The goal of the course is to provide the student a working knowledge in basic mathematical concepts and show how these tools are used in applied problems. It is divided in two main parts.
Part I is devoted to the study of ordinary differential equations (ODEs). Initially, the Cauchy problem and the study of its stability is introduced. Then, the main focus is on classical and modern discretisation methods for the simulation of ODEs and system of ODEs: one-step methods, multistep methods, Runge-Kutta, and spectral deferred correction methods.
In part II, after a brief recap about basic linear algebra concepts (vector spaces, scalar product, norm, orthogonal projection), the focus will be on the theory of transforms: Fourier series and integrals, Discrete and Fast Fourier Transform, Laplace, Zeta and Wavelet transforms.