Module Details |
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. |
Title | Geophysical Mathematics and Potential Theory | ||
Code | ENVS201 | ||
Coordinator |
Professor RT Holme Earth, Ocean and Ecological Sciences R.T.Holme@liverpool.ac.uk |
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Year | CATS Level | Semester | CATS Value |
Session 2022-23 | Level 5 FHEQ | Whole Session | 15 |
Aims |
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To provide mathematical training required for geophysical research, with a specific focus on: Mathematical methods, providing a bridge between Year One mathematics courses and geophysical applications in Year Three and Four. The application of these methods, with particular emphasis on applied potential theory (gravity and magnetic methods). |
Learning Outcomes |
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(LO1) Knowledge of mathematical methods appropriate for geophysical science. |
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(LO2) Advanced knowledge and understanding of the concepts of gravity and magnetic field potentials, fundamental mathematical framework of potential field theory, and application to data manipulation and interpretation. |
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(LO3) The ability to manipulate gravitational and magnetic data using potential field theory. |
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(LO4) Report writing from practical exercise, focussing on answering and reporting on conclusions of an associated scientific requestion |
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(S1) Problem solving skills |
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(S2) Numeracy |
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(S3) Communication skills |
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(S4) IT skills |
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(S5) Application of literacy, ability to produce clear, structured written work and oral literacy - including listening and questioning |
Syllabus |
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Introductory material, including basic calculus, complex numbers, series expansions and matrices. Eigenvalue and eigenvector analysis First and second order ordinary differential equations. Fourier methods. Partial differentiation, vector calculus. Introduction to partial differential equations. Class test Recap and review Foundations of potential theory Laplace's equation in cartesian coordinates Applied methods - Gauss' theorem, Directoral Derivatives Application practical one. Application practical two. Upward/downward continuation. Whole Earth potential theory. Spherical Harmonics Elipticity / flattening / Geoid Planetary magnetism Class test Recap and review |
Teaching and Learning Strategies |
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Teaching Method 1 - In person lectures Teaching Method 1 - Pre-recorded lectures Teaching Method 3- Tutorial Teaching Method 4 - Laboratory Work |
Teaching Schedule |
Lectures | Seminars | Tutorials | Lab Practicals | Fieldwork Placement | Other | TOTAL | |
Study Hours |
20 |
20 |
6 |
4 4 20 |
74 | ||
Timetable (if known) | |||||||
Private Study | 76 | ||||||
TOTAL HOURS | 150 |
Assessment |
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EXAM | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
Class Test, End of Semester 2 There is a Resit Opportunity. | 90 | 25 | ||||
Class test at end of first semester There is a resit opportunity. Standard UoL penalty applies for late submission. This is an anonymous assessment. Assessment Schedule (When): Sem 1 | 0 | 25 | ||||
CONTINUOUS | Duration | Timing (Semester) |
% of final mark |
Resit/resubmission opportunity |
Penalty for late submission |
Notes |
Maths problems 1 - vectors | 0 | 5 | ||||
Problem set 2 - Ordinary differential equations | 0 | 5 | ||||
Problem set 3 - Partial differentiation | 0 | 5 | ||||
Problem set 4 – Fourier methods | 0 | 5 | ||||
Curilinear coordinates | 0 | 5 | ||||
Partial differential equations | 0 | 5 | ||||
Gauss' theorem report derived from practical | 0 | 5 | ||||
Application of potential theory methods - report from practical | 0 | 5 | ||||
Spherical harmonics report from computer practical | 0 | 5 | ||||
Problem shhet 7 - Spherical potential theory | 0 | 5 |
Recommended Texts |
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Reading lists are managed at readinglists.liverpool.ac.uk. Click here to access the reading lists for this module. |