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 algorithms. (Dept. Mechanical Eng. / Robotics, B3)

1st4/ 9Introduction: Analytical solution, Numerical solution
2nd4/16MATLAB: matrices and vectors, ODE solver, graphs
3rd4/21MATLAB: optimization, parameters, random numbers
4th4/30ODE: canonical forms of ordinary differential equations, Runge-Kutta method
5th5/ 7ODE: Runge-Kutta-Fehlberg method, constraint stabilization method (CSM)
6th5/14(1st quiz)
7th5/28Linear equations: LU decomposition, pivoting LU decomposition
8th6/ 4Linear equations: pivot selecting LU decomposition, Cholesky decomposition
9th6/ 9Projection: projection matrix, Gram-Schmidt orthogonalization, QR decomposition
10th6/11Interpolation: piecewise linear interpolation, spline interpolation
11th6/25(2nd quiz)
12th7/ 2FEM: shape functions, stiffness matrix, static deformation of beam
13th7/ 9FEM: inertia matrix, dynamic deformation of beam
14th7/14FEM: planar deformation, inelastic deformationm
15th7/16Probabilistic algorithm: random numbers, Monte Carlo method

1st    Introduction reduced copy
2nd,3rd    MATLAB reduced copy    sample programs    reference
4,5th    ODE reduced copy    sample programs    problems
7,8th    Linear equations reduced copy    sample programs    reference    problems
9th    Projection reduced copy    sample programs    problems
10th    Interpolation reduced copy    sample programs    problems
12,13,14th    FEM reduced copy    reference    problems
15th    Probabilistic algorithm reduced copy    problems

Evaluation: Final Exam. 60% and Quiz 40%

Textbook: Numerical Methods for Mechanical Systems (4th 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)
Basic programs
Ordinary differential equations
Linear equations
Probabilistic algorithm