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## ES10006: Core skills for economists: mathematics 2

6
Certificate (FHEQ level 4)
Semester 2
EX 80%, OT 20% Supplementary Assessment: Like-for-like reassessment (where allowed by programme regulations)
Before taking this unit you must take ES10005 Description: Aims:
To extend students' knowledge and understanding of mathematics and the use of mathematical techniques in economic analysis, begun in ES10005. To provide students with knowledge of areas of mathematics that are relevant to undergraduate economics and to prepare them for more advanced units in economics and econometrics.

Learning Outcomes:
By the end of the course unit, students should be able to understand key mathematical concepts, solve mathematical problems, and apply mathematics to economic problems.

Skills:
Students will develop mathematical skills, specifically as listed below.

Content:

* Circular functions: cycles, circles and trigonometry; calculus with circular functions; Cartesian and polar coordinates.
* Complex Numbers: the complex number system; Euler's relation; De Moivre's theorem; complex exponentials and polynomials.
* Differential Equations: first order linear differential equations with constant coefficient and constant term, dynamics of market price; second order differential equations with constant coefficient and constant term, market model with price expectations.
* Difference Equations: discrete time, differences; first order difference equations, dynamic stability of equilibrium, the Cobweb model; second order linear difference equations; Samuelson multiplier acceleration interaction model.
* Eigenvalues and Eigenvectors: the concept of diagonalisable matrices, calculation of the characteristic polynomial, eigenvalues of symmetric matrices.
* Simultaneous Differential and Difference Equations: systems of difference and differential equations; solving simultaneous dynamic equations; phase diagrams.
Key texts:
A.C. Chiang Fundamental Methods of Mathematical Economics
Hoy, Livernois, McKenna, Rees and Stengos Mathematics for Economists. Programme availability:

#### ES10006 is Compulsory on the following programmes:

Department of Economics
• UHES-AFB03 : BSc (hons) Economics (Full-time) - Year 1
• UHES-AKB03 : BSc (hons) Economics (Full-time with Thick Sandwich Placement) - Year 1

#### ES10006 is Optional on the following programmes:

Department of Economics
• UHES-AFB01 : BSc (hons) Economics and Politics (Full-time) - Year 1
• UHES-AKB01 : BSc (hons) Economics and Politics (Full-time with Thick Sandwich Placement) - Year 1

NB. Programmes and units are subject to change at any time, in accordance with normal University procedures.