GEOGG121 Analytical and Numerical Methods

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)

Contact time = 40 hours

Key contacts:

MD = Mat Disney (mdisney@geog.ucl.ac.uk)

JI = Jon Iliffe (plewis@geog.ucl.ac.uk)