## Applied Mathematic III

Provides fundamental numerical algorithms including linear computations, Fourier transform, ordinary differential equations, finite element method, random numbers, digital filtering, and digital image processing. Students will write programs on these topics to understand and to use practically the alogorithms. (Dept. Mechanical Eng. / Robotics / Micro System Tech., B3)

 1st 4/ 9 Introduction: Analytical solution, Numerical solution 2nd 4/16 ODE: Canonical forms of ordinary differential equations, Euler/Heun/Runge-Kutta methods 3rd 4/23 ODE: Runge-Kutta-Fehlberg method, Holonomic constraints, Constraint stabilization method (CSM) 4th 4/30 Linear equations: Gaussian elimination, LU decomposition, Triangular matrices, Cholesky decomposition 5th 5/ 7 Projection: Minimum error solution, Projection matrix, Gram-Schmidt orthogonalization, QR decomposition 6th 5/21 (1st quiz) ODE, Linear equations 7th 5/26 Interpolation: Piecewise linear interpolation, Spline interpolation 8th 5/28 Variational principles: Lagrangian, Lagrangian under constraints, Lagrange eqs. of motion 9th 6/ 4 Variational principles: Open link mechanism, Closed link mechanism 10th 6/11 Variational principles: Rigid body rotation, Quaternions 11th 6/18 (2nd quiz) Projection, Interpolation, Variational principles 12th 6/25 FEM: Shape functions, Stiffness matrix, Static deformation of beam 13th 7/ 2 FEM: Inertia matrix, Dynamic deformation of beam 14th 7/ 9 Fourier Transform: Discrete fourier transform(DFT), Fast fourier transform (FFT) 15th 7/16 Fourier Transform: Matched filter, Phase-only correlation method 16th 7/30 (examination)

Handouts
 1st    Introduction (updated 2012/3/5) reduced copy 2nd,3rd    ODE (updated 2012/4/13) (updated 2012/3/5) reduced copy 4th    Linear equations (updated 2012/4/13) (updated 2012/3/16) reduced copy 5,6th    Projection (updated 2012/6/22) (updated 2012/3/21) reduced copy 7th    Interpolation (updated 2012/4/13) (updated 2012/3/23) reduced copy 8,9,10th    Variational principles (updated 2012/6/12) (updated 2012/6/11) (updated 2012/3/23) reduced copy 11,12,13th    FEM (updated 2012/7/2) (updated 2012/6/29) (updated 2012/3/26) reduced copy 14,15th    Fourier Transform (updated 2012/7/16) (updated 2012/6/20) reduced copy Numerical Methods for Mechanical Systems (2nd print) errata (updated 2012/7/4)

 Evaluation: Final Exam. 60% and Quiz 40%

 Textbook: Numerical Methods for Mechanical Systems (2nd print) ISBN 978-4-339-06094-2 errata References: Linear Algebra and Its Applications Gilbert Strang    Thomson Learning     ISBN 0-15-551005-3

Sample programs (MATLAB)

[Education]