16953 - Mathematics 1

Learning outcomes

Al termine del corso, lo studente possiede le conoscenze di base del calcolo differenziale e integrale per funzioni di una variabile reale, del calcolo vettoriale e dell'algebra lineare e dei numeri complessi. Acquisisce inoltre le nozioni fondamentali di geometria analitica nel piano e nello spazio

Course contents

Numeric sets and complex numbers. Geometry of three-dimensional space. Linear systems. Vector spaces. Bases. Linear maps. Matrices. Determinant. Eigenvalues and eigenvectors. Spectral theorem.

Elementary functions. Limits and continuity. Differential and integral calculus. Notes on functions of several variables.

Readings/Bibliography

Linear Algebra, Jim Hefferon

Linear Algebra As an Introduction to Abstract Mathematics, Isaiah Lankham, Bruno Nachtergaele, Anne Schilling

Linear Algebra, Serge Lang

Introduzione all'algebra lineare, Fioresi Morigi

What is Mathematics?, Richard Courant, Herbert Robbins

Matematica. Calcolo infinitesimale e algebra lineare, M. Bramanti, C. Pagani, S. Salsa, Zanichelli Editore

Elementi di Analisi Matematica, E. Giusti, Bollati Boringhieri

Teaching methods

Lectures and exercises in the classroom with slides and/or blackboard (traditional or electronic).

Assessment methods

The assessment is carried out through a written exam. The exam can be taken in a traditional format at the end of the course, or through two partial written exams scheduled during the course. In the latter case, both partial exams must be passed (with a grade of 18/30 or higher) and the final grade is the average of the grades from the partial exams. During all exam sessions, it is not allowed to consult notes.

Teaching tools

Blackboard (traditional or electronic) and projector.

Office hours

See the website of Giovanni Paolini

See the website of Salvatore Federico