabilization method (CSM)
5th5/12Linear equations: LU decomposition, pivot selection, solving linear equations
6th5/19Linear equations: properties of triangular matrices, determinants and inverse matrices, Cholesky decomposition
7th5/26(1st quiz) ODE, Linear equations
8th6/ 2Projection: least square meth, projection matrix, Gram-Schmidt orthogonalization, QR decomposition
9th6/ 9Interpolation: piecewise linear interpolation, spline interpolation
10th6/16FEM: shape functions, stiffness matrix, static deformation of beam
11th6/23FEM: inertia matrix, dynamic deformation of beam
12th6/30(2nd quiz) Projection, Interpolation, FEM
13th7/ 7Probabilistic algorithm: random numbers, Monte Carlo method
14th7/14Fourier transform: discrete Fourier transform (DFT), fast Fourier transform (FFT)
15th7/21Fourier transform: matched filter, phase-only correlation method

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
References: Linear Algebra and Its Applications
 Gilbert Strang    Thomson Learning     ISBN 0-15-551005-3

Sample programs (MATLAB)
Ordinary differential equations
Linear equations
Probabilistic algorithm
Fourier transform