75376 - CALCULUS

Conoscenze e abilità da conseguire

At the end of the course the student has comprehensive, in-depth coverage of the topics required in a one-term course in advanced calculus. The course is thought for students who have had a course in introductory algebra and undergraduate calculus. As for calculus, the student acquires a solid foundation in several variables calculus, vector analysis, linear algebra, systems of differential equations, vector fields, extremum problems. Furthermore, learns how advanced calculus can model and solve authentic real-world problems: thus tapping heavily into applied mathematics.

Contenuti

Preliminaries

Topologies and Metric Spaces

Measuring Sets

The Lebesgue Integral

Measurable Functions

Spaces of Continuos Functions

Lebesgue Spaces

Absolute Continuity

Differential Equations

 

Testi/Bibliografia

Recommended texts:

[1] A Probability Path

Sidney Resnick

 

https://www.amazon.it/Probability-Path-Sidney-I-Resnick/dp/0817684085

 

 

[2]

Measures, Integrals and Martingales

Rene' Schilling

 

https://www.amazon.it/gp/product/1316620247/ref=ox_sc_saved_title_4?smid=A11IL2PNWYJU7H&psc=1

Metodi didattici

Traditional black-board based classes and every lecture will be made available through online platforms.

Modalità di verifica e valutazione dell'apprendimento

Written ( and optional oral ) exams. The written exam is articulated in a series of 6 exercises each with a maximum grade of 5 points. Every exercise attains to elements of the syllabus and the relevant Bibliography covered during the course lectures or otherwise hinted at during classes. The (optional ) oral exam may cover the same range of topics as well, while keeping into accont the candidate's perfomance in the previously held written test.

Strumenti a supporto della didattica

Supplementary notes and material may be suggested and handed out during the course.

Orario di ricevimento

Consulta il sito web di Enrico Bernardi