Objectives

Students enrolling in the Ecole des HEC are often surprised to find a whole range of mathematics courses in their program. This is because the first year of studies has to provide them with "tools," and mathematics is one of these. The mathematics courses of the Ecole des HEC do not aim to teach theories for their own sake, but to introduce students to a certain number of notions -and their properties- which they will subsequently need to use.

Contents

Linear algebra deals with vectors and their properties. It also deals with matrices and operations that link them, determinants, and systems of linear equations. These lead to the study of linear transformations, quadratic forms, eigenvectors and eigenvalues. Several applications show the utility of such mathematical concepts when dealing with questions of industrial production and economic exchanges.

In this course we extend the concept of function to the setting of several variables. In this new environment we can deal with constraint optimization problems. In the examples considered, the constraints could be budgetary, or dictated by the principles of efficiency, utility, profitability, etc. The student learns how to "mathematize" a certain number of notions encountered in the parallel course in Economics.

Chapitre 6: Matrices (Linear Algebra, Part 1)

Chapitre 7: Mathematical Developments (Linear Algebra, Part 2)

Chapitre 8: Applications to Economics

Chapitre 9: Functions of Several Independent Variables

References

Recommended book:

Sydsaeter K. & Hammond P. (2014), Mathématiques pour l’économie,
éditions Pearson, Paris, ISBN-13 978-2-3260-0032-2.

Allen R.G.D., Mathematical Analysis for Economists, Macmillan, SBN 333-07831-4.

Black J. & Bradley J.-F., Essential Mathematics for Economists, John Wiley & Sons, C. 1973, ISBN 0-471-07713-5.

Commission Romande de Matématique, Algèbre Linéaire, éd. du Tricorne, 2009, EAN : 9782940501007.

Deschamps P., Cours de mathématiques pour économistes (manuel de 1er cycle), Ed. Dunod C. Bordas, Paris, 1988, ISBN : 2-04-018659-X.

Rommelfanger H., Mathematik für Wirtschaftswissenschaftler, B.I. - Hochschultaschen-bücher, Band 680, ISBN 3-411-00680-3.

Simon, C.P. et Blume L. Mathématiques pour économistes, 1998, De Boeck Université, Bruxelles.

Pre-requisites

Mathematics I

Evaluation

First attempt

Exam:

Written 3 hours

Documentation:

Not allowed

Calculator:

Allowed with restrictions

Evaluation:

If lecture halls are available, there will be a mid-term exam. If no mid-term exam can be organized (due to lack of available lecture halls), the final grade will be the final exam's grade.

Final Grade = 0.7*E + 0.3*max(E,ME) where E final exam's grade and ME is the mid-term exam's grade

Pocket calculators allowed: TI-30XIIB, TI-30XIIS, TI-30 Eco RS, HP 10S, or HP 10S+.

Retake

Exam:

Written 3 hours

Documentation:

Not allowed

Calculator:

Allowed with restrictions

Evaluation:

Same conditions as for the first attempt.