Numerical Computation

Provides fundamental numerical algorithms including numerical solution of ordinary differential equations, linear computations, projection matrices, and finite element method. Students will write programs on these topics to understand and to use practically the algorithms. (Dept. Mechanical Eng. / Robotics, B3)


1st 4/12Introduction: Analytical solution, Numerical solution
2nd 4/19MATLAB: matrices and vectors, ODE solver, graphs
3rd 4/26MATLAB: optimization, parameters, random numbers
4th 5/10ODE: canonical forms of ordinary differential equations, state variables, Runge-Kutta method
5th 5/17ODE: Runge-Kutta-Fehlberg method, constraints, constraint stabilization method
6th 5/24Linear equations: LU decomposition, pivoting LU decomposition
7th 5/31Linear equations: pivot selecting LU decomposition, Cholesky decomposition
8th 6/ 5Projection: projection matrix, Gram-Schmidt orthogonalization, QR decomposition
9th 6/ 7Interpolation: piecewise linear interpolation, spline interpolation
10th 6/14Probabilistic algorithm: random numbers, uniform random numbers, normal random numbers
11th 6/21Probabilistic algorithm: Monte Carlo method
12th 6/28FEM: shape functions, stiffness matrix, static deformation of beam
13th 7/ 5FEM: inertia matrix, dynamic deformation of beam
14th 7/12FEM: 2D/3D deformation, 2D/3D shape functions
15th 7/19FEM: 2D/3D inertia matrix, 2D/3D stiffness matrix

Handouts
1st    Introduction reduced copy
2nd,3rd    MATLAB reduced copy    sample programs
4,5th    ODE reduced copy    sample programs    Solving ODEs with MATLAB
6,7th    Linear equations reduced copy    sample programs
8th    Projection reduced copy    sample programs
9th    Interpolation reduced copy    sample programs
10,11th    Probabilistic algorithm reduced copy    sample programs
12,13,14,15th    FEM (1 dim) reduced copy    sample programs    sample programs (class ver.)
12,13,14,15th    FEM (2 dim) reduced copy    sample programs    sample programs (class ver.)


Sample Programs    sample programs (class ver.)


Evaluation: Quizzes, reports

TextbookReference
Numerical Methods for Mechanical Systems —Matlab version— Linear Algebra and Its Applications
Shinichi HiraiGilbert Strang
Corona Publishing ISBN 978-4-339-06119-2Thomson Learning ISBN 0-15-551005-3

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