# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

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# 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
 Academic year 2015/16, 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; the past paper will be made available. The time for the examination will be 2 hours as in the previous year. Friday of Week 7 (6 November 2015) at 4pm, Friday of week 10 (Friday 27 November) at 4pm Feedback Verbal feedback will be provided by the lecturer and the postgraduate tutor during the tutorial classes. The two coursework assessments will be marked and are designed to provide practice in solving the same type of problem which you are likely to find in the exam. Early in the course a further small assignment will be set and marked for formative purposes only. There are un-assessed homework problems every week; the answers to these will be provided once you have had time to try the problems for yourself. Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S1 (December) Mathematical Methods for Geophysicists 2:00
 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: Casey.Hollway@ed.ac.uk
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