Module Specification

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.
1. Module Title VECTOR CALCULUS WITH APPLICATIONS IN FLUID MECHANICS
2. Module Code MATH225
3. Year Session 2023-24
4. Originating Department Mathematical Sciences
5. Faculty Fac of Science & Engineering
6. Semester First Semester
7. CATS Level Level 5 FHEQ
8. CATS Value 15
9. Member of staff with responsibility for the module
Professor A Movchan Mathematical Sciences Abm@liverpool.ac.uk
10. Module Moderator
11. Other Contributing Departments  
12. Other Staff Teaching on this Module
Dr DJ Colquitt Mathematical Sciences D.Colquitt@liverpool.ac.uk
Dr SA Fairfax Mathematical Sciences Simon.Fairfax@liverpool.ac.uk
13. Board of Studies
14. Mode of Delivery
15. Location Main Liverpool City Campus
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other TOTAL
16. Study Hours 36

  12

      48
17.

Private Study

102
18.

TOTAL HOURS

150
 
    Lectures Seminars Tutorials Lab Practicals Fieldwork Placement Other
19. Timetable (if known)            
 
20. Pre-requisites before taking this module (other modules and/or general educational/academic requirements):

 
21. Modules for which this module is a pre-requisite:

 
22. Co-requisite modules:

 
23. Linked Modules:

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

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

26. Programme(s) (including Year of Study) to which this module is available on an optional basis:

27. Aims
 

Provide an understanding of the various vector integrals, the operators div, grad and curl and the relations between them.

Develop an appreciation of the many applications of vector calculus to physical situations.

Provide an introduction to the subjects of fluid mechanics and electromagnetism.

 
28. Learning Outcomes
 

(LO1) Work confidently with different coordinate systems.

 

(LO2) Know how to evaluate line, surface and volume integrals.

 

(LO3) Understand how the operators div, grad and curl together with the associated theorems of Gauss and Stokes are used.

 

(LO4) Recognise the many physical situations that involve the use of vector calculus.

 

(LO5) Apply mathematical modelling methodology to formulate and solve simple problems in electromagnetism and inviscid fluid flow.

 
29. Teaching and Learning Strategies
 

Material is presented during lectures (3 hours per week). Tutorials (1 hour per week) are used for consolidation and practice, and for help with individual questions.

 
30. Syllabus
   

Different coordinate systems.

Scalar and vector fields; electrostatic field, Lagrangian and Eulerian descriptions of a fluid.

Gradient; E = -grad Ф , dipole field, convective derivative D/Dt.

Surface and volume integrals; divergence, Gauss' theorem, equation of continuity, incompressible flows.

Curl, line integrals, Stokes' theorem; irrotational fields, conservative fields, velocity potential.

Maxwell's equations, wave equation, acceleration of a fluid particle.

Applications to fluid motion; inviscid fluids, boundary conditions, pressure, Euler equation and solutions for irrotational motion and steady motion.

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

Assessment

32. EXAM Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
  written exam 120 70
33. CONTINUOUS Duration Timing
(Semester)
% of
final
mark
Resit/resubmission
opportunity
Penalty for late
submission
Notes
  Homework 1 0 15
  Homework 2 0 15