## 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 Introduction: Analytical solution, Numerical solution 2nd ODE: Canonical forms of ordinary differential equations (ODEs) 3rd ODE: Euler method, Heun method, and Runge-Kutta method 4th ODE: Runge-Kutta-Fehlberg method 5th ODE: Constraint stabilization method (CSM) (1st quiz) 6th Linear equations: Gaussian elimination, LU decomposition 7th Linear equations: Pivot selection, Redundant equations 8th Projection: Minimum error solution, Projection matrix 9th Projection: Gram-Schmidt orthogonalization, QR decomposition 10th Approximation: Piecewise linear approx., Spline approx. 11th FEM: Variational principle in statics, system with constraints (2nd quiz) 12th FEM: 1D finite element method (FEM), 2D finite element method (FEM) 13th Fourier Transform: Discrete fourier transform(DFT) 14th Fourier Transform: Fast fourier transform (FFT) 15th Fourier 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)  Readme Readme Makefile Makefile Header file opt.h Linear computation mat.c mat-t0.c Numerical integral int.c int-t0.c int-t1.c Solution of equation eqs.c eqs-t0.c