The aim of the course is to provide the basic elements of differential and integral calculus for functions of one variable, and a short introduction to the theory of differential equations and to differential calculus for functions of several variables.
The first part of the course covers differentiation and integration of functions of one variable. The second part of the course provides the basic concepts of infinite series, differentiation of functions of two variables and it concludes with a brief discussion of linear differential equations.
The main expected learning outcomes are
Numerical sets, equations and inequalities, analytical geometry, trigonometry.
Lecture classes and exercise classes.
As part of the innovation learning project (adopted by the Bachelor Degree Course in Mechanical Engineering), 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
Functions of one real variable. 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. Sequences and series: the basic notions and examples. Limits of functions. Infinitesimal and infinite functions. Continuous functions and their local and global, derivative, 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. Taylor expansions and applications to critical points. Definite and indefinite integrals.
Functions of two (or more) real variables. Continuity, directional and partial derivatives, gradient. Differentiability and tangent plane. Level sets. Local minima and maxima: second order derivatives and the Hessian. Schwarz’s theorem.
Differential equations. Separation of variables. Linear differential equations: solving methods. Systems of differential equations. Existence and uniqueness for the Cauchy problem. General solution for systems of linear equations.
Ricevimento: By appointment, to be scheduled by e-mail
EDOARDO MAININI (President)
VALENTINA BERTELLA
ALBERTO DAMIANO
MAURIZIO CHICCO (President Substitute)
https://corsi.unige.it/8720/p/studenti-orario
The exam consists of
Alternatively, it is possible to take partial tests (one at the end of each semester)
To enroll the exam you must register by the deadline on the website https://servizionline.unige.it/studenti/esami/prenotazione
The examination modalities may change according to the evolution of the health emergency.
Multiple choice tests (partial tests). It is aimed to verift the student's ability to manage mathematical notation and to carry out simple computations and simple deductive reasoning. It consists of multiple-choice tests, each with one and only one correct answer.
Open questions and exercises. It is aimed to verify the knowledge of the main tools of differential and integral calculus. The test 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. Optional oral test. It is aimed at verifying the logical/deductive reasoning skills and consists of an oral test on the topics covered in the lectures, with particular focus on the correct statement of the theorems, the proofs of the results discussed during the lectures, and the solution to exercises. In particular, the student's logical/deductive ability and the degree of understanding of the concepts are assessed.
