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# ECON1005 Introduction to Mathematics for Economics

## Module Overview

This module provides a bridge between school mathematics and university mathematics. It provides a good grounding and 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 do not hold an A level in Mathematics at Grade B or above. It is compulsory for Joint-Honours courses with Economics for students who are not taking ECON1008. The module can also be taken as an optional module by students outside Economics who wish to follow a basic quantitative mathematics course. Topics of study include functions, univariate optimisation, elasticity, financial mathematics, multivariate optimisation, constrained optimization, matrices, integration and difference and differential equations. The module is designed to prepare students for further quantitative modules in 2nd and 3rd year. It also complements the teaching of first year microeconomics and macroeconomics modules. Co-requisite: ECON1007 One of the pre-requisites for ECON1002, ECON1007, ECON2001, ECON2002, ECON2003, ECON2004 and ECON2026

### 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 difference and differential equations.
• 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 and by parts 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, transposition and inversion.
• Solve simultaneous equations.

### 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 - Multivariate Optimization - Constrained Optimization - Matrix Algebra - Difference and Differential Equations

### Learning and Teaching

#### Teaching and learning methods

Lecture, tutorials, masterclasses, and private study.

TypeHours
Independent Study110
Seminar8
Teaching5
Lecture26
Completion of assessment task1
Total study time150

### Assessment

#### Assessment Strategy

This module is assessed as follows: Long take-home assignment (80%), Short take-home problem set (10%) and participation and performance in online quizzes (10%). This is accompanied by continuous formative assessment in form of problem sets.

#### Summative

MethodPercentage contribution
Assignment 80%
Problem sets 10%
Quizzes 10%

#### Repeat

MethodPercentage contribution
Assignment 100%

#### Referral

MethodPercentage contribution
Assignment 100%

#### Repeat Information

Repeat type: Internal & External

### Linked modules

#### Co-requisites

To study this module, you will need to also study the following module(s):

CodeModule
ECON1007Statistics for Economics

### Costs

#### Costs associated with this module

Students are responsible for meeting the cost of essential textbooks, and of producing such essays, assignments, laboratory reports and dissertations as are required to fulfil the academic requirements for each programme of study.

In addition to this, students registered for this module typically also have to pay for:

##### Books and Stationery equipment

It is not compulsory to purchase a textbook for the course. Recommended texts for this module are available in the University Library.

Please also ensure you read the section on additional costs in the University’s Fees, Charges and Expenses Regulations in the University Calendar available at www.calendar.soton.ac.uk.

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