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66877 - Calculus

Academic Year 2023/2024

                
                        Docente:
                        Mattia Francesco Galeotti
                    
                        Credits:
                        6
                    
                        SSD:
                        MAT/05
                    
                        Language:
                        Italian
                    
                        Teaching Mode:
                        Traditional lectures
                        
                            Campus:
                            Bologna
                        
                            Corso:
                            First cycle degree programme (L) in
                            Information Science for Management (cod. 8014)

                            Teaching resources on Virtuale
                        
                                    Course Timetable
                                
from Sep 18, 2023 to Dec 13, 2023

Learning outcomes

At the end of the module, the student is acquainted with the fundamental notions concerning differential and integral calculus of functions of one variable.

Course contents

Outlines of set theory and basic logic.
Sets of numbers: natural, integer, rational and real numbers. Topology of R.
Functions of one real variable: operations, properties, elementary functions.
Limits. Continuous functions and their properties.
Differential calculus: derivatives, Taylor formula and function study.
Integral calculus: the fundamental theorem, primitives; integration by substitution, by parts, integrals of rational and trigonometric functions.

Readings/Bibliography

E. Lanconelli, Lezioni di Analisi Matematica 1, Pitagora.
M. Bramanti, C.D. Pagani, S. Salsa, Analisi matematica 1, Zanichelli.

Teaching methods

Lectures.
Discussion of exercise resolutions.

Assessment methods

In order to pass the exam of the integrated course Mathematical Analysis - Linear Algebra on must pass the exam on each of the two parts; the grade of the integrated course is the mean of the grades of the two parts.

Mathematical Analysis exam:

Written and oral exams. The oral exam have to be taken not later then the second "appello" after the one of the written exam.
In order to attend the oral exam one must achieve at least a grade 15/30 in the written exam. The oral exam is crucial.
The written exam aims at verifying the ability of solving exercises akin to those assigned during the course. The steps leading to the solution must be given and justified. It is not allowed to use books, notes or calculators; only paper and pen. It lasts 2 hours.
The oral exam aims at verifying the knowledge of the theory developed during the course. It will be asked to give definitions and examples of concepts and to give statements and proofs of propositions, and to solve small exercises. Il lasts about half an hour.

Teaching tools

Tutoring and office hours.

Additional materials will be available on the course "Virtuale" page.

Office hours

See the website of Mattia Francesco Galeotti