# ORDINARY DIFFERENTIAL EQUATIONS - 2022/3

Module code: MAT2007

## Module Overview

This module builds on the differential equation aspects of the level 1 modules Calculus and Linear Algebra and considers qualitative and quantitative aspects of Ordinary Differential Equations.

### Module provider

Mathematics

TRONCI Cesare (Maths & Phys)

### Module cap (Maximum number of students): N/A

Independent Learning Hours: 84

Lecture Hours: 33

Captured Content: 33

Semester 1

MAT1030 Calculus

## Module content

• Indicative content includes:

• Scalar first-order differential equations; review of separable and linear equations.

• Phase portraits on the line; equilibria and their stability.

• Theorems on existence, uniqueness, continuous dependence on initial conditions.

• Linear systems of differential equations: the solution set, solution matrix and Wronskian.

• Scalar, linear higher order differential equations: relation with systems of differential equations.

• Linear, autonomous systems of differential equations: relation between stability and eigenvalues; classification of planar phase portraits.

• Nonlinear systems: equilibria and their classification, linear stability analysis, Lyapunov functions, phase portrait near an equilibrium.

• If time allows: Periodic solutions and their stability: Poincare maps; introduction to Floquet theory

## Assessment pattern

Assessment type Unit of assessment Weighting
School-timetabled exam/test In-semester test (50 minutes) 20
Examination Exam (2 hours) 80

N/A

## Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate

• Understanding of and ability to interpret and solve ODEs

• Subject knowledge through the recall of key definitions, theorems and their proofs.

• Analytical ability through the solution of unseen problems in the test and exam.

Thus, the summative assessment for this module consists of:

• One final examination worth 80% of the module mark.

• One in-semester test worth 20% module mark in total.

Formative assessment and feedback

Students receive written feedback via marked coursework assignments over an 11 week period.  In addition, verbal feedback is provided by the lecturer in class or during meetings of small groups e.g. in an office hour. Furthermore, weekly exercises for formative assessment are available online, feedback can be obtained in small group meetings during office hours and via online solutions (provided with a short delay).

## Module aims

• This module aims to study both qualitative and quantitative aspects of Ordinary Differential Equations.

## Learning outcomes

 Attributes Developed 1 Find exact solutions to certain types of differential equations KCT 2 Plot and interpret phase portraits on the line or in the plane KCT 3 Determine the stability of equilibria and periodic solutions KCT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

## Methods of Teaching / Learning

The learning and teaching strategy is designed to provide:

• A detailed introduction to the theory of ordinary differential equations (ODEs);

• Experience (through demonstration) of the methods used to interpret, understand and solve ODEs.

The learning and teaching methods include:

• lectures with notes written on the board to supplement the module handbook and Q + A opportunities for students;

• seminars for guided discussion of solutions to problem sheets provided to and worked on by students in advance;

• quizzes to recap material and provide Q+A opportunity for students.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Upon accessing the reading list, please search for the module using the module code: MAT2007

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics and Physics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MPhys 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MMath 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics MMath 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Music BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Economics and Mathematics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Financial Mathematics BSc (Hons) 1 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics MMath 1 Compulsory A weighted aggregate mark of 40% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2022/3 academic year.