## ES10006: Core skills for economists: mathematics 2

[Page last updated: 15 October 2020]

Owning Department/School: Department of Economics
Credits: 6      [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Certificate (FHEQ level 4)
Period:
Semester 2
Assessment Summary: CW 80%, MC 20%
Assessment Detail:
• MCQ Test (MC 20%)
• Coursework (CW 80%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites: Before taking this module 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:

* Integration: indefinite integration as the reverse of differentiation. Definite integration and the area under a curve.
* 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.
Programme availability:

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

Department of Economics
• UHES-AFB03 : BSc(Hons) Economics (Year 1)
• UHES-AAB03 : BSc(Hons) Economics with Study year abroad (Year 1)
• UHES-AKB03 : BSc(Hons) Economics with Year long work placement (Year 1)
• UHES-ACB03 : BSc(Hons) Economics with Combined Placement and Study Abroad (Year 1)

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

Department of Economics
• UHES-AFB01 : BSc(Hons) Economics and Politics (Year 1)
• UHES-AAB01 : BSc(Hons) Economics and Politics with Study year abroad (Year 1)
• UHES-AKB01 : BSc(Hons) Economics and Politics with Year long work placement (Year 1)
• UHES-ACB01 : BSc(Hons) Economics and Politics with Combined Placement and Study Abroad (Year 1)

 Notes: This unit catalogue is applicable for the 2020/21 academic year only. Students continuing their studies into 2021/22 and beyond should not assume that this unit will be available in future years in the format displayed here for 2020/21. Programmes and units are subject to change in accordance with normal University procedures. Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.Find out more about these and other important University terms and conditions here.