# ANALYSIS FROM AN ADVANCED STANDPOINT

## Learning outcomes of the course unit

Knowledge and skill of learning

At the end of the learning activity the student should acquired knowledge and skills related to the essentials elements of the Mathematical Analisys through the examination of some selected results.

The aim of this course is to provide students with essentials tools in Euclidean Geometry in the plane and in the space; students are requested also to apply their knowledge and understanding to problems concerning the spatial structure of real environment, graphical and architectonic structures.

Ability to apply knowledge and understanding

Through the exercises done in the classroom, the student learns how to apply the theoretical knowledge acquired to solve concrete problems related to the topics discussed in the course.

Autonomy of judgement.

The student must be able to value the consistency and rightness of the results obtained by him or others.

Communication skills.

The student should be able to communicate, in a clear and accurate way, mathematical contents related to the program, even outside of a purely applicative context. Classroom lessons and the dialogue with the teacher will improve the students's scientific vocabulary.

Learning skill.

The student after completing the course will be able to independently develop mathematical analysis topics and to arrange different sources to get an effective synthesis.

## Course contents

Complex numbers and the Algebra’s foundamental theorem.

The Fourier series with some classical examples.

The Stone-Weierstrass’s theorem.First elements of the calculus of Variations with some classical examples.

## Recommended readings

Notes provided by the professor

## Teaching methods

The course includes 4 hours of frontal teaching per week. During frontal lessons, in traditional mode, the

Topics will be formally and rigorously presented. These topics will be accompanied by significant examples and appropriate exercises.

## Assessment methods and criteria

Learning is verified through a written work in which the student develops a topic agreed with the teacher (which may be different from the ones discussed in the course), followed by a seminar in which the student exposes the agreed topic.

The exam is passed when the written work explains correctly the agreed topic and the student exposes it with language skills and master it in all its aspects.