Università degli Studi di Napoli "Parthenope"

Teaching schedule

Academic year: 
2022/2023
Belonging course: 
Course of Bachelor's Degree Programme on COMMAND AND MANAGEMENT OF A MARINE VESSEL
Disciplinary sector: 
MATHEMATICAL ANALYSIS (MAT/05)
Language: 
Italian
Credits: 
9
Year of study: 
1
Teachers: 
Cycle: 
First Semester
Hours of front activity: 
72

Language

Italian

Course description

to give to the student the necessary math knowledge to address the course
of study
KNOWLEDGE AND CAPACITY OF COMPRESSION: The student must
demonstrate understanding of differential calculus and its applications to
optimization problems and integral calculus.
CAPACITY TO APPLY KNOWLEDGE AND CAPACITY OF COMPRESSION The
student must demonstrate knowing how to apply the knowledge of
differential and integral calculus acquired to solve optimization problems.
For this purpose, the teacher during the course for the attendants and at
the reception for non-attendants provides several exercises.
JUDGMENT AUTONOMY: The student must demonstrate the ability to
further study independently, acquired knowledge by applying them also
through self-evaluation
COMMUCATIVE SKILLS: The student must be able to answer clearly,
concisely and exhaustively both in the written test questions and in the
oral test.
LEARNING ABILITY: The student must demonstrate a good learning ability
by deepening their knowledge on

Prerequisites

Noone

Syllabus

Real Numbers. Set theory. Injective, surjective, invertible functions.
Maximum, minimum of a set
Elementary functions and their Cartesian representation. Power,
exponential and logarithmic functions. Trigonometric functions. Inverse
trigonometric functions.
Exponential and logarithmic Inequalities. (24 hours of lectures)
Elements of linear algebra. Linear systems. Gauss method. Rank of a
matrix. Cramer theorem (24 hours of lectures)
Limits of functions. Continuous functions. Discontinuity of first and of
second kind. Zero theorem. Numerical solution of an equation. Bisection
method
Derivatives. Operations on derivatives. Derivatives of composite
functions. Geometric meaning of derivative. Derivatives of elementary
functions.
Fermat's theorem. Characterization of constant functions. Criteria
monotony.
The theorems of L'Hospital. Convexity, concavity, asymptotes. Graph of a
function.Functions of two variables, partial derivatives.
Definition of integral (24 hours of lecture)

Real Numbers. Set theory. Injective, surjective, invertible functions.
Maximum, minimum of a set
Elementary functions and their Cartesian representation.
Exponential and logarithmic Inequalities.
Elements of linear algebra. Linear systems. Gauss method.
Limits of functions. Continuous functions. Discontinuity of first and of
second kind. Zero theorem. Numerical solution of an equation. Bisection
method
Derivatives. Operations on derivatives. Derivatives of composite
functions. Geometric meaning of derivative. Derivatives of elementary
functions.
Fermat's theorem. Characterization of constant functions. Criteria
monotony.
The theorems of L'Hospital. Convexity, concavity, asymptotes. Graph of a
function.Functions of two variables, partial derivatives.
Definition of integral

Teaching Methods

Lectures with numerous exercises

Textbooks

Analisi Matematica I
Marcellini-Sbordone
Liguori Editore
Esercitazioni di matematica vol.1 parte 1
Paolo Marcellini, Carlo Sbordone
Liguori Editore

Learning assessment

The verification procedure consists of an oral examination (40% of the
vote) + Homework (60% of the vote) for the students that attend while a
written exam (60% of the vote) for the students that did not attend.
The objective of the verification procedure is to quantify the level of
achievement of the previously indicated training objectives.
The tests carried out (or written tests) evaluate the level of knowledge in
the field of linear algebra and mathematical analysis. The oral exam
assesses the level of knowledge and the overall skills on the theoretical
and applicative aspects of the topics of the program and the ability to
critically analyze the concepts

More information