MA2DE: Differential Equations

Module code: MA2DE

Module provider: Mathematics and Statistics; School of Mathematical, Physical and Computational Sciences

Credits: 20

Level: Level 2 (Intermediate)

When you'll be taught: Semester 1

Module convenor: Dr Peter Sweby, email: p.k.sweby@reading.ac.uk

Pre-requisite module(s): BEFORE TAKING THIS MODULE YOU MUST ( TAKE MA1CA AND TAKE MA1LA ) OR ( TAKE MA1LANU AND TAKE MA1DE1NU ) (Compulsory)

Co-requisite module(s):

Pre-requisite or Co-requisite module(s):

Module(s) excluded:

Placement information: NA

Academic year: 2024/5

Available to visiting students: Yes

Talis reading list: Yes

Last updated: 21 May 2024

Overview

Module aims and purpose

In this module we further develop the study of ordinary differential equations building on ODEs met in Part 1 and introduce and develop the study of partial differential equations and their applications. 

We continue the ODE work of Part 1 and consider more advanced topics such as ODEs with non-constant coefficients, integral and series solutions, Fourier series and the theory of boundary value problems. This is then extended into the study of partial differential equations, in particular the diffusion equation, the wave equation and Laplace’s equation, for which appropriate solution techniques are studied. 

Module learning outcomes

By the end of the module, it is expected that students will be able to: 

1. Solve constant and non-constant coefficient ODE IVPs and BVPs using a variety of suitable techniques; 
2. Derive the Fourier series of a function and use eigenfunction expansions to solve appropriate BVPs for ODEs and PDEs; 
3. Solve a variety of PDE IVP, BVP and IBVP problems, including for the diffusion equation, the wave equation and Laplace’s equation using appropriate techniques. 

Module content

Differential equations are at the heart of modern applied mathematics. For ODEs we continue the work of part 1 and consider more advanced topics such as ODEs with non-constant coefficients, Greens functions, Laplace transforms and series solutions, Fourier series and the theory of boundary value problems including eigenfunction expansion techniques for simple Sturm Liouville problems. For PDEs the module uses the diffusion, wave and Laplace’s equations as exemplars. Their solution properties are explored, including the different type of problems (IVP, IBVP and BVP). Solution techniques such as the heat kernel, Duhamel’s principle, separation of variables and D’Alembert’s solution are introduced as well as extending the Laplace transform, Greens functions and eigenfunction expansions to PDE problems. The relationship of PDEs to mathematical modelling of the physical sciences is highlighted. 

Structure

Teaching and learning methods

Lectures, supported by non-assessed problem sheets, weekly tutorials, computer demonstrations and exercises. 

Study hours

At least 54 hours of scheduled teaching and learning activities will be delivered in person, with the remaining hours for scheduled and self-scheduled teaching and learning activities delivered either in person or online. You will receive further details about how these hours will be delivered before the start of the module.

Please note the independent study hours above are notional numbers of hours; each student will approach studying in different ways. We would advise you to reflect on your learning and the number of hours you are allocating to these tasks.

Semester 1 The hours in this column may include hours during the Christmas holiday period.

Semester 2 The hours in this column may include hours during the Easter holiday period.

Summer The hours in this column will take place during the summer holidays and may be at the start and/or end of the module.

Assessment

Requirements for a pass

Students need to achieve an overall module mark of 40% to pass this module.

Summative assessment

Penalties for late submission of summative assessment

The Support Centres will apply the following penalties for work submitted late:

Assessments with numerical marks

• where the piece of work is submitted after the original deadline (or any formally agreed extension to the deadline): 10% of the total marks available for that piece of work will be deducted from the mark for each working day (or part thereof) following the deadline up to a total of three working days;
• the mark awarded due to the imposition of the penalty shall not fall below the threshold pass mark, namely 40% in the case of modules at Levels 4-6 (i.e. undergraduate modules for Parts 1-3) and 50% in the case of Level 7 modules offered as part of an Integrated Masters or taught postgraduate degree programme;
• where the piece of work is awarded a mark below the threshold pass mark prior to any penalty being imposed, and is submitted up to three working days after the original deadline (or any formally agreed extension to the deadline), no penalty shall be imposed;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

Assessments marked Pass/Fail

• where the piece of work is submitted within three working days of the deadline (or any formally agreed extension of the deadline): no penalty will be applied;
• where the piece of work is submitted more than three working days after the original deadline (or any formally agreed extension of the deadline): a grade of Fail will be awarded.

The University policy statement on penalties for late submission can be found at: /cqsd/-/media/project/functions/cqsd/documents/qap/penaltiesforlatesubmission.pdf

You are strongly advised to ensure that coursework is submitted by the relevant deadline. You should note that it is advisable to submit work in an unfinished state rather than to fail to submit any work.

Formative assessment

Formative assessment is any task or activity which creates feedback (or feedforward) for you about your learning, but which does not contribute towards your overall module mark.

Reassessment

Additional costs