GEOGG121 Analytical and Numerical Methods
CORE GEOGG121 - Analytical and Numerical Methods
(15 credits)
Term 1 (2013)
Staff:
Mat Disney (convenor), Jon Iliffe (CEGE),
Dr. M. Disney, room 113 Pearson Building, tel. 7679 0592 (x30592)
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, model fitting, numerical optimization
- Monte Carlo & Bayesian 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)
- Model selection
- Linear & non-linear model inversion (MD)
- MC methods, and Bayesian Methods II (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
