MT4005 Linear and Nonlinear Waves

Academic year

2024 to 2025 Semester 2

Further information on which modules are specific to your programme.

Key module information

SCOTCAT credits

15

The Scottish Credit Accumulation and Transfer (SCOTCAT) system allows credits gained in Scotland to be transferred between institutions. The number of credits associated with a module gives an indication of the amount of learning effort required by the learner. European Credit Transfer System (ECTS) credits are half the value of SCOTCAT credits.

SCQF level

SCQF level 10

The Scottish Credit and Qualifications Framework (SCQF) provides an indication of the complexity of award qualifications and associated learning and operates on an ascending numeric scale from Levels 1-12 with SCQF Level 10 equating to a Scottish undergraduate Honours degree.

Availability restrictions

Not automatically available to General Degree students

Planned timetable

9 am, Mon (odd weeks), Wed & Fri

This information is given as indicative. Timetable may change at short notice depending on room availability.

Module coordinator

Dr A N Wright

Dr A N Wright
This information is given as indicative. Staff involved in a module may change at short notice depending on availability and circumstances.

Module description

This module gives an introduction to wave motion and its importance in many areas of applied mathematics. It begins with a discussion of the linear approximation for small amplitude waves and discusses properties of these such as dispersion relations, phase and group velocities, dissipation and dispersion. Some nonlinear effects such as wave steepening are then treated and an introduction given to some of the equations, for example Burger's and Korteweg de Vries, which are used to model nonlinear wave propagation.

Relationship to other modules

Pre-requisites

BEFORE TAKING THIS MODULE YOU MUST ( PASS MT2506 OR PASS PH3081 ) AND PASS MT3504

Assessment pattern

2-hour Written Examination = 100%

Re-assessment

Oral examination = 100%

Learning and teaching methods and delivery

Weekly contact

2.5 lectures (x 10 weeks) and 1 tutorial (x 10 weeks).

Scheduled learning hours

35

The number of compulsory student:staff contact hours over the period of the module.

Guided independent study hours

115

The number of hours that students are expected to invest in independent study over the period of the module.

Intended learning outcomes

  • Linearise a wave equation, derive the dispersion relation and calculate the group and phase velocities
  • Understand the set of equations describing linear sound waves, understand how sound waves propagate in three dimensions, and be able to determine when gravity is important
  • Use the governing equations of fluid mechanics to describe water waves at an air-water interface in the linear limit and derive solutions for arbitrary depth water including surface tension
  • Understand the tendency for nonlinear waves to develop steep gradients leading to shocks (wave breaking/steepening), and the ability of diffusion (Burgers' equation) and dispersion (Korteweg de Vries equation) to both prevent unphysical behaviour and to permit soliton solutions.