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Department of Economics

Advanced Mathematical Methods

Course Code:
Course Not Running 2015/2016
Unit value:
Year of study:
Year 3
Taught in:
Full Year

The aim of the course is to provide a thorough treatment of advanced mathematical techniques used in macroeconomic and microeconomic analysis. Techniques to be discussed include advanced treatments of static optimisation, the key procedures of dynamic optimisation, common tools of comparative-static analysis, differential equations, dynamical systems, and an introduction to chaotic behaviour. Treatment of these techniques requires discussion of a number of techniques in pure mathematics, including topics in multivariable calculus, linear algebra, and the Laplace Transformation. Throughout the course’s discussions, techniques will be motivated and developed with reference to the relevant framework of economic analysis.

Objectives and learning outcomes of the course

On successful completion of the course, a student should be able to demonstrate the ability to: 

  • The Envelope and Implicit-Function Theorems
  • Constrained Optimisation, Concave Programming
  • Solutions of first- and second-order differential equations
  • The Laplace Transformation
  • Solutions to Linear Systems of Differential Equations
  • The Local Theory of Non-Linear Systems
  • Global Approaches to Non-Linear Systems, Chaotic Behaviour
  • Value Functions and Bellman’s Equation
  • Optimal Control and Pontryagin’s Maximum Principle

Method of assessment

Assessment weighting: Exam 80% / Coursework 20%. Resubmission of coursework regulations do not apply to this course.