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Often in mathematics, it is possible to prove the existence of a solution to a given problem, but it is not possible to "find it". For example, there are general theorems to prove the existence and uniqueness of an initial value problem for an ordinary differential equation. However, it is in general impossible to find an analytical expression for the solution. In cases like these numerical methods can provide an answer, albeit limited: for example, there are numerical procedures (called algorithms) that, given an initial value problem, will compute its solution.

This module is designed to cover four key areas: linear equations, quadratures (ie the evaluation of definite integrals) and the solution of Ordinary and Partial Differential Equations.

The nature of the module is eminently practical: we will cover relatively little of the mathematical background of the numerical techniques that we will study. On the other hand students will be
required to do a reasonable amount of programming in eg python; part of the assessment will test their ability to code in a suitable language and to put into practice the theoretical methods studied at lectures. Seven computer laboratory sessions are associated to this module and will complement the lectures.

Introduce the students to the practical application of a relatively wide spectrum of numerical techniques and familiarise the students with numerical coding.

Often in mathematics, it is possible to prove the existence of a solution to a given problem, but it is not possible to "find it". For example, there are general theorems to prove the existence and uniqueness of an initial value problem for an ordinary differential equation. However, it is in general impossible to find an analytical expression for the solution. In cases like these numerical methods can provide an answer, albeit limited: for example, there are numerical procedures (called algorithms) that, given an initial value problem, will compute its solution.

This module is designed to cover four key areas: linear equations, quadratures (ie the evaluation of definite integrals) and the solution of Ordinary and Partial Differential Equations.

The nature of the module is eminently practical: we will cover relatively little of the mathematical background of the numerical techniques that we will study. On the other hand students will be required to do a reasonable amount of programming in a language such as Matlab or Python; part of the assessment will test their ability to code in Matlab or Python and to put into practice the theoretical methods studied at lectures. Computer laboratory sessions are associated to this module and will
complement the lectures.

One of the pre-requisites for MATH6149

Modern macroeconomic research in academic, government and other institutions relies heavily on using numerical methods to simulate economic models and generate counterfactual outcome for policy analysis. This odule will familiarise the students with numerical methods that are state-of-the-art in macroeconomic research.

Modern macroeconomic research in academic, government and other institutions relies heavily on using numerical methods to simulate economic models and generate counterfactual outcome for policy analysis. This odule will familiarise the students with numerical methods that are state-of-the-art in macroeconomic research.

Modern macroeconomic research in academic, government and other institutions relies heavily on using numerical methods to simulate economic models and generate counterfactual outcome for policy analysis. This odule will familiarise the students with numerical methods that are state-of-the-art in macroeconomic research.

Modern macroeconomic research in academic, government and other institutions relies heavily on using numerical methods to simulate economic models and generate counterfactual outcome for policy analysis. This odule will familiarise the students with numerical methods that are state-of-the-art in macroeconomic research.

Mathematical models of key physical phenomena rely on nonlinear Partial Differential Equations, from industry to astrophysics to climate modelling. Detailed understanding of the solutions to these models requires, in general cases, numerical modelling. This module will introduce numerical methods for PDEs, together with analysis techniques for their stability and accuracy..

Mathematical models of key physical phenomena rely on nonlinear Partial Differential Equations, from industry to astrophysics to climate modelling. Detailed understanding of the solutions to these models requires, in general cases, numerical modelling. This module will introduce numerical methods for PDEs, together with analysis techniques for their stability and accuracy..

Mathematical models of key physical phenomena rely on nonlinear Partial Differential Equations, from industry to astrophysics to climate modelling. Detailed understanding of the solutions to these models requires, in general cases, numerical modelling. This module will introduce numerical methods for PDEs, together with analysis techniques for their stability and accuracy..

Mathematical models of complex phenomena are everywhere, from climate, to gravity, to industry. Most are complex, multi-dimensional sets of partial differential equations. The analytic solution of these equations is often impractical or impossible. This module will cover the numerical solution and analysis of a range of partial differential equations, with a focus on applications in fluid dynamics and climate modelling.