16953 - Mathematics 1

Learning outcomes

At the end of the course the student will know the basic notions of differential and integral calculus for functions of one real variable. In particular the student can: apply differential calculus for functions of one real variable; graph functions of one real variable; use trigonometric, polynomial, exponential and logarithmic functions.

Course contents

Basic functions: polynomials, exponentials, logarithms, trigonometric functions and their inverses. Limits and continuity. Derivatives and their applications. Fundamental theorems of differential calculus: of Rolle, Lagrange, De L'Hospital, Taylor. Maxima, minima and graph of a function. Primitives. Integration by substitution and by parts. Definite integrals and computation of areas.

Readings/Bibliography

- G. Zwirner "Istituzioni di matematiche. Parte I", CEDAM

- G. Zwirner "Esercizi di Analisi Matematica. Parte I", CEDAM

Teaching methods

Matematics 1 is a first semester course and represents the first part of the integrated  course Matematica (12 ects). The second part, Matematics 2, is held by Prof. André Martinez in the second semester. Each part counts for 6 ects. The part Matematics 1 consists of classroom lectures where, first of all, the theoretical aspects of each topic are illustrated. More precisely, after introducing the basic elements, then the main theorems and results of differential and integral calculus for functions of one real variable are stated and, in some cases, proved. Afterwards, several lectures are devoted to the applications of the notions and techniques previously introduced, and to solving exercises and problems.

Assessment methods

For the part Matematics 1 the assessment method consists in a final written test of 3 hours (use of books, lecture notes, electronic devices not allowed). The test is structured in two parts: the first part consists of 4 exercises to be solved. The second part consists of two open-ended questions regarding the theoretical aspects of the discipline.
In order to pass the test students must pass both parts. The score is out of thirties and takes into account the evaluations of both parts.

The final score relative to the whole integrated course Matematica is the arithmetic mean of the scores obtained in the two modules Matematics 1 and Matematics 2.

Office hours

See the website of Emanuela Caliceti