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

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

For the theory:

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

E. Lanconelli, Lezioni di Analisi Matematica 2, Pitagora, Bologna.

M. Bertsch - R. Dal Passo - L. Giacomelli, Analisi Matematica, McGraw-Hill.

For the exercises:

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 IOL.

Assessment methods

Written test followed (if appropriate) by oral test.

The written test in passed with a mark not less than 15/30.

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 available online on the platform IOL.

Office hours

See the website of Maria Carla Tesi