Module Details
The information contained in this module specification was correct at the time of publication but may be subject to change, either during the session because of unforeseen circumstances, or following review of the module at the end of the session. Queries about the module should be directed to the member of staff with responsibility for the module.
Title WAVES, MATHEMATICAL MODELLING
Code MATH427
Coordinator Prof N Movchan
Mathematical Sciences
Nvm@liverpool.ac.uk
Year CATS Level Semester CATS Value
Session 2016-17 Level 7 FHEQ Second Semester 15

Aims

This module gives an introduction to the mathematical theory of linear and non-linear waves. Illustrative applications involve problems of acoustics, gas dynamics and examples of solitary waves.


Learning Outcomes

Students will learn essential modelling techniques in problems of  wave propagation.   They will also understand that mathematical models of the same type can be successfully used to describe different physical phenomena.   Students will also study background mathematical theory in models of acoustics, gas dynamics and water  waves.


Syllabus
1  1

Hyperbolic PDEs.  Definitions. Characteristics.  Formulation of problems. D''Alembert''s formula.

Outline of inviscid fluid dynamics.  Linear theory.  Plane waves. Reflection and transmission at a plane interface. Spherical waves.

Dipole fields.  Scattering by a solid sphere.

Vibration of an infinite volume.  Poisson''s formula.

Introduction to non-linear theory.  Systems of quasi-linear first-order partial differential equations.  Characteristics. Riemann invariants.  Model examples.

Conservation laws, weak solutions and shocks.  Definitions and model examples. 

Water wave t heory.  Governing equations. Linearised model.  Dispersive waves.  Model examples.  Non-linear equations, solitary waves.


Recommended Texts
Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module.
Explanation of Reading List:

Pre-requisites before taking this module (other modules and/or general educational/academic requirements):
 

Co-requisite modules:
 

Modules for which this module is a pre-requisite:
 

Programme(s) (including Year of Study) to which this module is available on a required basis:
 

Programme(s) (including Year of Study) to which this module is available on an optional basis:
Programme:F344 Year:3,4 Programme:FGH1 Year:3,4 Programme:MMAS Year:1 Programme:G101 Year:3,4

Assessment
EXAM Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes
Written Exam  2.5 hours  Second semester  100  Standard University Policy    Assessment 1 Notes (applying to all assessments) Full marks will be awarded for complete answers to FOUR questions. Only the best 4 answers will be taken into account.  
CONTINUOUS Duration Timing
(Semester)		 % of
final
mark		 Resit/resubmission
opportunity		 Penalty for late
submission		 Notes