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)

1st4/11Introduction: Analytical solution, Numerical solution
2nd4/18MATLAB: vectors and matrices, matrix manipulation, graphs
3rd4/25ODE: canonical forms of ordinary differential equations, Euler/Heun/Runge-Kutta methods
4th5/ 2ODE: Runge-Kutta-Fehlberg method, holonomic constraints, constraint stabilization method (CSM)
5th5/ 9Linear equations: LU decomposition, pivot selection, solving linear equations
6th5/23Linear equations: properties of triangular matrices, determinants and inverse matrices, Cholesky decomposition
7th5/30(1st quiz; One A4 paper is available)
8th6/ 6Projection: least square meth, projection matrix, Gram-Schmidt orthogonalization, QR decomposition
9th6/13Interpolation: piecewise linear interpolation, spline interpolation
10th6/20FEM: shape functions, stiffness matrix, static deformation of beam
11th6/27FEM: inertia matrix, dynamic deformation of beam
12th7/ 2Probabilistic algorithm: random numbers, Monte Carlo method
13th7/ 4(2nd quiz; One A4 paper is available)
14th7/11Fourier transform: discrete Fourier transform (DFT), fast Fourier transform (FFT)
15th7/18Fourier 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%

Textbook: Numerical Methods for Mechanical Systems (3rd print)
            ISBN 978-4-339-06094-2
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

Sample programs (MATLAB)

Ordinary differential equations
Linear equations
Probabilistic algorithm
Fourier transform