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## MTH2004 - Vector Calculus and Applications (2022)

MODULE TITLE | Vector Calculus and Applications | CREDIT VALUE | 15 |
---|---|---|---|

MODULE CODE | MTH2004 | MODULE CONVENER | Dr Claire Foullon (Coordinator) |

DURATION: TERM | 1 | 2 | 3 |
---|---|---|---|

DURATION: WEEKS | 0 | 11 weeks | 0 |

Number of Students Taking Module (anticipated) | 250 |
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This introductory vector calculus course aims to increase your understanding of fluid dynamics and electromagnetism. It examines how one can use vector formalism and calculus together to describe and solve many problems in two and three dimensions. For example, the rules that govern the flow of fluids can be described using vector calculus, with resulting laws of motion described by partial differential equations rather than ordinary differential equations.

On successful completion of this module, **you should be able to:**

**Module Specific Skills and Knowledge:**

1 define and express vector calculus notation;

2 carry out manipulations with vector calculus in both differential and integral forms (line, surface and volume integrals);

3 implement and illustrate the application of vector calculus to problems in inviscid fluid mechanics and electromagnetism.

**Discipline Specific Skills and Knowledge:**

4 validate a number of mathematical modelling techniques with application to fluid dynamics and electromagnetism.

**Personal and Key Transferable/ Employment Skills and Knowledge:**

5 devise how to formulate and solve complex problems.

Scheduled Learning & Teaching Activities | 33.00 | Guided Independent Study | 118.00 | Placement / Study Abroad |
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Category |
Hours of study time |
Description |

Scheduled learning and teaching | 33 | Lectures including examples classes |

Scheduled learning and teaching activities | 5 | Tutorials |

Guided independent study | 112 | Lecture and assessment preparation; wider reading |

Form of Assessment | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
---|---|---|---|

Exercise sheets | 5 x 10 hours | 1, 2, 3, 4, 5 | Written/ oral feedback in tutorial classes and drop-ins; written/oral feedback on submitted solutions. |

Online Quizzes | 3x (8-30) min | 1,2 | Written/oral feedback online and in class. |

Coursework | 40 | Written Exams | 60 | Practical Exams |
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Form of Assessment | % of Credit | Size of Assessment (e.g. duration/length) | ILOs Assessed | Feedback Method |
---|---|---|---|---|

Written exam – closed book | 60 | 1.5 hours (January) | 1,2,3,4 | Written/verbal on request, SRS. |

Coursework 1 | 10 | 10 hours | All | Annotated script and written/verbal feedback online and in class |

Coursework 2 | 30 | 20 hours | 1,2,3,4 | Annotated script and written/verbal feedback online and in class |

Original Form of Assessment | Form of Re-assessment | ILOs Re-assessed | Time Scale for Re-reassessment |
---|---|---|---|

All above | Written exam (100%) | All | August Ref/Def period |

Reassessment will be by a single written exam only, worth 100% of the module. For referred candidates, the mark will be capped at 40%. For deferred candidates, the mark will be uncapped.

information that you are expected to consult. Further guidance will be provided by the Module Convener

ELE – http://vle.exeter.ac.uk

Reading list for this module:

Type | Author | Title | Edition | Publisher | Year | ISBN | Search |
---|---|---|---|---|---|---|---|

Set | Finney, R.L., Maurice, D., Weir, M. and Giordano, F.R. | Thomas' Calculus based on the original work by George B. Thomas, Jr. | 10th or later | Addison-Wesley | 2003 | 000-0-321-11636-4 | [Library] |

Set | Arfken, G.B. & Weber, H.J. | Mathematical Methods for Physicists | Electronic | Harcourt/ Academic Press | 2005 | 000-0-120-59825-6 | [Library] |

Set | Acheson, D.J. | Elementary Fluid Dynamics | Clarendon Press | 1990 | 978-0-198-59679-0 | [Library] | |

Set | Tritton D.J. | Physical Fluid Dynamics | 2nd | Clarendon Press, Oxford | 1988 | 000-0-198-54493-6 | [Library] |

Set | Batchelor G.K. | An Introduction to Fluid Dynamics | Cambridge University Press | 1999 | 000-0-521-04118-X | [Library] | |

Set | Matthews P.C | Vector Calculus | 1st | Springer | 1998 | 978-3540761808 | [Library] |

Set | Spiegel M.R., Lipschutz S., Spellman D. | Vector Analysis and an Introduction to Tensor Analysis | 2nd | McGraw-Hill | 2009 | 9780071615457 | [Library] |

Set | Paterson A.R. | A first course in fluid dynamics | Electronic | Cambridge University Press | 1983 | 9780521274241 | [Library] |

Set | Nahvi, M; Edminister, J | Schaum's Outline of Electromagnetics | 5th | McGraw-Hill Education | 2019 | 9781260120974 | [Library] |

CREDIT VALUE | 15 | ECTS VALUE | 7.5 |
---|---|---|---|

PRE-REQUISITE MODULES | None |
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CO-REQUISITE MODULES | None |

NQF LEVEL (FHEQ) | 5 | AVAILABLE AS DISTANCE LEARNING | No |
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ORIGIN DATE | Tuesday 10 July 2018 | LAST REVISION DATE | Friday 05 August 2022 |

KEY WORDS SEARCH | Vector calculus; differential operators; line, surface and volume integrals; integral theorems; curvilinear coordinates; inviscid fluid dynamics; electromagnetism |
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