# BSc Mathematics with Finance

Year of entry: 2024

## Course unit details:Methods of Applied Mathematics

Unit code MATH35041 20 Level 3 Semester 1 No

### Overview

This course unit provides students with the methodology to study problems which arise in applied mathematics.  Often, the analytical solution to such a problem involves approximation in terms of a small parameter. We consider asymptotic expansions, such that the error made is controlled.

### Pre/co-requisites

Unit title Unit code Requirement type Description
Calculus and Applications A MATH10222 Pre-Requisite Compulsory
Calculus and Applications B MATH10232 Pre-Requisite Compulsory
Partial Differential Equations and Vector Calculus A MATH20401 Pre-Requisite Compulsory

### Aims

This course unit introduces students to important topics in applied mathematics, developing their understanding of asymptotic methods and calculus of variations. The syllabus is motivated by physical applications of historical importance.

### Learning outcomes

• Apply asymptotic methods to obtain perturbation expansions of algebraic equations.
• Compute asymptotic expansions of integrals containing a parameter.
• Calculate asymptotic solutions to ODEs containing a parameter, matching the inner and outer solutions as appropriate.
• Interpret variational problems and solve the corresponding Euler-Lagrange equations.
• Calculate solutions to standard variational problems (e.g. the brachistochrone, Fermat’s principle, geodesics, minimal surface, the isoperimetric problem, the hanging chain).
• Formulate equations of motion in classical mechanics from a Lagrangian, via Hamilton’s Principle and describe solutions to mechanical problems using the Euler-Lagrange equations and/or perturbation theory.
• Estimate eigenvalues via the Rayleigh-Ritz method and apply to physical problems.

Method Weight
Written exam 80%
Report 20%

### Feedback methods

Individual feedback via marking comments, and cohort feedback document circulated.

### Study hours

Scheduled activity hours
Lectures 33
Tutorials 11
Independent study hours
Independent study 150

### Teaching staff

Staff member Role
Neil Morrison Unit coordinator
Paul Glendinning Unit coordinator