A master course that I taught at ETH Zurich for students specializing in Earth, Environmental, and Planetary sciences.

Summary

This course guides students in learning mathematical machinery used to describe and solve various physical problems. Special attention is paid to the analytical methods to solve partial differential equations describing physical processes such as heat transfer, electromagnetic induction, wave propagation. Students use a series of fundamental mathematical tools, including curvilinear coordinates, eigenfunctions, Green’s functions and tensors.

Objective

The goal of this course is to refresh and deepen students’ knowledge in mathematical methods relevant to the problems arising in solid Earth physics.

Content

• Vector calculus, Vector identities, Parametric Curves and Surfaces

• Calculus in curvilinear coordinates

• Partial Differential Equations, Laplace equation, Helmholtz equation, Separation of variables, eigenvalues and eigenfunctions, spherical harmonic analysis

• Special functions: Delta function, Heaviside function, Bessel functions, Green’s functions

• Tensors, Einstein notation, tensor algebra