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 prehonours 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 timedependent 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 halfspace
Week 11.
Revision or catchup time if needed.

Information for Visiting Students
Prerequisites  Mathematics 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:
 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, 9780521542616
Geodynamics, Turcotte, D. L. and Schubert, G 0521666244
Geophysical Theory, Menke, W. and Abbott, D. 9780231067928
Mechanics in the Earth and Environmental Sciences, Middleton, G. V. and Wilcock, P. R, 0521446694

Additional Information
Graduate Attributes and Skills 
Not entered 
Keywords  Math_Methods 
Contacts
Course organiser  Dr Hugh Pumphrey
Tel: (0131 6)50 6026
Email: Hugh.Pumphrey@ed.ac.uk 
Course secretary  Ms Casey Hollway
Tel: (0131 6)50 8510
Email: earth.sciences@ed.ac.uk 

