Linear Algebra

Full course description

Linear Algebra is one of the basic mathematics courses of the BSc Circular Engineering programme, just as is the case for most engineering and natural sciences programmes across the globe. It mostly builds on high school mathematics. It prepares for more advanced mathematics courses as well as for computational techniques and skills, which feature in applied modelling and engineering courses and in the projects.

This course is structured around three central themes: algebra, geometry, and dynamics.

Algebra – The first theme is concerned with the most frequently occurring mathematical problem in practical applications: How to solve a system of linear equations? For this problem, a complete algebraic solution procedure is developed which provides you with a way to deal with such problems systematically, regardless of the number of equations or the number of unknowns.

Geometry – The second theme addresses linear functions and mappings, which can be studied naturally from a geometric point of view. This involves geometric ‘objects’ such as points, lines and planes, and geometric ‘actions’ such as rotation, reflection, projection and translation. One of the main tools of linear algebra is offered by matrices and vectors, for which a basic theory of matrix-vector computation is developed. This allows one to bring these first two themes together in a common framework, in what turns out to be an exceptionally fruitful way. By introducing the notions of vector spaces, inner products and orthogonality, a deeper understanding of the scope of these techniques is developed. This opens up a large array of rather diverse application areas in engineering and the natural sciences.

Dynamics – The third theme surfaces when a dynamic perspective is taken, where the focus is on the effects of iteration, in this case the repeated application of a linear mapping. This gives rise to a basic theory of eigenvalues and eigenvectors, which have many applications in various branches of science as will be discussed.

Many examples and exercises are provided to clarify the issues and to develop practical computational skills. They also serve to demonstrate practical applications where the results of this course can be successfully employed.

You will gain insight into algebraic and geometric concepts including vectors, matrices, linear transformations, eigenvalues and eigenvectors, inner products and orthogonality. You will learn to perform basic algorithmic calculations (matrices, equations, etc.) and solve more abstract algebraic problems. You will also gain insights into the applications of linear algebra in several engineering and scientific disciplines.