Examination

2 - Written exam - 75

Set Exercises

1 - Set exercises - 25

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<ul><li>Classification of linear second order partial differential equations: elliptic, parabolic, and hyperbolic. Dirichlet and Neumann boundary conditions. Separation of variables. </li><li>Green’s Theorem and Green’s functions. Application to equations of elliptic type. </li><li>The Laplace equation. Cartesian and Polar coordinates. Boundary value problems and Fourier series. The shape of membranes in tension.</li><li>The Heat conduction equation. Insulated and conducting boundaries. Gauss’ fundamental solution.  </li></ul>

Feedback is provided in a number of ways throughout your module. This includes feedback you receive during teaching from both peers and lecturers and that provided for formative assessment. Following an assessment, you will be given your marks and feedback in line with the assessment regulations and policy. More information on the timing and type of feedback that will be provided for each assessment will be available from the module leader. <a href='https://www.citystgeorges.ac.uk/about/governance/policies/student-policies-and-regulations'>https://www.citystgeorges.ac.uk/about/governance/policies/student-policies-and-regulations</a>

This module will support the development of all the graduate attributes. Your module leader will provide you with information about how your learning, teaching and assessment activities support your development of these attributes. The graduate attributes are: - Always learning - Engaged in the world - Technical and digital - Connected Professional - Creating Impact

In-Person - 

Synchronous online - 

Self-directed - 

Introduction to differential equations with boundary value problems 

Fundamentals of Differential Equations

Partial Differential Equations in Physics 

Elementary differential equations and boundary value problems  

Partial differential equations 

MA3618 - Differential Equations 2

MA3618-PRD2-BLE-ALV1

Teaching and Learning methods are designed to foster your knowledge of and enthusiasm for the subject and stimulate engagement and participation in the learning process.  They encourage learning in depth and encourage you to reflect on and take responsibility for your own learning and to develop your academic self-confidence. 
Lectures are the principal introduction to new material.  They are relatively formal in style and are presented to the whole student group.  Each lecture is of 50 minutes duration with the timetable based on units of one hour to allow for short breaks.  Full, prompt attendance is expected. Some lectures are also used to provide help with questions arising from the background exercises.  
In addition to the taught elements of the programme, there will be the need for private study.  This time will be spent working on background reading, revision of notes, work on tutorial problems, and preparation of the set exercises. Key learning and teaching resources will be put on the module website on Moodle.

Differential Equations 2

Evaluate solutions for second-order linear partial differential equations, using a range of techniques including separation of variables and Green’s functions. 

Skills

Relate different types of partial differential equations to specific problems in applied mathematics. 

Knowledge

Evaluate advanced analytical tools which originated in the theory of differential equations but are of fundamental importance in other areas of Mathematics.  

Select a variety of coordinate systems in which differential equations of interest adopt their simplest forms. 

To place the theory of partial differential equations in the wider context of applied mathematics and recognise both its utility and its fundamental contribution to many areas of scientific research. 

Values and attitudes

Evaluate the behaviour of their solutions, both qualitatively and quantitatively. 

Apply Fourier series to the solution of classical boundary-value problems. 