## 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/ 8 Introduction: Analytical solution, Numerical solution 2nd 4/22 MATLAB: matrices and vectors, ODE solver, graphs 3rd 4/27 MATLAB: optimization, parameters, random numbers 4th 4/29 ODE: canonical forms of ordinary differential equations, Runge-Kutta method 5th 5/13 ODE: Runge-Kutta-Fehlberg method, constraint stabilization method (CSM) 6th 5/27 (1st quiz) 7th 6/ 3 Linear equations: LU decomposition, pivoting LU decomposition 8th 6/10 Linear equations: pivot selecting LU decomposition, Cholesky decomposition 9th 6/17 Projection: projection matrix, Gram-Schmidt orthogonalization, QR decomposition 10th 6/24 Interpolation: piecewise linear interpolation, spline interpolation 11th 7/ 1 Probabilistic algorithm: random numbers, Monte Carlo method 12th 7/ 8 (2nd quiz) 13th 7/15 FEM: shape functions, stiffness matrix, static deformation of beam 14th 7/22 FEM: inertia matrix, dynamic deformation of beam 15th 7/23 FEM: planar deformation, inelastic deformationm

Handouts

 Evaluation: Final Exam. 50% and Quiz 50%

 Textbook: Numerical Methods for Mechanical Systems (4th print) ISBN 978-4-339-06094-2 errata 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)

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