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)

1st4/ 9Introduction: Analytical solution, Numerical solution
2nd4/16ODE: Canonical forms of ordinary differential equations, Euler/Heun/Runge-Kutta methods
3rd4/23ODE: Runge-Kutta-Fehlberg method, Holonomic constraints, Constraint stabilization method (CSM)
4th4/30Linear equations: Gaussian elimination, LU decomposition, Triangular matrices, Cholesky decomposition
5th5/ 7Projection: Minimum error solution, Projection matrix, Gram-Schmidt orthogonalization, QR decomposition
6th5/21(1st quiz) ODE, Linear equations
7th5/26Interpolation: Piecewise linear interpolation, Spline interpolation
8th5/28Variational principles: Lagrangian, Lagrangian under constraints, Lagrange eqs. of motion
9th6/ 4Variational principles: Open link mechanism, Closed link mechanism
10th6/11Variational principles: Rigid body rotation, Quaternions
11th6/18(2nd quiz) Projection, Interpolation, Variational principles
12th6/25FEM: Shape functions, Stiffness matrix, Static deformation of beam
13th7/ 2FEM: Inertia matrix, Dynamic deformation of beam
14th7/ 9Fourier Transform: Discrete fourier transform(DFT), Fast fourier transform (FFT)
15th7/16Fourier Transform: Matched filter, Phase-only correlation method

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
References: Linear Algebra and Its Applications
 Gilbert Strang    Thomson Learning     ISBN 0-15-551005-3

Sample programs (MATLAB)
Ordinary differential equations
Linear equations