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)

1stIntroduction: Analytical solution, Numerical solution
2ndODE: Canonical forms of ordinary differential equations (ODEs)
3rdODE: Euler method, Heun method, and Runge-Kutta method
4thODE: Runge-Kutta-Fehlberg method
5thODE: Constraint stabilization method (CSM) (1st quiz)
6thLinear equations: Gaussian elimination, LU decomposition
7thLinear equations: Pivot selection, Redundant equations
8thProjection: Minimum error solution, Projection matrix
9thProjection: Gram-Schmidt orthogonalization, QR decomposition
10thApproximation: Piecewise linear approx., Spline approx.
11thFEM: Variational principle in statics, system with constraints (2nd quiz)
12thFEM: 1D finite element method (FEM), 2D finite element method (FEM)
13thFourier Transform: Discrete fourier transform(DFT)
14thFourier Transform: Fast fourier transform (FFT)
15thFourier Transform: Matched filter, Phase-only correlation method

Evaluation: Final Exam. 60% and Quiz 40%

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

Sample programs

Basic computations (linear computation, numerical integral, solution of equation)
Ordinary differential equation (Runge-Kutta method)
Optimization (quasi-Newton method, Nelder-Mead method, multiplier method)
Random numbers and digital filtering