Real numbers. Order and algebraic properties of real numbers. Infimum and supremum of sets of real numbers; the continuity axiom. Mathematical language and syntax. The terminology of set theory. Basic elements of logic. Functions and their graphs. Differential calculus in one real variable. Optimization problems. The Riemann integral and the Fundamental Theorem of Calculus. Convex functions. The Taylor formula. Asymptotic expansions. ODE. Sequences and series of real numbers.
Mariano Giaquinta, Giuseppe Modica
"Note di Analisi matematica. Funzioni di una variabile". Pitagora Editrice Bologna. (2014; but also the previous editions of 2005 and subsequent editions).
Pierluigi Benevieri "Esercizi di Analisi Matematica I", Citta' Studi Edizioni (2007)
Learning Objectives
Provide the skill to connect and express in appropriate mathematical language the topics taught during the lectures, and to develop mathematical models aimed to understand and solve real world problems.
Prerequisites
Basic notions of mathematics taught in high school. In particular: formal calculus; polynomials; algebraic, exponential and logarithmic equations. Basic notions in analytic geometry (the Cartesian plane, lines circles, parabolas, etc.). Trigonometric functions.
Teaching Methods
Lectures and exercise classes.
Further information
More textbooks.
Giacomo Tommei
"Matematica di base", Apogeo Ed. 2010.
Giovanni Malafarina
"Matematica per i precorsi", McGraw-Hill 2003.
Type of Assessment
The final exam is made of a written and an oral part. In the break of January-February there will be an intermediate test. In case this has a positive grade, the final written part of the exam will concern only the remaining part of the content of the course. The final exam aims to verify the skills of: connect and express in mathematical language the topics of the course, develop mathematical models to understand and solve applied problems.
Course program
Real numbers. Order and algebraic properties of real numbers. Infimum and supremum of sets of real numbers; the continuity axiom. Mathematical language and syntax. The terminology of set theory. Basic elements of logic. Functions and their graphs. Differential calculus in one real variable.Optimization problems. The Riemann integral and the Fundamental Theorem of Calculus. Convex functions. The Taylor formula. Asymptotic expansions. ODE. Sequences and series of real numbers.