Università degli Studi di Napoli "Parthenope"

Teaching schedule

Academic year: 
2019/2020
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

Language

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.

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). For beginners students the university organizes preparatory courses of Mathematics during the month of September.

Syllabus

Part I (24 hours)
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

The course is divided into three parts of 24 hours each. The first part is about functions: definition, properties, elementary functions and study of limits and continuity. The second part is about differential calculus and the third one is about optimization in two variables, integrals and linear algebra.

Part I (24 hours)
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

Teaching Methods

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

Textbooks

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

The exam is divided in two parts, one written and one oral. The written part lasts 90 minutes and it is structured to evaluate the achievement of the learning objective. It consists of 4 exercises: study of a function (12 points), finding of global maxima and minima of a function (6 points), resolution of a linear system of equation (6 points), partial derivatives of a function with variables and finding of critical points (6 points). The oral part is a test on the arguments of the program of the course. To sustain the oral exam the student must achieve at least 18/30 points to the written exam. To pass the written exam allows to sustain the oral exam only in the same round.
The final vote will depend on the result of both parts.
During the written exam it is possible to consult the book.

More information

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.