週次 |
日期 |
單元主題 |
第1-1週 |
09/14 |
Course overview |
第1-2週 |
09/16 |
Solution of equations: Bisection, Newton's, & fixed-point methods |
第2-1週 |
09/21 |
Order of convergence of iterative methods |
第2-2週 |
09/23 |
Exercise session: Computer center 212 & Physics dept. computer room (condensed matter bldg. 3F) |
第3-1週 |
09/28 |
Secant method, Mueller method, Aitken Delta^2 process |
第3-2週 |
09/30 |
Exercise session: Computer center 212 & Physics dept. computer room (condensed matter bldg. 3F) |
第4-1週 |
10/05 |
Interpolation problem |
第4-2週 |
10/07 |
Exercise session: Computer center 212 & Physics dept. computer room (condensed matter bldg. 3F) |
第5-1週 |
10/12 |
Barycentric Lagrange interpolation |
第5-2週 |
10/14 |
Exercise session: Computer center 212 & Physics dept. computer room (condensed matter bldg. 3F) |
第6-1週 |
10/19 |
Spline interpolation |
第6-2週 |
10/21 |
Exercise session: Computer center 212 & Physics dept. computer room (condensed matter bldg. 3F) |
第7-1週 |
10/26 |
Numerical integration |
第7-2週 |
10/28 |
Exercise session: Computer center 212 & Physics dept. computer room (condensed matter bldg. 3F) |
第8-1週 |
11/02 |
Numerical quadrature |
第8-2週 |
11/04 |
Gauss quadrature rules |
第9-1週 |
11/09 |
Convergence of Gauss quadrature and others |
第9-2週 |
11/11 |
Exercise session: Computer center 212 |
第10-1週 |
11/16 |
Richardson extrapolation and its applications to numerical
integration and differentiation |
第10-2週 |
11/18 |
Numerical differentiation: finite difference approach |
第11-1週 |
11/23 |
Computer demos for computing weights of finite difference formula & numerical solver for ODEs |
第11-2週 |
11/25 |
Numerical ODE solvers: linear multistep methods |
第12-1週 |
11/31 |
No class (to Hong Kong for a conference) |
第12-2週 |
12/02 |
Exercise session: Computer center 212 |
第13-1週 |
12/7 |
LMM and pade approximates |
第13-2週 |
12/9 |
Zero stability |
第14-1週 |
12/14 |
LMM absolute stability |
第14-2週 |
12/16 |
ODE solvers for BVPs |
第15-1週 |
12/21 |
Solving linear system: LU factorization |
第15-2週 |
12/23 |
Exercise session: Computer center 212 |
第16-1週 |
12/28 |
Solving linear system: iterative methods |
第16-2週 |
12/30 |
Computer programming test |
第17-1週 |
2010/01/04 |
Least squares problems |
第17-2週 |
2010/01/06 |
QR algorithm & remarks for further topics in computational mathematics |
第18-1週 |
01/11 |
Exercise session |
第18-2週 |
01/13 |
Written test |