ACM41000

This module is a synthesis of modern Applied Mathematics and Statistical Inference, and introduces students to statistical methods to determine model parameters in otherwise deterministic mathematical models. The module starts with a review of deterministic models – ordinary and partial differential equations (both linear and nonlinear). Included in this review is a topical summary of nonlinear ordinary differential equations, reaction-diffusion partial differential equations, and optimization of partial-differential equation models using an adjoint method. Students will learn how to use these equation systems to model physical systems. In doing so, various model parameters appear, which in turn need to be modelled. These parameters can be determined by reference to experimental data, which can then be used to make predictions. As such, in the second part of the module students will learn how to estimate and attain confidence limits for the parameters of the differential equations from noisy and often partially observed data.