Lecture | Date | Main Topic | Chapter |
1 | Tu 01/29 | Overview | |
2 | Th 01/31 | Gaussian elimination: LU factorization | 8 |
3, #1 | Tu 02/05 | Taylor's theorem in one dimension | 1 |
4 | Th 02/07 | Taylor's theorem in higher dimensions | 1 |
5, #2 | Tu 02/12 | Interpolation: existence and uniqueness | 3 |
6 | Th 02/14 | Interpolation: Newton divided differences, error theorem | 3 |
7 | Tu 02/19 | Interpolation: cubic spline interpolation | 3 |
8 | Th 02/21 | Interpolation: problems with equidistant nodes | 3 |
9, #3 | Tu 02/26 | Numerical differentiation: idea and methods | 5 |
10 | Th 02/28 | Numerical differentiation: errors and effect of round-off | 5 |
11 | Tu 03/05 | Numerical integration: idea and trapezoidal rule | 5 |
12, #4 | Th 03/07 | Numerical integration: Simpson and other rules | 5 |
13 | Tu 03/12 | Numerical integration: Gaussian quadrature | 5 |
14 | Th 03/14 | Midterm exam | |
15 | Tu 03/19 | Approximation: orthogonal polynomials | 4 |
16, #5 | Th 03/21 | Approximation: concepts and theory | 4 |
Tu 03/26 | Spring Break | ||
Th 03/28 | Spring Break | ||
17 | Tu 04/02 | Rootfinding: basic methods | 2 |
18 | Th 04/04 | Rootfinding: theory of fixed-point methods | 2 |
19 | Tu 04/09 | Systems of nonlinear equations: Newton's method | 2 |
20, #6 | Th 04/11 | Systems of nonlinear equations: Newton's method | 2 |
21 | Tu 04/16 | Numerical o.d.e.'s: problem and mathematical theory | 6 |
22 | Th 04/18 | Numerical o.d.e.'s: basic methods, local truncation error | 6 |
23 | Tu 04/23 | Numerical o.d.e.'s: theory of Euler's method | 6 |
24, #7 | Th 04/25 | Numerical o.d.e.'s: accuracy and stability | 6 |
25 | Tu 04/30 | Numerical o.d.e.'s: linear multi-step methods | 6 |
26 | Th 05/02 | Numerical o.d.e.'s: Runge-Kutta methods | 6 |
27 | Tu 05/07 | Numerical o.d.e.'s: methods for stiff problems | 6 |
28, #8 | Th 05/09 | Computer numbers: IEEE-standard for floating-point numbers | 1 |
29 | Tu 05/14 | Review | |