## Linear Algebra and Calculus II

### Full course description

A problem that occurs ubiquitously, when modelling real world phenomena (e.g., brain processes such as perception, or neural computations), is how to deal with instantaneous changes, and infinitely small quantities. This second part of the course will provide foundations of infinitesimal calculus, which are needed for the analysis as well as computational modelling of brain data and related behavioural data and serves as a substrate for more specific mathematical and modelling topics. The course will introduce the concepts of functions and their inverses, complex numbers as well the concepts of infinite series, limits, integration, differentiation, and multivariable calculus.

Each week consists of one or two lectures, together with homework, both pen and paper and computer assignments. Furthermore, a weekly debriefing session will take place to discuss the homework and assignments, under the guidance of a tutor.

The course links broadly through selected applications with concepts (e.g. retinotopy, tonotopy, memory decay, action potential) that are described in parallel and future such as Introduction to Cognitive Neuroscience, Learning and Memory and Brain Cells.

“Please note: the final assessment for this course is a grade between 1-10."

### Course objectives

- understand functions and inverse functions of a single variable
- understand and manipulating complex numbers
- understand the decomposition of a function into an infinite series
- understand the concepts of limits, derivatives and integration and their relation
- know how to perform differentiation and integration
- understand the concept of differential equation and its solution
- help each other and exchange background and skill in addressing the challenges posed by the mathematical problems discussed in the exercise (debriefing) sessions.