# Mathematics

## ECM2702 - Differential Equations (2015)

MODULE TITLE CREDIT VALUE Differential Equations 15 ECM2702 Prof Vadim N Biktashev (Coordinator)
DURATION: TERM 1 2 3
DURATION: WEEKS 11 weeks 0 0
 Number of Students Taking Module (anticipated) 230
DESCRIPTION - summary of the module content

Differential equations are at the heart of nearly all modern applications of mathematics to natural phenomena. Computerised applications play a vital role in many areas of modern technology. Mathematically, all rates of change and acceleration can be described by derivative functions. These include the growth of plants and organisms, the spread of diseases, physical forces acting on an object or even the fluctuations of the stock market. You will learn the basic principles of differential equations, and will apply that knowledge to some every day phenomena. Then you will learn about calculation methods and computer models for general applications.

This course will enable you to demonstrate an understanding of, and competence in, a range of analytical tools for posing and solving differential equations, specifically as applied to engineering situations.

Prerequisite modules: ECM1702 and ECM1705 or NSC1002 (Natural Science Students)  or equivalent

AIMS - intentions of the module

The aim of this module is to introduce you to some representative types of ordinary and partial differential equations and to introduce a number of analytical techniques used to solve them exactly or approximately.

INTENDED LEARNING OUTCOMES (ILOs) (see assessment section below for how ILOs will be assessed)

On successful completion of this module, you should be able to:

Module Specific Skills and Knowledge:
1 demonstrate a working knowledge of how to identify, classify and solve a range of types of ordinary and partial differential equation;
2 reveal an insight into their application and derivation;
3 show some knowledge of a selection of special functions and series methods used for solution of these differential equations.
Discipline Specific Skills and Knowledge:
4 exhibit an understanding of range of analytical tools for posing and solving differential equations;
5 display competence in applying these tools;
6 prove an understanding of mathematical modelling in areas such as fluid mechanics, quantum theory or mathematical biology.
Personal and Key Transferable/ Employment Skills and  Knowledge:
7 demonstrate an ability to monitor your own progress and to manage time;
8 show an ability to formulate and solve complex problems.

SYLLABUS PLAN - summary of the structure and academic content of the module

- review of methods for solving linear first order ordinary differential equations (ODEs) and linear second order ODEs with constant coefficients;

- the general linear second order ODE and reduction of order;

- method of variation of parameters, method of Frobenius;

- orthogonal functions including Legendre and trigonometric functions;

- further examples of special functions and their use in solving ODEs;

- basic examples of partial differential equations (PDEs) and their solution;

- coordinate systems in 3D and simple examples of applications;

- solution of PDEs using normal modes and series expansions of solutions, including Fourier series;

- applications to boundary value problems including polar coordinates; waves in strings; other examples.

LEARNING AND TEACHING
LEARNING ACTIVITIES AND TEACHING METHODS (given in hours of study time)
 Scheduled Learning & Teaching Activities Guided Independent Study Placement / Study Abroad 44 106 0
DETAILS OF LEARNING ACTIVITIES AND TEACHING METHODS
 Category Hours of study time Description Scheduled learning and teaching activities 33 Lectures including examples classes Scheduled learning and teaching activities 11 Tutorials Guided independent study 106 Lecture and assessment preparation; wider reading

ASSESSMENT
FORMATIVE ASSESSMENT - for feedback and development purposes; does not count towards module grade
Form of Assessment Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Fortnightly exercise 66 hours overall All Discussion at tutorials and solutions provided in ELE

SUMMATIVE ASSESSMENT (% of credit)
 Coursework Written Exams 20 80
DETAILS OF SUMMATIVE ASSESSMENT
Form of Assessment % of Credit Size of Assessment (e.g. duration/length) ILOs Assessed Feedback Method
Written exam – closed book 80 2 hours All Verbal
Coursework – questions submitted for summative assessment 20 40 hours overall All Comments by markers and solutions provided in ELE

DETAILS OF RE-ASSESSMENT (where required by referral or deferral)
Original Form of Assessment Form of Re-assessment ILOs Re-assessed Time Scale for Re-reassessment
All above Written exam (100%) All August Ref/Def period

RE-ASSESSMENT NOTES

If a module is normally assessed entirely by coursework, all referred/deferred assessments will normally be by assignment.

If a module is normally assessed by examination or examination plus coursework, referred and deferred assessment will normally be by examination. For referrals, only the examination will count, a mark of 40% being awarded if the examination is passed. For deferrals, candidates will be awarded the higher of the deferred examination mark or the deferred examination mark combined with the original coursework mark.

RESOURCES
INDICATIVE LEARNING RESOURCES - The following list is offered as an indication of the type & level of
information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE: http://vle.exeter.ac.uk

Web based and Electronic Resources: