Università degli Studi di Napoli "Parthenope"

  1. Teaching
  2. CIVIL AND ENVIRONMENTAL ENGINEERING FOR THE MITIGATION OF RISKS
  3. Mathematics I - Mod 1

Stampa

Mathematics I - Mod 1

Teaching schedule

Academic year: 
2020/2021
Teaching: 
Mathematics I
Belonging course: 
Course of Bachelor's Degree Programme on CIVIL AND ENVIRONMENTAL ENGINEERING FOR THE MITIGATION OF RISKS
Location: 
Napoli
Disciplinary sector: 
MATHEMATICAL ANALYSIS (MAT/05)
Credits: 
10
Year of study: 
1
Teachers: 
Prof.ssa BETTA MARIA FRANCESCA
Cycle: 
Annualita' Singola
Hours of front activity: 
80

Language

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)
Linear dependence in the plane and in the space of geometric vector. Inner product standard- Orthogonal frames. Cartesian orthogonal monometric frame in spaces- Vector product in the space of geometric vectors. Changes of frames.
Vector product in the space of geometric vectors.
-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

Textbooks

Robert A. Adams, Christopher Essex, Calculus: A Complete Course, Pearson Canada.

Learning assessment

The objective of the exam is to check the level of achievement of the above-mentioned training objectives.
The exam is divided into two parts:
- A written test that aims to evaluate the ability to correctly use the theoretical knowledge acquired during the course to solve mathematical problems. The student who does not show sufficient mastery of the arguments is not admitted to the next test. The expected time is 2 hours.
- an oral test in which the ability to link and compare different aspects of the course will be evaluated.
The final vote takes into account the evaluation of both tests.

More information

Lectures are in Italian. The professor is fluent in English and is available to interact with students in English, also during the examination.

Time table: Monday from 14 to 16. I am also available on other days by appointment by e-mail.

Mutuazioni

  • MATHS I - MOD A
    Study course INGEGNERIA INFORMATICA, BIOMEDICA E DELLE TELECOMUNICAZIONI - Training course in PERCORSO GENERICO