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

2020/2021
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. Basic knowledge of analytic geometry (line equation, parallelism, perpendicularity).
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

The aim of the course is to provide basic knowledge of Mathematics and Calculus to deal with the field of Management, Economics and Statistics.

### Textbooks

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

Alternatively:
P. Marcellini, C. Sbordone. Matematica generale, Liguori Editore, Napoli, 2007.

P. Marcellini, C. Sbordone. Esercitazioni di Matematica 1, parte I e II, Liguori Editore, Napoli, 1991.

### Learning assessment

During the exam, the student will have to demonstrate that they have acquired theoretical knowledge, passing a multiple choice test consisting of 10 questions. Every correct answer gives one points, missed 0 point, wrong -0.33 points. The quiz is passed with a score of 5/10. Students that pass the quiz has to take the oral part showing theoretical-practical skills, supporting the carrying out of exercises with the theoretical motivations regarding the chosen resolution methods. The final score depends on a global evaluation of both parts of the exam.
During the test it is not allowed to use books.