CORE GEOGG121 – Analytical and Numerical Methods
(15 credits)
Term 1 (2011)
Note the sessions are TBC as of June 2011
Staff:
Mat Disney (convenor), Jon Iliffe (CEGE), plus Gavin Simpson
Dr. M. Disney, room 113 Pearson Building, tel. 7679 0592 (x30592)
mdisney@geog.ucl.ac.uk
Course web page
http://www2.geog.ucl.ac.uk/~mdisney/teaching/GEOGG141/GEOGG141.html
Aims:
 To provide an introduction to mathematical and computational methods for modelling
applications, both analytical and numerical
 To provide a general framework for the problems and issues of developing forward and inverse
models
 To provide practical analytical and numerical skills for both forward and inverse modelling
 To provide example applications of the techniques covered
 To cover generic issues arising in application of analytical and numerical approaches including
the discretisation, detail vs computation time, stochastic processes etc.
 To provide exposure to numerical tools that are used in a wide range of modelling applications
Content:
The module will provide an introduction to a range of fundamental concepts and principles for handling
and manipulating data. The module will cover:
 Elementary differential and integral calculus and its applications (equations of motion, areas and
volumes etc)
 Linear algebra and matrix methods, including computational issues (decomposition for eg) and
generalised linear models
 Overview of statistical methods
 Introduction to ODEs and their applications
 Numerical methods (e.g. finite differences), model fitting, numerical optimisation, including Monte
Carlo & Bayesian methods
 Time series analysis and spatial methods
The main sessions include:









Introduction to calculus methods (JI)
Introduction to linear algebra, matrices (JI)
Statistics and further statistics (JI)
Least Squares and further least squares (JI)
Differential equations (MD)
Bayesian Methods (MD)
Further Bayes, model selection and MC methods (MD)
Linear & non-linear model inversion (MD)
Time series analysis (GS)
Assessment:
Assessed coursework for the first part of the course, handed in online; 2 hour unseen examination for
the second part, which takes place at the start of Term 2.
Format:
The course is based on lectures and practical sessions.
Learning Outcomes:
At the end of the course students should:
 Understand the general requirements for forward and inverse modelling in environmental
sciences
 Understand and be able to apply a range of mathematical and technical concepts and methods
to environmental modelling problems
 Be aware of the strengths and limitations of some of the more common mathematical and
technical approaches in modelling
 Demonstrate knowledge and understanding of a range of mathematical and computational
modelling tools
 Have some knowledge of the wider literature, both technical and theoretical, covering
implementation and application of the methods covered in the course
Class schedule:
This module runs in Term 1
Sessions (TBC as of June 2011)
Week
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
Date
Day/Time
Duration
Class
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
Contact time = 40 hours
Key contacts:
MD = Mat Disney (mdisney@geog.ucl.ac.uk)
Mathematical Techniques: CALCULUS
Mathematical Techniques: MATRICES
Statistics: 1
Statistics: 2
Statistics II: 1
Statistics II: 2
Least Squares I: 1
Least Squares I: 2
Least Squares II: 1
Least Squares II: 2
Differential equations: 1
Differential equations: 2
Bayesian Methods: 1
Bayesian Methods: 2
Model selection, MC: 1
Model selection, MC: 2
Model-fitting, non-linear inversion: 1
Model-fitting, non-linear inversion: 2
Time series: 1
Time series: 2
Room
xx
xx
xx
xx
xx
xx
xx
xx
xx
xx
xx
xx
xx
xx
xx
xx
xx
xx
xx
xx
Lecturer
JI
JI
JI
JI
JI
JI
JI
JI
JI
JI
MD
MD
MD
MD
MD
MD
MD
MD
GS
GS
JI = Jon Iliffe (plewis@geog.ucl.ac.uk)
Reading list (provisional):
Material and examples are taken from some of these texts. Where a text is key, this will be detailed in
the lectures and/or practicals:
Barnsley, M. J., 2007, Environmental Modeling: A Practical Introduction, CRC Press, 432pp.
Boas, M. L., 198s (2nd ed) Mathematical Methods in the Physical Sciences, Wiley, 793pp.
Boeker, E. and van Grondelle, R., 2001, Environmental Science, Physical Principles and Applications,
2nd ed, Wiley.
Flake, W. G., 2000, Computational Beauty of Nature, MIT Press.
Gauch, H., 2002, Scientific Method in Practice, CUP.
Gershenfeld, N., 2002, The Nature of Mathematical Modelling, CUP.
Goodchild, M.F., Parks, B.O. and Steyaert, L.T. 1993 Environment al Modelling with GIS, Oxford:
Oxford University Press.
Hardisty et al., 1993, Computerised Environmental Modelling: A practical introduction using Excel,
John Wiley and Sons.
Haynes-Young, R. and Petch, J. 1986 Physical Geography: its nature and methods, (London: Harper
Row).
Kirkby, M. J., Naden, P. S., Burt, T. P. and Butcher, D.P. 1993 Computer Simulation in Physical
Geography, (Chichester: John Wiley and Sons).
Monteith, J. L. and Unsworth, M. H., Principles of Environmental Physics, Edward Arnold.
Sivia, D. S., with J. Skilling, 2008 (2nd ed) Data Analysis: A Bayesian Tutorial, OUP, 246pp.
Wainwright, J. and Mulligan, M., 2004, Environmental modelling: finding simplicity in complexity,
Chichester, Wiley.