This is an archived handbook for a previous year. The current undergraduate and postgraduate handbooks can be viewed using the links above.

Undergraduate Handbook 2016-2017 (archived)

Module MATH3101: CONTINUUM MECHANICS III

Department: Mathematical Sciences

MATH3101: CONTINUUM MECHANICS III

Type	Level	Credits	Availability	Module Cap	Location
Open	3	20	Not available in 2016/2017		Durham

Pre-requisites

(Problem Solving and Dynamics I (MATH1041) AND Analysis in Many Variables II (MATH2031) AND one extra 20 credit Level 2 mathematics module) OR (Analysis in Many Variables II (MATH2031) AND Analysis I (MATH1051) (if taken in Year 2) AND Problem Solving and Dynamics I (if taken in Year 2)) OR (Foundations of Physics I (PHYS1122) AND Analysis in Many Variables II (MATH2031) AND one extra 20 credit Level 2 mathematics module.)

Corequisites

One 20 credit Level 3 mathematics module.

Excluded Combinations

Continum Mechanics IV (MATH4081).

Aims

To introduce a mathematical description of fluid flow and other continuous media to familiarise students with the successful applications of mathematics in this area of modelling.
to prepare students for future study of advanced topics.

Content

Kinematic description of fluid flows: streamlines and trajectories, mass conservation and continuity equation
Review of tensors, stress and rate of strain.
Dynamical models of fluid flows: Euler and Navier-Stokes equation.
Some methods to solve Euler and Navier-Stokes equations.
Waves: sound and water waves, linear and nonlinear
Topics from: thermodynamics, scaling and dimensional analysis, hydrodynamic stability, NSE and turbulence, non-Newtonian fluid flows

Learning Outcomes

Subject-specific Knowledge

By the end of the module students will: be able to solve novel and/or complex problems in Continuum Mechanics.
have a systematic and coherent understanding of theoretical mathematics in the fields Continuum Mechanics.
have acquired coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas: Kinematics of fluid flows.
Equations of motion and their derivation for fluids.

Subject-specific Skills

In addition students will have specialised mathematical skills in the following areas which can be used with minimal guidance: Modelling.
They will be able to formulate and use mathematical models in various situations.

Key Skills

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

Teaching Methods and Learning Hours

Activity	Number	Frequency	Duration	Total Hours
Lectures	40	2 per week for 19 weeks and 2 in term 3	1 Hour	40
Problems Classes	8	Four in each of terms 1 and 2	1 Hour	8
Preparation and Reading				152
Total				200

Summative Assessment

Component	Component Weighting	Element	Length/Duration	Element Weighting	Resit Opportunity
Examination	100%	three hour written examination		100%

Formative Assessment

Four written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students

Students who do not attend monitored activities shown under Teaching Methods and Learning Hours, or who fail to complete the summative or formative assessment(s) specified above, may be subject to the Academic Progress procedures defined in the University's General Regulation V, and may be required to leave the University.