Lecture plan. Updated continously.
| Week | Theme | Curriculum |
|---|---|---|
| 3 | Introduction to MATLAB, floating point numbers, loss of significance | Ch. 1.1, 1.3, 1.4 |
| 4 | Bisection method, method of false position, Newton's method | Ch. 3.1, 3.2 |
| 5 | Modifications of Newton's method, Newton's method for nonlinear systems, fixed-point iterations | Ch. 3.2, 3.3,note |
| 6 | Linear systems, Gaussian elimination | Ch. 2.1, 2.2, |
| 7 | Gaussian elimination, banded and tridiagonal linear systems, matrix factorization | Ch. 2.2, 2.3 (not pentadiagonal systems), 8.1 |
| 8 | Matrix factorization, eigenvalues, iterative solvers for linear systems. | Ch. 8.1, 8.2 (only first 4 pages), 8.4 (not conjugate gradient) |
| 10 | Polynomial interpolation (Lagrangian interpolation, divided differences), interpolation errors. | Ch. 4.1, 4.2 |
| 11 | Interpolation errors, estimation of derivatives, Richardson extrapolation | Ch. 4.2, 4.3 |
| 12 | Numerical integration, Trapezoid rule (regular, composite, recursive), Romberg integration, Simpsons rule (regular) | Ch. 5.1, 5.2, 5.3 |
| 14 | Numerical integration, Simpsons rule (composite, adaptive), Newton Cotes rules | Ch. 5.3 |
| 15 | Gaussian quadrature, Splines (linear, quadratic) | Ch. 5.4, 6.1 (Not "Subbotin Quadratic Splines") |
| 16 | Splines (General, cubic), Least squares methods | Ch. 6.2, 9.1, 9.2 (only up to p. 439), 9.3 (Only "Inconsistent Systems") |
| 17 | Least squares methods, Initial value problems | 9.3 (Only "Use of a Weight Function w(x)"), 7.1, 7.2 |
| 17 | Initial value problems | 7.2, 7.3, 7.4 |