Calculus and Linear Algebra

The goal of this course is to lay a strong foundation for the various and numerous applications of calculus and linear algebra, both directly within the field of electrical engineering as well as in general engineering mathematics.

This course consists of two halves: calculus and linear algebra.

The first half of this course starts directly where the previous calculus course ended, by introducing parametric surfaces and surface integrals, as well as the curl and divergence of a vector field. Then, all topics in multivariate and vector calculus are connected by means of Stokes theorem and the divergence theorem. Afterwards, the focussed is shifted towards series. These are introduced and analysed by means of various convergence tests, such as the integral test, the alternating series test, comparison tests and the ratio test. Finally, power series are introduced, which results in a treatise of Taylor series.

The second half of this course starts from scratch with methods from Linear Algebra to solve and analyse systems of linear equations. Here concepts like vectors, linear combination, span and linear independence play a central role. In addition, matrices and matrix algebra are key concepts that will be discussed, with a major focus on invertibility of matrices. Finally, a lot of time will be devoted towards the more geometrical aspects of linear algebra, such as linear transformations, LU factorisation, subspaces, coordinates, dimension, orthogonality, orthogonal projections and least-squares problems.