## 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 4/11 Introduction: Analytical solution, Numerical solution 2nd 4/18 MATLAB: matrices and vectors, ODE solver, graphs 3rd 4/25 MATLAB: optimization, parameters, random numbers 4th 5/ 2 ODE: canonical forms of ordinary differential equations, state variables, Runge-Kutta method 5th 5/ 9 ODE: Runge-Kutta-Fehlberg method, constraints, constraint stabilization method 6th 5/16 Linear equations: LU decomposition, pivoting LU decomposition 7th 5/23 Linear equations: pivot selecting LU decomposition, Cholesky decomposition 8th 5/30 Projection: projection matrix, Gram-Schmidt orthogonalization, QR decomposition 9th 6/ 6 Interpolation: piecewise linear interpolation, spline interpolation 10th 6/13 Probabilistic algorithm: random numbers, uniform random numbers, normal random numbers 11th 6/20 Probabilistic algorithm: Monte Carlo method 12th 6/27 FEM: shape functions, stiffness matrix, static deformation of beam 13th 7/ 4 FEM: inertia matrix, dynamic deformation of beam 14th 7/11 FEM: 2D/3D deformation, 2D/3D inertia matrix, 2D/3D stiffness matrix 15th 7/18 FEM: inelastic deformation, nodal point forces

 Evaluation Quizzes, reports

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

[Education]