The class of Geodynamic Numerical Modelling includes an introductory section about the numerical solution of first and second-order partial differential equations with the finite difference methods. Numerical methods and some relevant approximation scheme for partial derivatives will be then applied to the Fourier's heat equation, the continuity equation, and the Stokes equations (1D-2D). In the final part of the course, these three equations will be combined into fully-coupled thermo-mechanical Matlab codes to simulate geodynamic processes.