Differential Equations - entry

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: MTH1002 or NSC1002 (Natural Science Students)  or equivalent.

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.

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.

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

- sufficient conditions to guarantee a solution to an ODE; uniqueness of solution;

- 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;

- 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. 

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.

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

Web based and Electronic Resources:

http://www.mat.univie.ac.at/~gerald/ftp/book-ode/
 

Reading list for this module: