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
Numerical sets, equations and inequalities, analytical geometry, trigonometry.
Lecture classes and exercise classes.
As part of the innovation learning project novel tools will be used for the active learning of students. The goal is to increase students' skills via interactive, experience-based, learning methodologies (e-learning, teamwork, etc.) for enhanced participation, using an advanced level of communication that makes the student more aware and autonomous
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: The teacher receives students on a day in the week at the office located at the degree course building. The day will be fixed at the beginning of lectures. The e - mail address is : marco.baronti@unige.it
Ricevimento: By appointment.
MARCO BARONTI (President)
FILIPPO DE MARI CASARETO DAL VERME (President Substitute)
The timetable for this course is available here: EasyAcademy
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.
Students are recommended to follow all lectures, exercises sessions and tutors hours.
