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 9/28Introduction: Analytical solution, Numerical solution
2nd10/ 5MATLAB: matrices and vectors, ODE solver, graphs
3rd10/12MATLAB: optimization, parameters, random numbers
4th10/19ODE: canonical forms of ordinary differential equations, state variables, Runge-Kutta method
5th10/26ODE: Runge-Kutta-Fehlberg method, constraints, constraint stabilization method
6th11/ 2Linear equations: LU decomposition, pivoting LU decomposition
7th11/ 9Linear equations: pivot selecting LU decomposition, Cholesky decomposition
8th11/16Projection: projection matrix, Gram-Schmidt orthogonalization, QR decomposition
9th11/23Interpolation: piecewise linear interpolation, spline interpolation
10th11/30Probabilistic algorithm: random numbers, uniform random numbers, normal random numbers
11th12/ 7Probabilistic algorithm: Monte Carlo method
12th12/14FEM: shape functions, stiffness matrix, static deformation of beam
13th12/21FEM: inertia matrix, dynamic deformation of beam
14th 1/ 9FEM: 2D/3D deformation, 2D/3D shape functions
15th 1/18FEM: 2D/3D inertia matrix, 2D/3D stiffness matrix

1st    Introduction reduced copy
2nd,3rd    MATLAB reduced copy    sample programs
4,5th    ODE reduced copy    sample programs
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

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