## MATH1400 Modelling with Differential Equations

### 10 creditsClass Size: 230

Module manager: Dr Sam Pegler
Email: s.pegler@leeds.ac.uk

Taught: Semester 2 (Jan to Jun) View Timetable

Year running 2022/23

### Pre-requisite qualifications

MATH1050 and (MATH1060 or MATH1331). Note that MATH1060 can be taken as a co-requisite.

### This module is mutually exclusive with

 LUBS1275 Mathematics and Statistics for Economics and Business 1A LUBS1285 Mathematics and Statistics for Economics and Business 1B MATH1005 Core Mathematics

This module is approved as a discovery module

### Module summary

The applied mathematician attempts to give a mathematical description (a mathematical model) of things in the real world. In the real world most things change with time. Mathematically a rate of change is expressed as a derivative so the applied mathematician deals mostly with equations involving derivatives - so called differential equations. This module develops the theory of differential equations and applies it to produce mathematical models describing eg the way in which the population of the world varies with time, and the way in which an influenza virus propagates through a university campus. Students will complete a mini-project to practice presentation skills.

### Objectives

To introduce the concept of mathematical modelling. To illustrate its application in various areas and to develop relevant methods for the solution of first and second order ODEs.

On completion of this module, students should be able to:
(a) set up simple first and second order differential equations to model processes such as radioactive decay, Newton cooling, population growth and mixing problems;
(b) solve first order differential equations of various types such as separable, homogenous, linear, and to apply initial conditions to the general solution;
(c) solve second order linear differential equations with constant coefficients by finding complementary functions and particular integrals, and to apply either initial or boundary conditions.
(d) develop communication and group working skills.

### Syllabus

1. The modelling process via simple examples: exponential growth and decay etc.
2. Solution of first order ODEs: linear via integrating factor, nonlinear via substitutions.
3. Application of first order ODEs to modelling population growth, etc.
4. Solution of second order ODEs (linear with constant coefficients) and simultaneous ODEs. Reduction of order.
5. Application of second order ODEs to examples.

### Teaching methods

 Delivery type Number Length hours Student hours Lecture 22 1.00 22.00 Tutorial 9 1.00 9.00 Private study hours 69.00 Total Contact hours 31.00 Total hours (100hr per 10 credits) 100.00

### Private study

Studying and revising of course material.
Completing of assignments and assessments.

### Opportunities for Formative Feedback

Regular example sheets.

!!! In order to pass the module, students must pass the examination. !!!

### Methods of assessment

Coursework
 Assessment type Notes % of formal assessment In-course Assessment . 15.00 Project . 5.00 Total percentage (Assessment Coursework) 20.00

There is no resit available for the coursework component of this module. If the module is failed, the coursework mark will be carried forward and added to the resit exam mark with the same weighting as listed above.

Exams
 Exam type Exam duration % of formal assessment Standard exam (closed essays, MCQs etc) 2 hr 00 mins 80.00 Total percentage (Assessment Exams) 80.00

Normally resits will be assessed by the same methodology as the first attempt, unless otherwise stated