27213 - Mathematical Analysis 2

Learning outcomes

At the end of the course the student is familiar with the fundamental notions of the differential and integral calculus for functions of several variables and with related arguments (differential equations, linear integrals, etc). Moreover the student is able to use classical instruments from Mathematical Analysis in several different areas.

Course contents

The Fourier transform. Notes on metric spaces and R^n. Differential calculus for functions of several variables. Differentiable manifolds in R^n, constrained extrema. Differential equations and systems of differential equations. Curves in R^n, line integrals, vector fields. Guass, Green and Stoke's theorems. Multiple integrals in R^n. Sketches to L^1 and L^2 spaces. During the course we will solve several exercices, with particular regard to questions related to astrophysics.

Readings/Bibliography

The teacher will make available on the platform Virtuale, as a pdf file, the notes of Prof Venni, to which the course is largely inspired. These notes are sufficient for the preparation of the exam.

Additional suggestions for the theory:

- M. Bertsch - R. Dal Passo - L. Giacomelli, Analisi Matematica, McGraw-Hill (this book contains both Analysis 1 and 2, and is very well organised).

- C.D. Pagani - S. Salsa, Analisi Matematica 2, Masson, Milano

Concerning the exercises, the teacher will make available on Virtuale different tests of the past years, with the solutions or traces of the solutions.

If desired, students can also practice the following books:

- M. Bramanti- Esercitazioni di Analisi Matematica 2, Esculapio.

- Salsa - Squellati Esercizi di Analisi matematica 2, Zanichelli

Teaching methods

Lectures given by the Teacher.

All the work done in class is immediately made available on the platform Virtuale. It is strongly recommended to sign in on the Virtuale platform.

Assessment methods

Written test followed (if appropriate) by oral test. The written part last 3 hours (in person or online).

The written test in passed with a mark not less than 16/30.

The oral test is intended to verify the knowledge of the arguments explained in class. The student is supposed to know all the definitions and also the proofs of some major theorem.

The final mark is based on the results obtained in both the written and the oral tests.

Teaching tools

All the lectures given by the teacher are made available online on the platform Virtuale.

Office hours

See the website of Maria Carla Tesi