Give the bases of calculus for functions of one real variable, in such a way that the students are able to solve simple problems in the field. Students should be able to draw and read graphs of functions of one variable, to study functions of one real variable and real sequences, and to compute elementary integrals.
Mathematics taught in high schools
Course contents summary
Real numbers, elementary algebra, equations and inequalities. Functions and their graphs, elementary functions. The principle of induction. Maximum, minimum, supremum and infimum of sets of real numbers. Limits of sequences and of functions of a real variable. Continuity, derivatives, primitives and their properties. Integrals of continuous functions over intervals. Study of the graphs of functions of one real variable.
P. Marcellini, C. Sbordone: Calcolo, Liguori Editore
G. Prodi: Istituzioni di Matematica, Mc-Graw-Hill Italia
A. Nannicini, L. Verdi, S. Vessella: Note ed esercizi svolti di Calcolo 1, Pitagora Editrice
G. De Marco: Analisi Zero, Decibel-Zanichelli
A. Zaccagnini, M.G. Rinaldi: Esercizi per i corsi di Istituzioni di Matematica, Azzali Editore
Lectures and exercises in the classroom
Assessment methods and criteria
The examination consists of a written test followed by an oral one. Students with sufficient marks in the written test are allowed to the oral part. The final mark will be the mean value between the marks of the written and of the oral tests.