This course consists of 2h/week of lectures and 2h/week of tutorials, during semester 1.

It is composed of three main topics :

1) Tensor calculus

2) Special functions

3) statistics.

The first part is an introduction to the concept of tensors, which are geometric objects that describe linear relations between vectors, scalars, and other tensors (e.g. the dot product).
Important applications of tensors are provided by continuum mechanics (the stresses inside a solid body or fluid are described by a tensor).

The second part deals with the derivation and use, in geophysics, of spherical harmonics.
They are the angular portion of a set of solutions to Laplace's equation, and play an important role in many theoretical and practical applications.
For example, they can be used to parameterise the Earth's mantle in the framework of global seismic tomography.

The third part is a brief introduction to solving problems with probabilities and statistics (e.g. Bayes' theorem), which can be used to correctly interpret geophysical data sets.
These notions will be expanded in the inverse problems course in the year 2.