## Learning objectives

In an ever increasing number of contexts, it is advisable that a graduate student in

Economics is able to use quantitative measurements and tools. The main objective

of this course is to provide the student the basic mathematical instruments to

construct simple models for economic problems and take informed and justified

decisions.

At the end of the course, the student

should:

- understand and properly treat the main models

presented in the course;

- be able to analyze, formalize and solve practical (economical) problems;

- show good skills in making judgement;

- clearly communicate what he/she has learned using an appropriate language.

## 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

Oral lectures.

During the classes, a theoretical exposition of the contents of the course will be

given.

Then, a great number of examples and exercises will be discussed, with a particular

focus on economic applications. The students will be asked to discuss and propose

possible solutions to the exercises.

On the Elly platform the detailed program and the exams of the previous years will be uploaded at the beginning of the course. To download the material, registration to the online

course is required

## Assessment methods and criteria

Written exam.

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), a problem (2) and three theoretical

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 problem (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 use of an appropriate technical language will be

checked through three open questions (3) about the

theoretic subjects of the Course.

Indicative marks:

(1): 3/30

(2): 15/30

(3): 12/30

If the exam is excellent (for completeness,

brightness and organization of the answers,

concepts not specifically treated in the course), it is

valuated with full marks cum laude.

The teacher reserves the right to complete the exam

with an oral test, if

necessary.

Results will be communicated to the students within 10 days, via Esse3. The solution of the exam will be uploaded on the Elly platform within 7 days.

## Other information

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