## Learning objectives

In an ever increasing number of contexts it is advisable that a graduate in economic disciplines is able to use quantitative measurements and tools.

The main objective of the course is to allow the student to "take

possession" of these tools in order to separate thestructure of a problem from the context so that he/she can understand and communicate as effectively as possible what is needed to take

informed and justified economic decisions.

In an ever increasing number of contexts it is advisable that a graduate in economic disciplines is able to use quantitative measurements and tools.

The main objective of the course is to allow the student to "take possession" of these tools in order to separate the structure of a problem from the

context so that he/she can understand and communicate as effectively as possible what is needed to take informed and justified economic decisions.

Furthermore, at the end of the course:

- as far as concerns knowledge and understanding: the student should understand and properly treat the main models presented in the course;

- as far as concerns applying knowledge and understanding: the student should be able to solve practical problems;

- as far as concerns making judgements: the student should show good skills in making judgement, developing reasoning and critical capacities;

- as far as concerns communication skills: the student should clearly communicate what he/she has learned;

- as far as concerns learning skills: the student should update and consolidate his/her quantitative

knowledge and relate this knowledge and competence to other disciplines in the degree course.

Furthermore, the student should be able to formalize in quantitative terms some economic problems, by individuating initial data and the more adequate mathematical instruments in order to obtain an efficient and rigorous solution and to provide an economic interpretation of the obtained results.

## Prerequisites

First and second order equations and inequalities. Properties of exponentiation.

## Course unit content

Linear functions and models. Linar systems and matrices. Economic applications.

Non-linear functions.

Differential Calculus and economic applications.

Integrals. Functions in several variables. Economic applications.

## Full programme

Real functions. Graph of a function.

Linear functions and models. Economic applications.

Systems of linear equations.

Linear algebra: vectors and matrices.

Non-linear models: quadratic functions, exponential functions, logarithm.

Limits and continuity of functions. First and second derivatives.

Maxima and minima of functions.

Economic applications.

Integration theory: indefinite and definite integral. Fundamental theorem of calculus.

Integration by parts and by substitution.

Improper integrals.

Introduction to functions of several variables. Partial derivatives of first and second

order. Hessian matrix.

Maxima and minima of functions of two variables.

Constrained optimization:Lagrange's multipliers.

## Bibliography

S. Waner, S.R. Costenoble, Strumenti quantitativi per la gestione aziendale,

Maggioli Editore, 2018.

## Teaching methods

1) Knowledge and understanding: teacher-fronted sessions.

2) Applying knowledge and understanding: practice sessions.

3) Making judgements: teacher-fronted sessions and practice sessions.

4) Communication skills: practice sessions.

5) Learning skills: teacher-fronted sessions and practice sessions.

## Assessment methods and criteria

Written examination (60 minutes).

During the exam, the student can use a scientific calculator. Graphic calculators, smartphone, tablet, laptops and smartwatch are not allowed.

The knowledge and the skill in comprehension will be tested through three questions about elementary mathematics (1), three short problems (2) and three theoretic/practical questions (3).

The quality of learning, the skill in the applications of the concepts and the independence of judgement will be verified through the economic problems (2). In order to solve such a problem, the student will individuate an opportune mathematical model, by obtaining the solution through the analytical tools presented in Course.

The knowledge of an appropriate technical language will be checked through the three theoretical/practical questions (3).

Indicative marks:

(1): 3/30

(2): 15-16/30

(3): 12-13/30

If a correct result is not justified by suitable computations in the paper given to the student, no mark will be assigned.

If the test, possibly integratd by an oral exam, is excellent, it will be valuated with full marks cum laude.

The teacher could ask for an oral test and/or partially modify the modality of examination, also according to the need of integration with possible

online activities.

The University will send the students an email message to their

University email address with the result of the exam (through Essetre

system). The students can reject the mark in a week, through an online

procedure clearly described in the message.

## Other information

Further teaching materials, the Syllabus, the detailed program of thecourse and the exams already assigned will be published on Elly.

Furthermore, the teachers could modify some indications, in particular about lessons and examinations, also according to the evolution of the pandemic situation.

Every change will be communicated well in advance to students through the usual channels.