Ateneo - UPO

Vector spaces and basis, operations between vectors, matrices and operations between matrices, linear systems, linear maps, eigenvalues ​​and eigenvectors, diagonalization of symmetric operators.
Elements of general topology in n-dimensional Euclidean space, limits and continuity for functions of several real variables, partial differentiation, multiple integration, line and surface integrals, differential forms and vector fields, Gauss-Green, divergence and curl formulas.

Recommended textbooks:

Bramanti, Pagani, Salsa, "Mathematical Analysis 1 with elements of geometry and linear algebra", Ed. Zanichelli, 2014.

The text indicated is the same that will be adopted for the course of Mathematics I.

F. Gazzola, "Mathematical Analysis 2", Ed. Esculapio, 2022.

M. Bramanti, C. D. Pagani, S. Salsa, "Mathematical Analysis 2", Ed. Zanichelli, 2009.

For a deeper analysis of the subject we also suggest the more recent edition of the following textbook:

C. D. Pagani, S. Salsa, "Mathematical Analysis 2", Ed. Zanichelli, 2016.

Acquisition of skills in solving exercises on the main topics of differential and integral calculus for functions of several real variables.

Contents of the Mathematics I course on differential and integral calculus for real functions of one real variable. In particular, people who intend to
attend this course and pass the related exam, must achieve the expected learning outcomes for the Mathematics I course which we recall below:
- know the basic notions of Mathematical Analysis in one real variable (functions in one variable, limits, derivatives, integrals);
- ability to apply knowledge and understanding: you must have developed a mastery of the notions learned which allows you to connect them together independently and use them jointly in solving simple theoretical problems;
- ability to communicate what has been learned: you must be able to clearly explain both the notions themselves and their use in general terms or in the specific case of a problem.

The course is organized with frontal lessons on the resolution of exercises corresponding to the topics covered in the main course. Particular attention will be paid to the exercises in preparation for the written test.

Appropriate teaching materials will be provided by the teacher who will be in charge of the course.

Students with physical disabilities, Learning Disabilities or Special Codice Descrizione Education Needs can request specific services and tools via the Staff Sviluppo e Coordinamento Carriere e Servizi alle Studentesse e agli Studenti, consulting the University webpage:
https://www.uniupo.it/en/services/services-students-physical-or-learningdisabilities
Students with disabilities, learning disabilities or special education needs, once they have contacted the University Staff, can refer to the tutor in charge of the course to define the examination modalities, concerning academic aspects.

The exam consists of a written test and a subsequent oral test including the topics of both modules of Geometry and Analysis II. The written test usually consists of 4-6 exercises on different topics of the course. In each written test, most of the topics contained in the course are covered. The presence of questions on the theoretical part is not excluded. The oral exam consists of a discussion on the exercises contained in the written test and some final questions on the statements and demonstrations of the main theoretical results. Admission to the oral test is subject to passing the written test with a grade greater than or equal to 16/30; the final grade will be obtained having as a starting point the grade of the written test to which points will be added or subtracted based on the progress of the oral test. Passing the written test, even with full marks, does not guarantee passing the exam in the event of an insufficient oral test.

Exercises will be carried out on all the topics covered in the main course, which for completeness are recalled below.
Vector spaces and basis, operations between vectors, matrices and operations between matrices, linear systems, linear maps, eigenvalues ​​and eigenvectors, diagonalization of symmetric operators.
Partial differentiation, stationary points, relative maximum and minimum points, differential forms and vector fields and related line integrals, multiple integration, line and surface integrals, Gauss-Green, divergence and curl formulas.

- Knowledge and understanding: acquisition of the main notions of matrix and vector calculus.
- Ability to apply knowledge and understanding: being able to deduce the main properties of vectors, matrices and functions between vector spaces.
- Ability to learn: the student will have to acquire a certain mastery in the use of logical reasoning and in the application of methodological rigor needed to tackle problems based on mathematical modeling.