The aim of the course is to provide the basic elements of differential calculus for functions of one variable
The course provides some basic concepts of mathematical analysis and the first elements of differential calculus for functions of one variable
The main expected learning outcomes are • to master the mathematical notation • the knowledge of the properties of the main elementary functions • the ability to follow the logical concatenation of arguments • to master simple demonstration techniques • the ability to solve exercises, discussing the reasonableness of the results
Transversal skills:
Literacy (basic level): Ability to communicate effectively in written and oral form, adaptation of one's communication to the context, use of sources and aids of various kind
Numerical sets, equations and inequalities, analytical geometry, trigonometry
Lecture classes and exercise classes.
For the transversal skills, a problem solving based approach will be used
Real numbers, the oriented real line. The Cartesian plane, graphs of elementary functions. Operations on functions and their graphical interpretation. Monotonicity. Composition and inversion. Powers, exponentials and logarithms. Supremum and infimunm. Numerical sequences: the basic notions and examples. Limits of functions. Infinitesimal and infinite functions. Continuous functions and their local and global properties. Derivatives and derivation rules. Derivatives of elementary functions. Sign of derivatives in the study of monotonicity and convexity. The classical theorems of Rolle, Cauchy, Lagrange and de l'Hôpital. Study of the graph of functions. Taylor expansions and theoir applications.
• C. Canuto, A. Tabacco, Analisi Matematica 1, 4a edizione, Springer-Verlag Italia, 2014, • M. Baronti, M., F. De Mari, R. van der Putten, I. Venturi, Calculus Problems, Springer International Publishing Switzerland, 2016
Ricevimento: By appointment, to be scheduled by e-mail
ANDREA BRUNO CARBONARO (President)
MARCO BARONTI (President Substitute)
SIMONE DI MARINO (President Substitute)
CLAUDIO ESTATICO (President Substitute)
EDOARDO MAININI (President Substitute)
CHIARA ROMANENGO (President Substitute)
https://corsi.unige.it/en/corsi/8720/studenti-orario
The exam consists of • Multiple choice test • Written exam
To enroll the exam you must register by the deadline on the website
https://servizionline.unige.it/studenti/esami/prenotazione
Multiple choice tests: It is aimed to verify the student's ability to manage mathematical notation and to carry out simple computations and simple deductive reasoning. It is necessary to be successful in the multiple choice test in order to access the written exam
Written exam: This part includes open questions and exercises. It is aimed to verify the knowledge of the main tools of differential calculus. The written exam consists of exercises with several questions of different difficulty. The student must be able to solve the exercises correctly and to justify the necessary steps to obtain the final result, and to use the correct formalism.
Ask the professor for other information not included in the teaching schedule.
