# 05012 - Mathematical Supplement

## Learning outcomes

At the end of the course the student will know the basic notions of series, power series expansions and reach a sufficient knowledge to solve solve problems regarding linear algebra, integral and differential calculus and applied sciences.

## Course contents

- Complex Numbers, basic properties

- Linear second order ODE, methods of solution

- Series, convergence criteria

- Taylor's expansion of a real functions

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

- M. Bramanti, C. D. Pagani, S. Salsa, "Matematica: calcolo infinitesimale e algebra lineare", 2a ed., Zanichelli, 2004

## Teaching methods

This course takes place in the second semester and represents the third part (3 cfu) of the integrated course Matematica (15 cfu). The first part (Matematica 1, 6 cfu) and the second part (Mathematics 2, 6 cfu) are held respectively in the first and second semester and are held by Prof.ssa Emanuela Caliceti and Prof. André Martinez.

The course consists  of  frontal lectures starting with the theoretical aspects and then constructing examples and applications that clarify the properties and the applications of  mathematical objects. 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 Complementi di Matematica the assessment method consists, in a final written test (together with Matematica 2) of 3 hours and a half(use of books, lecture notes, electronic devices not allowed). The test is structured in two parts: the first part consists of exercises on Matematica 2 to be solved, with a score out of 20's. The second part consists of exercises on Complementi di Matematicato be solved, with a score out of 10's.

In order to pass the test students must obtain a score larger or equal to 16 for the first part, and to 6 for the second part.

The final score relative to the whole integrated course Matematica is the weighted mean (based on the ects) of the scores obtained in the two test of Matematica 1 (6 ects)and the (joint) test of Matematics 2 and Complementi di Matematica (9 ects). To register the score students must sign up through Almaesami and attend oneof the dedicated sessions.

## Teaching tools

The assessment method for this course consists, together with Matematica 2, of a final written test of 3 hours and a half (use of books, lecture notes, electronic devices not allowed). The test is structured in two parts: the first part consists of exercises on Matematica 2 to be solved, with a score out of 20's. The second part consists of exercises on Complementi di Matematici to be solved, with a score out of 10's.

In order to pass the test students must obtain a score larger or equal to 18 out of thirties.

The final score relative to the whole integrated course Matematica is the weighted mean (based on the ects) of the scores obtained in the two test of Matematica 1 (6 ects)and the (joint) test of Matematics 2 and Complementi di Matematica (9 ects). To register the score students must sign up through Almaesami and attend one of the dedicated sessions.

## Office hours

See the website of Emanuele Mingione