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DRPS : Course Catalogue : School of Geosciences : Earth Science

Undergraduate Course: Mathematical Methods for Geophysicists (EASC09021)

Course Outline
SchoolSchool of Geosciences CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 9 (Year 3 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThis 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
No classes

Week 3
Great Circle arcs and spherical geometry.

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.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: ( Earth Dynamics (EASC08001) AND Introduction to Geophysics (EASC08008)) OR Earth Science Fundamentals for Geophysicists (EASC08022) AND ( Algebra and Calculus (PHYS08041) OR Linear Algebra and Several Variable Calculus (PHYS08042)) AND Physics of the Earth (EASC08016)
Prohibited Combinations Other requirements None
Additional Costs None.
Information for Visiting Students
Pre-requisitesMathematics to the level of vector calculus and simple differential equations.
High Demand Course? Yes
Course Delivery Information
Not being delivered
Learning Outcomes
On completion of this course, the student will be able to:
  1. 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.
  2. Have a critical understanding of vectors and how they are implemented in this field.
  3. 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
Course organiserDr Hugh Pumphrey
Tel: (0131 6)50 6026
Course secretaryMs Casey Hollway
Tel: (0131 6)50 8510
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