- Department: Mathematics
- Credit value: 20 credits
- Credit level: H
- Academic year of delivery: 2023-24
- See module specification for other years: 2024-25
The field of numerical analysis allows for the numerical approximation of solutions of mathematical equations using computational algorithms. This module introduces methods for mathematical problems such as the approximation of roots, derivatives and integrals of a function, and solutions to ODEs and PDEs.
Occurrence | Teaching period |
---|---|
A | Semester 2 2023-24 |
The field of numerical analysis allows for the numerical approximation of solutions of mathematical equations using computational algorithms. This module introduces methods for mathematical problems such as the approximation of roots, derivatives and integrals of a function, and solutions to ODEs and PDEs.
By the end of this module students will be expected to:
Apply an appropriate numerical technique to approximate the solution to various mathematical problems.
Mathematically analyse the stability and/or error of a given numerical technique (e.g. the local truncation and total error of a particular integration method or the region of stability for a Runge-Kutta method).
Use a computational coding language (such as MATLAB, MAPLE, C++, Python, etc.) to apply a numerical technique learned in the module.
The module will cover basic numerical techniques used in the vast majority of applications in science and technology. Specifically, methods for (1) root finding (Binomial, Secant, and Newton's methods), (2) calculation of the solution to a system of linear equations such as Ax=b, (3) interpolation of data points using polynomials and splines, (4) numerical approximation of derivatives and integrals, (5) the minimization of functions, and (6) solutions to ODEs and PDEs.
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 60 |
Essay/coursework | 40 |
None
The coursework mark will be made up of 10 smaller pieces of work completed during the semester.
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 60 |
Essay/coursework | 40 |
Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy.
Burden, Faires “Numerical analysis”
Butcher, “Numerical Methods for ODEs”
Press et al, “Numerical Recipes in C++”