MA2DE2NU-Differentiable Equations II

Module Provider: Mathematics and Statistics
Number of credits: 20 [10 ECTS credits]
Level:5
Semesters in which taught: Semester 2 module
Pre-requisites: MA0MANU Mathematical Analysis and MA1LANU Linear Algebra and MA1DE1NU Differential Equations I
Non-modular pre-requisites:
Co-requisites:
Modules excluded:
Current from: 2022/3

Module Convenor: Dr Peter Sweby
Email: p.k.sweby@reading.ac.uk

Type of module:

Summary module description:

This module is designed to teach students of mathematics a brief introduction to partial differential equations. Students learn in the class could be helpful for them in subsequent courses and research as well as in their career and in life in the long run.

The Module lead at NUIST is Dr Vahid DarvishÌýDarvish (vdarvish@gmail.com).

Aims:

This module is intended to teach students of mathematics fundamental knowledge of partial differential equations.

Assessable learning outcomes:

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

1. Solve linear first-order PDE with different methods.


2. Solve the heat equation and use Duhamel’s principle to treat sources in the diffusion equation.


3. Solve the wave equation by using D’ Alembert’s method and be introduced to ideas of causality, domain of dependence, and range of influence.


4. State and apply maximum principles to conclude uniqueness results.


5. Solve wave equations, heat equations, Laplace equations and Helmholtz equations on a finite interval by separation of variables and derive simple Green’s functions.


6. Know the fundamental properties of a solution to the Laplace equations.


7. Classify the 2nd order partial differential equations.

Additional outcomes:

By the end of the module, it is expected that students should be able to apply the above skills to further study and research.Ìý

Outline content:

• Overview of PDEs; Classification of 2nd order partial differential equations; Conservation laws; First order linear equations; Laplace Transform,


• Method of the characteristics; the inviscid Burgers' equation.


• The Heat Equation on whole line and half-line, the heat kernel and Duhamel's principle.


• The Wave equation, including derivation, D' Alembert's formula and causality. The Wave equation on a finite and semi-infinite interval.


• Laplace's equation on rectangles, cubes, the exterior of circles, wedges, annuli and on a ball.


• The Poison Equation. Green's identities and Green's function


• Maximum principles.


• Separation of variables for the heat, wave and Laplace's equations on finite spatial regions.

Brief description of teaching and learning methods:

Lectures supported by problem sheets and weekly tutorials.

Contact hours:

Ìý	Semester 1	Semester 2
Lectures		96
Guided independent study:	Ìý	Ìý
Ìý Ìý Wider reading (independent)		68
Ìý Ìý Wider reading (directed)		20
Ìý Ìý Peer assisted learning		16
Ìý	Ìý	Ìý
Total hours by term	0	200
Ìý	Ìý	Ìý
Total hours for module	200

Summative Assessment Methods:

Method	Percentage
Written exam	70
Class test administered by School	30

Summative assessment- Examinations:

3 hours.

Summative assessment- Coursework and in-class tests:

One examination and a number of class tests.

Formative assessment methods:

Problem sheets.

Penalties for late submission:

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

• 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 five working days;
• where the piece of work is submitted more than five working days after the original deadline (or any formally agreed extension to the deadline): a mark of zero will be recorded.

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

Assessment requirements for a pass:

A mark of 40% overall.

Reassessment arrangements:

One examination paper of 3 hours duration in August/September - the resit module mark will be the higher of the exam mark (100% exam) and the exam mark plus previous coursework marks (70% exam, 30% coursework).

Additional Costs (specified where applicable):

1) Required text books:Ìý

2) Specialist equipment or materials:Ìý

3) Specialist clothing, footwear or headgear:Ìý

4) Printing and binding:Ìý

5) Computers and devices with a particular specification:Ìý

6) Travel, accommodation and subsistence:Ìý

Last updated: 22 September 2022