## 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 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.

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.

## Course unit content

Linear functions and models.

Linear systems and matrices. Economic

applications.

Non-linear models.

Differential Calculus and economic applications.

Integrals. Economic applications.

Functions in several variables.

## Full programme

Functions and Linear Models

The concepts of function and mathematical model.

Representation of a function.

Common types of function. Examples of mathematical economic models.

Linear functions.

Linear economic models.

Systems of linear equations and matrices

Systems of linear equations.

The reduction algorithm of Gauss-Jordan.

Economic applications of linear systems.

Linear algebra and applications

Concept of matrix and vector.

Matrix operations.

Matrix form of a linear system.

Inverse matrix and its use for the resolution of a linear system.

Determinant of a matrix calculation for arrays of size 2x2.

Non-linear models

General aspects: bounded functions, monotone functions, maxima and minima, infimum and supremum, even functions and odd functions, composite functions, inverse function, concave and convex functions (definition only).

Quadratic functions, exponential and logarithmic functions.

Economic models: quadratic, exponential and logarithmic.

The derivative

Average (or quotient) and instantaneous (or derivative) rate of change.

The derivative as the slope. Link between sign of the derivative and growth / decreasing function. Derivation rules.

Marginal analysis.

Limits: definition and examples of calculation. Continuity.

Techniques of differentiation

Rule of derivation of the product and ratio.

Rule of derivation of composite functions.

Derivatives of logarithmic and exponential functions.

Applications of the derivative

Maxima and minima. Applications.

Second derivative and study the graph.

Elasticity of demand.

The integral

The indefinite integral.

Integration by substitution.

Definite Integral.

The fundamental theorem of calculus.

Integrals: techniques and applications

Integration by parts.

Generalized integrals (notes).

Functions of several variables

Functions of several variables.

Notes on the graphs of functions of two variables.

Sections and contours.

Partial derivatives.

Maxima and minima.

Free and constrained optimization.

## Bibliography

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

aziendale, Apogeo, Milano, 2019.

## 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 and five theoretic/practical questions.

The quality of learning, the skill in the applications of

the concepts and the independence of judgement

will be verified through economic problems: the

student will individuate an opportune mathematical

model, obtaining the solution through the analytical

tools presented in Course.

The use of an appropriate technical language will be

checked through open questions about the theoretic

subjects of the Course.

Marks:

first part: 3/30

second part: 28/30

If the exam, possibly integrated by an oral exam, is

excellent, it will be valuated with full marks cum

laude.

The teacher reserves the right to complete the exam

with an oral test, if necessary.

The University will send to the students an email

message to their University email address with the

result of the exam (through Essetre system). The

students can reject the result in a week, through an

online procedure, clearly described in the message.

## Other information

Further teaching materials, the Syllabus, the

detailed program of the

course and the exams already assigned will be

published on Elly.

## 2030 agenda goals for sustainable development

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