The first goal of this course is to acquire the skill in understanding and applying Fourier analysis which is applied to all kinds of periodic records and processes (e.g. Milankovitch cycles in paleoclimate and paleoenvironment, solar sun spot cycles, or waves travelling through the Earth).

The second goal is to set up and solve (partial) differential equations for a large variety of situations in the Earth sciences. Fundamental and classical examples include the potential (geomagnetism, gravity), diffusion (heat transport, magnetic induction) and wave (seismology) equations.

The latest edition of the book - commonly known as BOAS - will be used:

Mary L. Boas (2006), Mathematical Methods in the Physical Sciences (3rd edition)

The chapters / sections from the text-book that will be treated during this course are:

- Chapt.1 (series, convergence, expansion), sections 1-13

- Chapt.2 (complex numbers), sections 1-17

- Chapt.7 (Fourier series and transforms), sections 1-13

- Chapt.8 (1st order ordinary differential equations), sections 1-14

- Chapt.13 (partial differential equations), sections 1-4

Lectures

- Series (Lecture notes)
- Complex numbers (Lecture notes)
- Fourier series and transforms (Lecture notes)
- Ordinary differential equations (Lecture notes)
- Laplace equation (Lecture notes)
- Partial differential equations ( Lecture notes 1, Lecture notes 2, Lecture notes 3 )