# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2016/2017

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DRPS : Course Catalogue : School of Geosciences : Earth Science

# Undergraduate Course: Mathematical Methods for Geophysicists (EASC09021)

 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 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.
 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) Co-requisites Prohibited Combinations Other requirements None Additional Costs None.
 Pre-requisites Mathematics to the level of vector calculus and simple differential equations. High Demand Course? Yes
 Not being delivered
 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.
 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
 Graduate Attributes and Skills Not entered Keywords Math_Methods
 Course organiser Dr Hugh Pumphrey Tel: (0131 6)50 6026 Email: h.c.pumphrey@ed.ac.uk Course secretary Ms Casey Hollway Tel: (0131 6)50 8510 Email: earth.sciences@ed.ac.uk
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