Class | Date | Main Topic | Section(s) |
1 | We 08/31 | Overview | |
Mo 09/05 | Labor Day | ||
2, #1 | We 09/07 | Gaussian elimination: LU factorization | 8.1 |
3 | Mo 09/12 | Taylor's theorem in one dimension | 1.1 |
4 | We 09/14 | Taylor's theorem in higher dimensions | 1.1 |
5, #2 | Mo 09/19 | Interpolation: existence and uniqueness | 3.1 |
6 | We 09/21 | Interpolation: Newton divided differences, error theorem | 3.2 |
7 | Mo 09/26 | Interpolation: problems with equidistant nodes | 3.5 |
8, #3 | We 09/28 | Interpolation: cubic spline interpolation | 3.7 |
9 | Mo 10/03 | Numerical differentiation: idea and methods | 5.7 |
10, #4 | We 10/05 | Numerical differentiation: errors and effect of round-off | 5.7 |
11 | Mo 10/10 | Numerical integration: idea and trapezoidal rule | 5.1 |
12, #5 | We 10/12 | Numerical integration: Simpson and other rules | 5.2 |
13 | Mo 10/17 | Numerical integration: Gaussian quadrature | 5.3 |
14, #6 | We 10/19 | Approximation: concepts and theory | 4.1-4.3 |
15 | Mo 10/24 | Approximation: orthogonal polynomials | 4.4 |
16, #7 | We 10/26 | Approximation: relation to interpolation | 4.5-4.7 |
17 | Mo 10/31 | Midterm exam | |
18, #8 | We 11/02 | Rootfinding: basic methods | 2.0-2.3 |
19 | Mo 11/07 | Rootfinding: theory of fixed-point methods | 2.5 |
20, #9 | We 11/09 | Systems of nonlinear equations: Newton's method | 2.10, 2.12 |
21 | Mo 11/14 | Systems of nonlinear equations: Newton's method | 2.11 |
22, #10 | We 11/16 | Numerical o.d.e.'s: problem and mathematical theory | 6.1 |
23 | Mo 11/21 | Numerical o.d.e.'s: basic methods, local truncation error | 6.2-6.5 |
24, #11 | We 11/23 | Numerical o.d.e.'s: accuracy and stability | 6.2 |
25 | Mo 11/28 | Numerical o.d.e.'s: linear multi-step methods | 6.8 |
26, #12 | We 11/30 | Numerical o.d.e.'s: Runge-Kutta methods | 6.10 |
27 | Mo 12/05 | Numerical o.d.e.'s: methods for stiff problems | 6.9 |
28, #13 | We 12/07 | Computer numbers: IEEE-standard for floating-point numbers | 1.2 |
29 | Mo 12/12 | Computer numbers: IEEE-standard for floating-point numbers | 1.2 |
Mo 12/19 | 03:30-05:30 Final Exam Note the date and time! | ||