Undergraduate Course: Mathematical Methods for Geophysicists (EASC09021)
Course Outline
| School | School of Geosciences |
College | College of Science and Engineering |
| Credit level (Normal year taken) | SCQF Level 9 (Year 3 Undergraduate) |
Availability | Available to all students |
| SCQF Credits | 10 |
ECTS Credits | 5 |
| Summary | This course takes the mathematics which students have learned in the pre-honours Mathematics for Physics courses and applies it to the study of the Earth, extending mathematical skills and exploring the insights that can be developed through quantitative modelling of geological processes. Many examples and applications are drawn from the book "Geodynamics" by Turcotte & Schubert.
Topics covered include the following.
1) Vectors and their use in describing positions and directions on the Earth's surface.
2) Spherical geometry and plate tectonics.
3) Potential fields and the gradient and divergence operators applied to gravity and heat flow.
4) Ordinary differential equations applied to heat flow in the Earth.
5) The diffusion equation applied to time-dependent heat flow into the Earth.
6) Teaching is by means of a series of "workshops", in which short lectures on the underlying mathematical techniques and their geological and geophysical applications are mixed with example classes. |
| Course description |
Week 1
Vectors: addition and multiplication.
Week 2
Great Circle arcs and spherical geometry.
Week 3
No classes.
Week 4
Vector Fields.
Week 5
Applications of gradient. Divergence.
Week 6
Differential Equations (Ordinary and Partial) Week 7. Models of steady heat flow.
Week 7
Models of steady heat flow.
Week 8
Time dependent heat flow. Separation of variables Week 9. Penetration of periodic temperature variations into the Earth Week 10. The instantaneous heating or cooling of a half-space Week 11. Revision or catch-up time if needed.
Week 9
Penetration of periodic temperature variations into the Earth
Week 10
The instantaneous heating or cooling of a half-space
Week 11
Revision or catch-up time if needed.
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Information for Visiting Students
| Pre-requisites | Mathematics to the level of vector calculus and simple differential equations. |
Course Delivery Information
|
| Academic year 2014/15, Available to all students (SV1)
|
Quota: None |
| Course Start |
Semester 1 |
Timetable |
Timetable |
| Learning and Teaching activities (Further Info) |
Total Hours:
100
(
Lecture Hours 10,
Seminar/Tutorial Hours 20,
Feedback/Feedforward Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
66 )
|
| Assessment (Further Info) |
Written Exam
60 %,
Coursework
40 %,
Practical Exam
0 %
|
| Additional Information (Assessment) |
Written Exam: 60%, Course Work: 40 %, Practical Exam: 0%.
The course work will consist of two sets of mathematical problems; each set is worth 20% of the total mark. These are to be handed in at the times noted below. Answers may be hand-written.
The examination will take the same form as the previous year, with the past paper made available. The time for the examination will be extended to 2 hours; the 2013-14 class found the time given in that year to be insufficient. |
| Feedback |
Not entered |
| Exam Information |
| Exam Diet |
Paper Name |
Hours & Minutes |
|
| Main Exam Diet S1 (December) | Mathematical Methods for Geophysicists | 1:30 | |
Learning Outcomes
On completion of this course, the student will be able to:
- Have a broad and integrated understanding of how to apply their mathematical skills in an Earth science context and what insights can be gained from the quantitative modelling of geological processes.
- Have a critical understanding of vectors and how they are implemented in this field.
- Be able to solve a variety of ordinary and partial differential equations and to apply them in a variety of Earth science contexts.
|
Reading List
A guided tour of mathematical methods for the physical sciences, Roel Sneider. Cambridge University Press, 978-0521542616
Geodynamics, Turcotte, D. L. and Schubert, G 0-521-66624-4
Geophysical Theory, Menke, W. and Abbott, D. 978-0-231-06792-8
Mechanics in the Earth and Environmental Sciences, Middleton, G. V. and Wilcock, P. R, 0-521-44669-4 |
Additional Information
| Graduate Attributes and Skills |
Not entered |
| Keywords | Math_Methods |
Contacts
| Course organiser | Dr Hugh Pumphrey
Tel: (0131 6)50 6026
Email: h.c.pumphrey@ed.ac.uk |
Course secretary | Mr Ken O'Neill
Tel: (0131 6)50 8510
Email: koneill3@exseed.ed.ac.uk |
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