The aim of the course is to provide the basic elements of integral calculus for functions of one variable, of the theory of ordinary differential equations and of differential calculus for functions of several variables.
The course provides an introduction to integral calculus, to ordinary differential equations and to the theory of functions of several variables
The main expected learning outcomes are • the knowledge of the analytical and geometrical meaning of integral calculus • the knowledge of the basic tools of differential calculus for functions of several variables • the knowledge of the basic methods for solving ordinary differential equations • the ability to solve exercises, discussing the reasonableness of the results
Transversal skills:
Learn to learn (basic level): awareness of one's preferred learning strategies, organization and assessment of personal learning according to what has been understood and learned
Contents of the course Mathematical Analysis 1A.
Lecture classes and exercise classes.
For the transversal skills, a problem solving based approach will be used
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
Integral calculus and series. Definite and indefinite integrals. Improper integrals. Numerical series and convergence criteria.
Functions of several variables. Continuity, directional and partial derivatives, gradient. Differentiability and tangent plane. Level sets. Local minima and maxima: second order derivatives and the Hessian. Schwarz 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.
• C. Canuto, A. Tabacco, Analisi Matematica 1, 4a edizione, Springer-Verlag Italia, 2014, • C. Canuto, A. Tabacco, Analisi Matematica 2, 2a 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
EDOARDO MAININI (President)
MAURIZIO CHICCO
MARCO BARONTI (President Substitute)
ANDREA BRUNO CARBONARO (President Substitute)
SIMONE DI MARINO (President Substitute)
CLAUDIO ESTATICO (President Substitute)
https://corsi.unige.it/en/corsi/8720/studenti-orario
The exam consists of • Written exam • Oral test (optional)
To enroll the exam you must register by the deadline on the website
https://servizionline.unige.it/studenti/esami/prenotazione
Written exam. This part includes open questions and exercises. It is aimed to verify the knowledge of the main tools of calculus that have been introduced through the course. 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.
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.
