1) Real Numbers; 2) Limits and continuity for one variable functions; 3) Differential Calculus; 4) Integral calculus; 5) Series; 6) Ordinary Differential Equations.
1) "Note ed Esercizi di Calcolo 1" A. Nannicini, L. Verdi, S. Vessella. Pitagora, 2) Bologna Bertsch - Dal Passo - Giacomelli, Analisi Matematica, seconda edizione, McGraw-Hill
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
During the course some tests of verification are provided, the overcoming of which gives the right to support only the theory test. For those who do not pass the tests in itinere, or do not support them, the final test is based on a written test to verify the acquired computational skills, and a proof of knowledge of the theory. Both these test aim 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.