# MATHEMATICAL METHODS FOR ECONOMICS cod. 1006537

1° year of course - First semester
Professor
- Marzia DE DONNO
Metodi matematici dell'economia e delle scienze attuariali e finanziarie (SECS-S/06)
Field
Statistico-matematico
Type of training activity
Characterising
70 hours
of face-to-face activities
10 credits
hub: PARMA
course unit
in ITALIAN

## 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.

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