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)

1st4/ 8Introduction: Analytical solution, Numerical solution
2nd4/22MATLAB: matrices and vectors, ODE solver, graphs
3rd4/27MATLAB: optimization, parameters, random numbers
4th4/29ODE: canonical forms of ordinary differential equations, Runge-Kutta method
5th5/13ODE: Runge-Kutta-Fehlberg method, constraint stabilization method (CSM)
6th5/27(1st quiz)
7th6/ 3Linear equations: LU decomposition, pivoting LU decomposition
8th6/10Linear equations: pivot selecting LU decomposition, Cholesky decomposition
9th6/17Projection: projection matrix, Gram-Schmidt orthogonalization, QR decomposition
10th6/24Interpolation: piecewise linear interpolation, spline interpolation
11th7/ 1Probabilistic algorithm: random numbers, Monte Carlo method
12th7/ 8(2nd quiz)
13th7/15FEM: shape functions, stiffness matrix, static deformation of beam
14th7/22FEM: inertia matrix, dynamic deformation of beam
15th7/23FEM: planar deformation, inelastic deformationm

1st    Introduction reduced copy
2nd,3rd    MATLAB reduced copy    sample programs    reference
4,5th    ODE reduced copy    sample programs    problems
7,8th    Linear equations reduced copy    sample programs    reference    problems
9th    Projection reduced copy    sample programs    problems
10th    Interpolation reduced copy    sample programs    problems
11th    Probabilistic algorithm reduced copy    sample programs    problems
13,14,15th    FEM reduced copy    sample programs    reference    problems

Evaluation: Final Exam. 50% and Quiz 50%

Textbook: Numerical Methods for Mechanical Systems (4th print)
            ISBN 978-4-339-06094-2
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)
Basic programs
Ordinary differential equations
Linear equations
Probabilistic algorithm