The University of Southampton
Courses

# ECON1008 Mathematics for Economics

## Module Overview

This module provides a bridge between A-level mathematics and university mathematics. It provides a good grounding and an in depth understanding of the theory and application of differential calculus, and other techniques widely used in Economics and Finance. It is aimed at students who hold an A level in Mathematics at Grade B or above. Topics of study include functions, univariate optimisation, elasticity, financial mathematics, multivariate optimisation, constrained optimization, matrices, integration, difference and differential equations, and Taylor/Maclaurin series expansions. What distinguishes this module from ECON1005 is not so much the techniques or the applications, but the greater confidence in using mathematics in applications and students' subsequent capacity for abstract thought. The module is designed to prepare students for more advance quantitative modules in 2nd and 3rd year. It also complements the teaching of first year microeconomics and macroeconomics modules. Co-requisite: ECON1007 Pre-requisite for ECON1011 One of the pre-requisites for MATH2040, MATH3085, ECON1007, ECON2001, ECON2002, ECON2003, ECON2004, ECON2026 and ECON3016

### Aims and Objectives

#### Learning Outcomes

##### Learning Outcomes

Having successfully completed this module you will be able to:

• Solve unconstrained optimization problems involving functions of single and multiple variables.
• Solve simultaneous equations using matrix inversion and Cramer's Rule.
• Solve differential equations.
• Apply the Taylor/Maclaurin series expansions.
• Use the Lagrange multiplier method to solve constrained optimization problems involving functions of single and multiple variables.
• Distinguish the types of stationary points.
• Perform basic integration.
• Calculate arc and point elasticity.
• Solve problems involving variables that discretely and continuously grow over time, and compute present discounted values, future compounded values, and rates of growth.
• Manipulate exponential and logarithmic functions and solve problems involving such functions.
• Perform basic matrix operations, including addition and subtraction, scalar multiplication, matrix multiplication, and transposition.
• Find the inverse of a matrix.

### Syllabus

- Single Variable Optimisation - Economic Applications of functions, derivatives and single variable optimisation - Integration and Economic Applications - Elasticity - Compound growth and discounting - Exponential and Logarithmic Functions - Functions of Several Variables - Multivariable Optimization - Constrained Optimization - Matrix Algebra - Difference and Differential Equations - Taylor/Maclaurin series expansions

### Learning and Teaching

#### Teaching and learning methods

Lectures, tutorials, and private study.

TypeHours
Teaching34
Independent Study116
Total study time150

### Assessment

#### Assessment Strategy

Coursework counts for 10% of the total mark. The final exam counts for 90% of the final mark.

#### Summative

MethodPercentage contribution
Coursework 10%
Exam  (2 hours) 90%

#### Referral

MethodPercentage contribution
Exam  (2 hours) 100%

#### Repeat Information

Repeat type: Internal & External