Optimisation techniques, system of linear equations and dynamic models are important mathematical tools for economic analysis.

The goal of Mathematics B is to equip students in economics and business with the mathematical techniques needed in macro- and micro-economics and econometrics, and also to help them further developing their mathematical logic. The main focus is on optimisation techniques, system of linear equations, and dynamic models.

In Mathematics B we study optimisation problems involving functions of two real variables and derive necessary and sufficient conditions for extreme points, with and without constraints. We then define definite and indefinite integrals and study their relation as stated by the fundamental theorem of calculus. Integrals are then applied to describe the distribution of continuous random variables and to determine present values of continuous cash flows. Next, we introduce matrix theory and study the properties of vectors, which are then used to analyse and solve systems of linear equations. Finally, we introduce and solve difference equations of order one, which are useful mathematical tools to build dynamic models.

The topics of covered by **Mathematics B** are:

- extreme points without constraints
- extreme points with constraints
- definite integral
- indefinite integral
- improper integral
- fundamental theorem of calculus
- applications of integration (density functions, surfaces)
- operation with matrices
- inverse matrix
- determinants
- properties of vectors
- linear dependence and independence of vectors
- rank of a matrix
- gradient
- vector spaces
- existence and uniqueness of solutions of systems of linear equations
- Gaussian method
- eigenvalues and eigenvectors
- difference equations of order one

To access the content of the Mathematics B exercise booklet, please click on the cover page below: