Course Brief Description
This course is a continuation of MATH/CMPSC 455. We will
describe numerical algorithms for solving nonlinear equations,
approximation functions and data, numerical integration,
solving linear systems, Eigenvalue problems, Solving ordinary
differential equations and boundary-value problems. We will
also discuss the underlying mathematical principles and theories
of these numerical methods and their implementations.
Some knowledge of either MATLAB, Octave, Fortran, C, or C++ is
strongly
recommended. MATLAB is used for exposition of algorithms
during the class. You can choose any computer language as a
platform for homework and projects.
Grading Policy
- Homework & Computer projects (50 %);
- Midterm exam (20 %): March 2;
- Final exam (30 %).
Details about midterm and final exam will be announced later.
Lecture Notes & Slides
0. Introduction:
slides
1.1 Newton' Method:
slides
1.2 Quasi-Newton Methods:
slides
1.3 FPI and Aitken Acceleration:
slides 1
&
slides
2
2.1 Polynomial Interpolation:
slides
2.2 Trigonometric Interpolation:
slides
2.3 Piecewise Interpolation:
slides
2.4 Least Square Method:
slides
3.1 Adaptive Quadrature:
slides
4.2 Basic Linear Iterative Methods:
slides
4.3 Krylov Subspace Method:
slides
5. Eigenvalue Problems:
slides
6.1 Ordinary Differential Equations:
slides
7.1 Finite Difference Method:
slides
7.2 Finite Element Method:
slides
