# Università degli Studi di Napoli "Parthenope"  ## Teaching schedule

2021/2022
Belonging course:
Course of Bachelor's Degree Programme on MANAGEMENT DELLE IMPRESE TURISTICHE
Disciplinary sector:
MATHEMATICAL METHODS OF ECONOMY, FINANCE AND ACTUARIAL SCIENCES (SECS-S/06)
Language:
Italian
Credits:
9
Year of study:
1
Teachers:
Cycle:
First Semester
Hours of front activity:
72

Italian

### Course description

The aim of the course is to provide basic knowledge of Mathematics and
Calculus to deal with the field of Management, Economics and Statistics.
Expected learning outcomes
Knowledge and understanding: the student has to prove to be able to use
the mathematical tools and understand which of them are needed to
model and to solve problem in the fields of economics, finance and
management.
Ability to apply knowledge and understanding: the student must be able
to apply the mathematical techniques to solve real problems in
economics, finance and management. In particular, the student must
prove the ability to solve simply problems of optimization, that is to find
maximum and minimum of functions.
Autonomy of judgment: the student has to be able to formulate a real
problem in mathematical language.
Communication skills: the student has to be able to express rigorously
the acquired knowledge, answering clearly and exhaustively to the
questions of the oral part of the exam.
Lifelong learning skills: the student has to prove to be able to assimilate
the methodologies studied and use the mathematical tools to solve
application problems.

### Prerequisites

Elements of set theory, set of integers, rationales and reals. Equation and
inequality of I and II degree. Basic knowledge of analytic geometry (line
equation, parallelism, perpendicularity). Prerequisites will be recalled
during the first week of lesson.

### Syllabus

Part I (24 hours)
Prerequisites: Elements of set theory, set of integers, rationales and
reals. Equation and inequality of I and II degree.
Functions
Function between sets – Numerical functions – Injective, surjective and
bijective or invertible function – Inverse function – Composed function –
Global maximum and minimum of a function – Supremum and infimum of
a function – Monotonic functions – Graph – Domain
Elementary functions
Linear function – Absolute value function – Power, root, exponential and
logarithmic functions.
Limits
Definition of limit – Indeterminate form – Some important limits
Continuity
Definition of continuous function – Weierstrass theorem (only statement)
– Bolzano theorem (only statement).
Part II (24 hours)
Differential calculus
Definition
of
derivatives
and
derivable
functions:
geometric
interpretation. Derivation rules – Derivative of composed function –
Derivative of elementary functions.
Applications of differential calculus
Criterion of monotonicity of derivable functions - Local maximum and
minimum – Concavity and convexity – Criterion of concavity/convexity –
De L’Hopital theorem (only statement) – Asymptotes – study of the graph
of a function
Economic applications: demand and supply, elasticity of the demand
respect to the price – market equilibrium
Part III (24 hours)
Functions of two real variables
First and second partial derivatives – Hessian matrix – Unconstrained and
constrained maximum and minimum of two variables
Economic applications: profit maximization, costs minimization
Introduction to integral calculus
Antiderivatives – Indefinite integral (only definition).
Linear algebra
Vectors – Matrix – Determinant – Rank – Operation between matrices –
Linear systems

Functions: Injective, surjective and bijective or invertible function –
Inverse function – Composed function – Global maximum and minimum–
Supremum and infimum – Monotonic functions – Graph – Domain
Elementary functions: Linear – Absolute value – Power, root, exponential
and logarithmic functions.
Limits: Definition – Indeterminate form – Important limits
Continuity: Definition – Weierstrass theorem – Bolzano theorem.
Differential calculus
Definition
of
derivatives
and
derivable
functions:
geometric
interpretation. Derivation rules – Derivative of composed function –
Derivative of elementary functions.
Applications of differential calculus:
Criterion of monotonicity - Local maximum and minimum – Concavity and
convexity – Criterion of concavity/convexity – De L’Hopital theorem –
Asymptotes – study of the graph of a function
Economic applications: demand and supply, elasticity
– market
equilibrium
Functions of two real variables:
First and second partial derivatives – Hessian matrix – Unconstrained and
constrained maximum and minimum of two variables
Economic applications: profit maximization, costs minimization
Introduction to integral calculus:
Antiderivatives – Indefinite integral (only definition).
Linear algebra: Vectors – Matrix – Determinant – Rank – Operation
between matrices – Linear systems

### Teaching Methods

Classroom and practices to use mathematical methods studied with students’ interaction.

### Textbooks

A. Guerraggio, Matematica - terza edizione, Pearson, 2020

### Learning assessment

During the exam, each candidate must demonstrate that they have acquired theoretical knowledge and developed theoretical-practical skills by passing a written test divided into two parts. The first part consists of a multiple choice test consisting of 10 questions on theory. Each correct answer assigns a point, each omitted answer zero points, each wrong answer -0.33 points. This part is considered passed with a score of 18/30 which is reached with a score of 4/10 in the quiz. The second part of the test includes exercises and can be composed of either a function study, or two exercises between the calculation of absolute maximums and minimums of a function, resolution of a linear system using the Gauss method and calculation of the critical points of a function in two variables. Also for this second part the vote is calculated in thirtieths. The final grade is the average of the votes of the two parties. In order to pass the exam, passing must be achieved in both parts of the task.

Expected learning outcomes
Knowledge and understanding: the student has to prove to be able to use
the mathematical tools and understand which of them are needed to
model and to solve problem in the fields of economics, finance and
management.
Ability to apply knowledge and understanding: the student must be able
to apply the mathematical techniques to solve real problems in
economics, finance and management. In particular, the student must
prove the ability to solve simply problems of optimization, that is to find
maximum and minimum of functions.
Autonomy of judgment: the student has to be able to formulate a real
problem in mathematical language.
Communication skills: the student has to be able to express rigorously
the acquired knowledge, answering clearly and exhaustively to the
questions of the oral part of the exam.
Lifelong learning skills: the student has to prove to be able to assimilate
the methodologies studied and use the mathematical tools to solve
application problems.