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

Handouts

 Evaluation: Quizzes, reports

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