CORE GEOGG121 – Analytical and Numerical Methods
(15 credits)
Term 1 (2011)
Note session title/order may change slightly after 24/11 session
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/GEOGG121/GEOGG121.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, 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)
Time series analysis (GS)
Linear models, inversion methods and applications (MD)
Non-linear models, parameter estimation, curve fitting (MD)
Introduction to Bayesian parameter estimation (MD)
Introduction to differential equations (MD)
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 (Lecture order subject to change)
Week
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
11
11
12
12
Date
Day/Time
Duration
6/10
6/10
13/10
13/10
20/10
20/10
27/10
27/10
3/11
3/11
10/11
10/11
17/11
17/11
24/11
24/11
1/12
1/12
8/12
8/12
15/12
15/12
Th 09:00
Th 14:00
Th 09:00
Th 14:00
Th 09:00
Th 14:00
Th 09:00
Th 14:00
Th 09:00
Th 14:00
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
Th 11:00
Th 14:00
Th 11:00
Th 14:00
Th 11:00
Th 14:00
Th 11:00
Th 14:00
Th 11:00
Th 14:00
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
2 hrs
Contact time = 40 hours
Class
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
Reading Wk
Reading Wk
Time series: lecture
Time series: practical
Model fitting 1: linear
Model fitting 1: practical
Model fitting 2: non-linear
Model fitting 2: practical
Bayesian Methods: lecture
Bayesian Methods: practical
Differential equations: lecture
Differential equations: practical
Room
Lecturer
Chadwick 102
Chadwick 102
Chadwick 102
Chadwick 102
Chadwick 102
Chadwick 102
Chadwick 102
Chadwick 102
Chadwick 102
Chadwick 102
JI
JI
JI
JI
JI
JI
JI
JI
JI
JI
PB 305
PB 110
PB 110
PB 110
PB 110
PB 110
PB 110
PB 110
PB 110
PB 110
GS
GS
MD
MD
MD
MD
MD
MD
MD
MD
Key contacts:
MD = Mat Disney (mdisney@geog.ucl.ac.uk)
JI = Jon Iliffe (plewis@geog.ucl.ac.uk)
GS = Gavin Simpson (gavin.simpson@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.
Campbell, G. S. and J. Norman (1998) An Introduction to Environmental Biophysics, Springer NY, 2nd
ed.
Croft, A., Davison, R. & Hargreaves, M. (1996) Engineering Mathematics, 2nd ed., Addison Wesley.
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).
Lewis, P. (2010) Some notes on linear modelling, unpub. lecture material.
Monteith, J. L. and Unsworth, M. H., Principles of Environmental Physics, Edward Arnold.
Riley, K. F., M. Hobson & S. Bence (2006) Mathematical Methods for Physics & Engineering, 3rd ed.,
CUP.
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.