# BA Modern Language and Business & Management (Portuguese)

Year of entry: 2022

## Course unit details:Adv Maths - BAEcon & BSc Econ

Unit code ECON10071 10 Level 1 Semester 1 Economics Yes

### Overview

This unit provides students with the essential mathematical toolkit required by economics students. At the core of the unit are constrained, multivariate optimisation problems. Such problems form a core element of many economics units and students who took Advanced Mathematics will be familiar with the required solution techniques.

Students will also be introduced to the principles of modelling dynamic variables. Simple difference equations will be introduced to model the rate of change of variables.

Students will be provided with detailed material through lectures, tutorial, reading and online videos. A discussion board will allow students to receive frequent feedback on their understanding.

### Pre/co-requisites

A Level Maths or very good AS level

### Aims

The aim of this course is to introduce mathematical techniques useful in the economic and social sciences to those students who have the appropriate advanced mathematical background.

### Learning outcomes

The objectives of this course are that students will be able to:

1. Solve simple linear equations, find roots a quadratic and understand the solution to non-linear equations.
2. Understand functions, continuity and basic differentiation.
3. Solve one and two-variable unconstrained and constrained optimisation problems using the Lagrangian method.
4. Demonstrate their understanding of linear univariate difference equations.

### Syllabus

The preliminary syllabus is

• Preliminaries and Pre-requisites. A review of your mathematical background and some observations on logic
• Functions & Univariate Calculus. Functions, continuity. Roots of equations. Limits and basic differentiation. Stationary points and optimisation. Concavity and convexity.
• Vectors and Matrices. An introduction to vectors and matrices: their mathematical manipulation - addition, multiplication. Inverse matrix. Determinants. Rank. Quadratic Forms.
• Bivariate Functions
Surfaces in 3D, contours. Partial functions and partial differentiation: the Jacobian and Hessian. Optimisation; saddle points. Concavity/convexity. Finding maxima/minima of functions of two variables subject constraints; e.g., maximising utility subject to a budget constraint.
• Dynamics. Simple dynamics. Geometric Series. Linear difference equations

### Teaching and learning methods

Online Learning and Guided self-study

### Employability skills

Analytical skills
Problem solving
Other
Using library, electronic and online resources.Numeracy, time management, improving own learning.

### Assessment methods

30% Mid-Term Online Tests

70% Final Exam

### Feedback methods

• Mock exam.
• Online quizzes.
• Tutorial feedback.
• PASS sessions.
• Office hours.
• Discussion boards.

Detailed prescribed reading is provided on the BLACKBOARD site.

The ESSENTIAL TEXT is:

A Pearson Custom Publication

Compiled by Mario Pezzino

This text has been compiled specifically for this course from three sources:

Essential Mathematics for Economic Analysis (3rd Edition), by Knut Sydsæter and Peter Hammond

Further Mathematics for Economic Analysis (2nd Edition), by Knut Sydsæter, Peter Hammond, Atle Seierstad and Arne StrØm

This text will be available as a free online textbook from the unit’s Blackboard page.

### Study hours

Independent study hours
Independent study 0

### Teaching staff

Staff member Role
Ralf Becker Unit coordinator