Aim of this course is to learn the foundations of vector analysis and Fourieranalysis and can be seen as continuation of the lecture Analysis 2 of the previous semester. The course is also suitable for students in higher semesters of the Bachelor degree.

The course starts with the concept of real submanifolds on which we want to develop an integration theory. The aim of this first half of the course is the divergence theorem. This is the generalisation to dimension bigger than one of the main theorem of calculus: the integral of a derivative is equal to an integral of the antiderivative over the boundary of the domain of integration. We will then see also the theorem of Stokes. These results have many applications, both in applied Sciences as Physics (for instance in Electromagnetism) as  also in many fields of Mathematics.

In the second part of the course we study the classical theory of Fourier series. In this classical chapter of mathematics one studies the approximation of periodic functions via series of simple oscillatings functions, namely sin and cos. At the end of the course we will study the continuous version of the Fourier series: the Fourier transform.

The lecture addresses students of the following Bachelor study paths: mathematics, Wirtschaftsmathematik and mathematische Biometrie as also Lehramtskandidaten.