Dear student,

Welcome to the learning environment (ELE) to support the book *Mathematics for Business Economics *(ISBN 978 90 395 2677). On this freely accessible ELE you can find the main mathematical outlines and key issues of the book. (The ELE does not provide a full overview of the book, in particular applications are not treated.) These outlines are accompanied by examples, films and multiple-choice questions. The ELE is not self-supporting and is meant to support the book (and the corresponding lectures at the University), not to replace it. You can use the ELE for instance to study some notions that were not completely clear to you after the lecture, or to practice some more before a test, etc.

The structure of the ELE is as follows. In Chapter 1 we lay the foundation by discussing functions of one variable. In Chapter 2 we discuss how to differentiate these functions. In Chapter 3 functions of two variables are treated and the central theme in Chapter 4 is to differentiate such functions. This technique is needed in Chapter 5 to optimize functions of one or two variables, also under constraints. In Chapter 6 you learn how to calculate the area of a region below the graph of a function by the use of integrals.

Every chapter is split into a number of sections, which consist of a number of topics. Each topic has its own page, possibly with other subpages, providing additional explanation, examples, films and exercises, attached to it. You can determine yourselves what part is relevant for you.

In order to use multiple-choice questions optimally as a tool for learning and practicin, you will have to solve the questions with a pen and paper to select an answer. Each answer provides specific feedback. The correct answers (briefly) shows the corresponding calculation or explanation, while after a wrong answer you are pointed to the most likely mistake, possibly with a reference to some theory or an example.

For questions, remarks, suggestions or improvements with respect to this ELE you can email to wiskunde1-tisem@tilburguniversity.edu.