Ateneo - UPO

Linear algebra and advanced calculus.

+ M. Bramanti, C.D. Pagani, S. Salsa, Analisi Matematica 1 con elementi di geometria e algebra lineare, Ed. Zanichelli, 2008.
+ M. Bramanti, C.D. Pagani, S. Salsa, Analisi Matematica 2, Ed. Zanichelli, 2009.

Knowledge of the main elements of linear algebra and functions of several variables. The ability to apply that knowledge in solving problems and exercises. Communication skills: the students will be able to use an appropriate vocabulary in relation to the topics covered in the course.
Autonomy of judgement: the course also aims to develop the critical sense that allows the student to draw conclusions on issues related to the topics covered, stimulating class discussions.

Course contents: Calculus I.

Theoretical lessons with practical exercises, stimulating discussion among students.

The control of ongoing learning will be carried out by carrying out exercises in the classroom with the active participation of students.

The exam consists of a written test and an oral test. The written test consists in carrying out exercises related to the program carried out during the lessons and lasts one hour. The oral test is at the discretion of the teacher and consists of a discussion on the written test. During the written test it is allowed to keep textbooks and calculator. At the end of the written test, the teacher corrects it and communicates the results on the DIR platform. This is usually followed by the oral exam the following days. The day and the classroom in which the oral exam will take place is communicated to the students at the institutional e-mail address. The results of the exam highlight the degree of understanding of theoretical concepts and the ability to use them to solve new problems. Sufficiency requires the ability to correctly adopt the chosen methodology, excellence requires the ability to contextualize.

Finite dimensional vector spaces, bases, matrices, determinants, eigenvalues and eigenvectors. Functions of several variables: domain and level curves, partial derivatives, tangent plane, stationary points. Least squares regression line. Ordinary differential equations: separation of variables, linear first-order differential equations, linear second-order differential equations. Sequences: definitions and basic properties. Numerical series and power series.

1) Knowledge and understanding - ability to identify a solution methodology and develop it correctly.
2) Ability to apply knowledge and understanding - ability to use learned tools.
3) Autonomy of judgment - ability to critically analyze the results.
4) Ability to continue studying independently - to be able to read, understand and comment on technical material from books or other sources.