MAT/05 - 9 CFU - 1° Semester

The course aims to present the elements of differential calculus of one-variable functions, of linear algebra and analytic geometry, showing the relevance of this topics to a diverse range of disciplines and in everyday's life. Another important course objective is to train the students to mathematical rigour and to refine their abstraction ability, two skills which are of fundamental importance in the study of every scientific discipline.

More specifically, these are the course objectives:

**Knowledge and understanding: **students will be able to read and understand a mathematical text and to understand the statement of a mathematical problem.

**Applying knowledge and understanding: **students will be able to use the main tools of differential calculus, linear algebra and analytic geometry, and to see how they are applied in the solution of scientific problems.

**Making judgements:** students will be trained in a variety of proof techniques and will be able to discuss ther correctness and completeness of a mathematical proof.

**Communication skills**: students will be able to present various mathematical topics in a clear fashion and to motivate the techniques used in the solution of an exercise, both orally and in written form.

**Learning skills: **students will be encouraged to deepen their knowledge of certain topics, even through the use of group projects, and those who wish will be given the chance to present in class.

The course is made up of lectures and recitation sessions. Usually the lecturer will alternate discussion of theory and solution of exercises in the same lecture. Students will be invited to take an active role in the lecture, by means of in class exercise sessions. In these sessions, the lecturer will propose several problems at the blackboard and invite students to solve them, suggesting approaches and providing hints. In case the course will be held online, we reserve the right to make suitable adjustments to the course structure.

- The real numbers.
- One-variable functions.
- Limits of sequences.
- Function limits and continuity.
- Differential calculus of one-variable functions.
- Elements of linear algebra.
- Elements of plane analytic geometry.

- Marco Bramanti, Carlo D. Pagani e Sandro Salsa, "Analisi Matematica 1, con elementi di geometria e algebra lineare", Zanichelli editore, Bologna, 2014.
- Paolo Marcellini e Carlo Sbordone, "Esercitazioni di Matematica", primo volume (parte prima), Liguori Editore, Napoli, nuova edizione, 2013.
- Paolo Marcellini e Carlo Sbordone, "Esercitazioni di Matematica", primo volume (parte seconda), Liguori Editore, Napoli, nuova edizione, 2014.