The aim of the course is to provide the basic elements of differential calculus for functions of one variable.
To provide the fundamentals of differential calculus in one variable and the operational knowledge of some basic mathematical tools, while maintaining the necessary methodological rigor.
The main expected learning outcomes are
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 in the plane, trigonometry.
Lecture classes and exercise classes.
For the transversal skills, a problems solving based approach will be used.
We advice working students and students with dysfunctionalities or disabilities or other special educational needs to contact the professor at the beginning of the course in order to devise an adequate teaching method and exams, which are in line with the learning outcomes as well as the individual learning skills.
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 their applications.
Ricevimento: By appointment.
MARCO BENINI (President)
LAURA CAPELLI (President Substitute)
https://easyacademy.unige.it/portalestudenti/index.php?view=easycourse&_lang=it&include=corso
The timetable for this course is available here: EasyAcademy
The exam consists of
To enroll the exam you must register by the deadline on the website
https://servizionline.unige.it/studenti/esami/prenotazione
Multiple choice test: 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.
