Undergraduate Programme and Module Handbook 2016-2017 (archived)
Module MATH3101: CONTINUUM MECHANICS III
Department: Mathematical Sciences
MATH3101:
CONTINUUM MECHANICS III
Type |
Open |
Level |
3 |
Credits |
20 |
Availability |
Available in 2017/18 and alternate years thereafter |
Module Cap |
|
Location |
Durham
|
Prerequisites
- (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 Combination of Modules
- 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
- 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.
- 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.
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: Examination |
Component Weighting: 100% |
Element |
Length / duration |
Element Weighting |
Resit Opportunity |
three hour written examination |
|
100% |
|
Four written assignments to be assessed and
returned. Other assignments are set for self-study and complete solutions
are made available to students
■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University