MA3PDANU: Partial Differential Equations and Applications

Module code: MA3PDANU

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

Credits: 20

Level: Level 3 (Honours)

When you'll be taught: Semester 1

Module convenor: Dr Nick Biggs, email: n.r.t.biggs@reading.ac.uk

NUIST module lead: Riaz Ahmad, email: 100102@nuist.edu.cn

Pre-requisite module(s): BEFORE TAKING THIS MODULE YOU MUST TAKE MA2DE2NU (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: No

Talis reading list: No

Last updated: 12 September 2024

Overview

Module aims and purpose

The objective of this course is to provide an elementary, but rigorous mathematical presentation of various partial differential equations (PDEs), which appear in practical applications and natural phenomena. The focus of the course is on the PDEs, which are relevant to continuum mechanics, in particular to fluid mechanics and its application, water waves and wave scattering theory.

Module learning outcomes

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

1. Formulate fluid mechanical problems with appropriate set of boundary conditions
2. Use different mathematical techniques to analyse representative fluid mechanical problems relevant to applications in industry and environment studies
3. Formulate and solve simple problems in linear water wave theory
4. Formulate and solve problems in linear wave scattering

Module content

In the first half of the semester, we first demonstrate how one of the most complex and behaviour-rich systems of PDEs, the system of the Navier-Stokes equations, appears from the main principles. Further in the course, we study how to formulate well-defined, mathematically, fluid mechanical problems. We then consider some representative problems and demonstrate the pathways how the original system of PDEs can be reduced to much simpler PDEs. We consider stability of some basic flows and routes to turbulence, the complex behaviour commonly observed in liquid motion.

The second half of the semester will first focus the investigation of fluid mechanics onto linear water waves. These waves will then motivate the examination of a range of phenomena related to linear wave scattering, including reflection, refraction and diffraction.

Structure

Teaching and learning methods

Lectures supported by formative problem sheets and tutorials.

Study hours

At least 55 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: https://www.reading.ac.uk/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.

A number of selected problems from tutorial problem sheets.

Reassessment

Additional costs