# Università degli Studi di Napoli "Parthenope"

## Teaching schedule

2022/2023
Belonging course:
Course of Bachelor's Degree Programme on COMPUTER SCIENCE
Disciplinary sector:
MATHEMATICAL ANALYSIS (MAT/05)
Language:
Italian
Credits:
12
Year of study:
1
Teachers:
Cycle:
Annualita' Singola
Hours of front activity:
96

Italian

### Course description

to give 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 relevant bibliographic references relevant to the field of study.

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### 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) + 3 Trials (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