# Università degli Studi di Napoli "Parthenope"

## Teaching schedule

2020/2021
Teaching:
Belonging course:
Course of Bachelor's Degree Programme on MANAGEMENT ENGINEERING
Location:
Napoli
Disciplinary sector:
MATHEMATICAL ANALYSIS (MAT/05)
Credits:
10
Year of study:
1
Teachers:
Cycle:
Annualita' Singola
Hours of front activity:
80

Italian

### Course description

The aim of this course is to learn basic calculus and some theorems of real analysis (differential and integral calculus, sequences and series of real numbers and real functions). A further aim is to apply analytical techniques in other scientific disciplines.  Learning outcomes (declined compared with the Dublin descriptors)  -Knowledge and understanding. Knowledge of the differential and integral calculus for functions of one real variable. The student will be able to state and prove basic theorems of Mathematical Analysis. -Applying knowledge and understanding. The ability to understand the problems proposed during the course, the ability to correctly apply the theoretical knowledge. The student will be able to study of the graphs of elementary functions, to solve integration problems of elementary character, to discuss the nature of numerical sequences and series. -Making judgments. Develop the ability to critically evaluate the problems and propose the most appropriate approach -Communication skills. Ability to report and present the results with a ogical-deductive and synthetic exposition -Ability to learn.Ability to develop, outline, summarize the contents

### Prerequisites

Algebra of polynomials. Elements of analytic geometry. Elements of goniometry and trigonometry. Elementary equations and inequalities.

### Syllabus

-Real numbers and numeric functions (10 hours). Review of elementary set theory. The real number system. -The concept of function.; elementary functions.
-Vector in the plane and in the space (4 hours)
-Sequences of real numbers (8 hours). Sequences: limit definition; and related theorems; operations with indefinite limits and forms; monotone sequences.
-Differential Calculus for Function of one Variable (24 Hours) Numeric Functions:  limit of a function and its properties; continuous functions; considerable limits; monotone functions; Weierstrass theorem. Derivative, Definition and Its Geometric meaning; derivation of elementary functions and derivation rules; maximum and minimum relative; Rolle theorem, Lagrange theorem and consequences; de l'Hopital theorem; Taylor's formula; concave and convex functions, asymptotes.
-Integral Calculus for Function of one Variable (12 Hours) Primitive of a Function, Indefinite Integral; integration rules; Riemann integral; integrability of continuous functions; mean value theorem, fundamental theorem of integral calculus.
- Differential equation (10 hours)

The real number system. The concept of function. Vectors. Sequences of real numbers. Continuous functions and related theorems. Differential calculus for functions of one variable. Integral calculus for functions of one variable. Differential equations.

### Teaching Methods

Lectures, exercise sessions