Course overview
This course provides a rigorous and analytical treatment of classical and modern numerical methods for solving mathematical problems arising in science and engineering. Emphasis is placed on understanding the mathematical foundations of numerical algorithms, including consistency, stability, convergence, and error analysis. A distinctive component of this course is the integration of programming using Python with theory. Students will implement numerical algorithms, examine their behavior through computational experiments, and compare theoretical error estimates with practical performance. The objective is to develop both mathematical insight and computational proficiency.
- Classes will be held at N308 in Nila campus on Tuesday and Thursday 12.00 - 12.50 PM.
Syllabus
General documnets
Lecture notes
Class notes
| Lecture No. | Description | Notes |
|---|---|---|
| 1 | Review of Calculus 1 | Open |
| 2 | Review of Calculus 2 | Open |
| 3a | Taylor's Theorem | Open |
| 3b | Order of Convergence | Open |
| 4 | Mean Value Theorem for Integrals | Open |
| 5a | Error Analysis 1 | Open |
| 5b | Error Analysis 2 | Open |
| 5c | Error Analysis 3 | Open |
| 6 | Bisection Method | Open |
| 7 | Fixed Point Iterations | Open |
| 7b | Fixed Point Iterations (Cont.) | Open |
| 8 | Newton's Method | Open |
| 8b | Newton's Method (Cont.) | Open |
| 9 | Regula Falsi Method | Open |
| 9b | Regula Falsi Method (Cont. Convergence) | Open |
| 10 | Secant Method | Open |
| 11 | Aitken Extrapolation, Multiple Roots | Open |