The course aims to:
Provide a basic introduction to calculus and basic statistical methods
Provide an introduction to mathematical and computational methods for modelling applications
Introduce general conceptual frameworks for the problems and issues of developing forward and inverse models
Provide practical analytical and numerical examples for both forward and inverse modelling, particularly linear v non-linear, approaches to solving and generic aspects of implementation
Provide example applications of the techniques covered, including use of Jupyter Python notebooks
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, including an introduction to Bayes Theorem and Monte Carlo methods among others.
The module will provide an introduction to a range of fundamental concepts and principles for handling and manipulating data. The first half of the module (taught with CEGE) provides a basic introduction to stats and linear algebra, and important basic concepts; the second half covers slightly more advanced applications of methods and tools for data analysis. 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
Differential equations and applications
Overview of statistical methods including an intro to Bayes Theorem
Numerical methods, model fitting, numerical optimization Monte Carlo and Metropolis-Hastings
The main sessions include:
Introduction to calculus methods
Introduction to linear algebra, matrices
Statistics and further statistics
Least Squares and further least squares
Differential equations
Introduction to Bayes Theorem
Model selection
Linear & non-linear model inversion
Monte Carlo methods and related numerical tools,
