## 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 will be able to analyze and formalize some

economic problems. In particular, she/he will be able to identify the data of the

problem and to construct the most suitable model, choosing the appropriate

mathematical methods to solve the problem in an efficient and rigorous way. The

student will also be able to give an economic interpretazion to the results of her/his

analysis.

## 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,

Apogeo, Milano, 2006

## 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.

## Assessment methods and criteria

Written exam.

The acquisition of knowledge and understanding will be tested by 3 questions about

the prerequisites, a problem and 3 questions about the theory.

In particular, 3 initial questions (1 pt each) will be used to test the mastery of the

preliminary notions required for the course.

To evaluate the learning ability, the capacity of applying the learned concepts to real

problems and the independence of judgement, a problem (value: 15 pt.)will be

proposed to the student, who must choose the appropriate mathematicalmodel and

method to find a solution and interpret the obtained results.

The acquisition of a technical language will be evaluate through 3 questions (4 pt.

each) on theoretical topics covered in the course.

## Other information

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