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## Mathématiques I

• Teacher(s):   A.Arnold   C.Darbellay   F.Dufresne
• English title: Mathematics I
• Course given in: French
• ECTS Credits: 6 credits
• Schedule: Autumn Semester 2022-2023, 3.0h. course + 1.0h exercices (weekly average)
•  sessions
•  course website
• Related programmes:
Bachelor of Science (BSc) in Economics

Bachelor (BSc) in Economic Sciences

Bachelor of Science (BSc) in Management

### 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 Faculté 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. Of the three classical features of mathematics -abstraction, logic and utility- the course stresses utility and the training of logical reflection.

Warning: Due to health developments related to COVID-19, study plans may be subject to adjustments during the semester.

### Contents

Mathematical analysis studies the properties of functions of real variables. The course deals first of all with functions of a single variable. The basic operation is derivation, with its reciprocal operation of integration. Taylor's development gives good local approximation and is the most important tool enabling one to find particularly useful values, e.g. extreme values. Basic techniques for finding the solution of differential equations are also presented. The student learns how to "mathematize" a certain number of notions encountered in the parallel course in Economics.

In addition, one third of the course consists in an introduction to financial mathematics. We discuss the concepts of discounting and accumulation (present and future values), equivalence of payments, the evolution of a debt, the evaluation of a bond, and different notions regarding interest rates.

Warning: Due to health developments related to COVID-19, study plans may be subject to adjustments during the semester.

### References

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

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

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

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. - Hochschultaschenbücher, Band 680, ISBN 3-411-00680-3.

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

None.

### Evaluation

#### First attempt

Exam:
Written 3 hours
Documentation:
Not allowed
Calculator:
Allowed with restrictions
Evaluation:

Written final examination.

No documentation allowed.

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

If sanitary conditions permit and sufficient rooms are available, a facultative midterm test will take place.

The final mark will be equal to the mark of the final examination if no facultative midterm test takes place OR if the mark of the final examination is greater than or equal to the mark of the facultative midterm test.

The final mark will be equal to 70% of the mark of the final examination plus 30% of the mark of the facultative midterm test, which would have taken place, if the mark of the final examination is less than the mark of the facultative midterm test.

#### Retake

Exam:
Written 3 hours
Documentation:
Not allowed
Calculator:
Allowed with restrictions
Evaluation:

Same conditions as for the first attempt.

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