68356 - LABORATORY IN MATHEMATICS

Scheda insegnamento

Anno Accademico 2018/2019

Conoscenze e abilità da conseguire

At the end of the course the student knows the basics of mathematics: the notion of function and its related concepts (limits, derivative, integration). Furthermore the student learns how to solve basic differential equations.

Programma/Contenuti

Introduction to Real Analysis

Sets and functions

Proofs by induction

Finite and infinite sets

Countable and uncountable sets

Supremum and infimum

Completeness property of R

Density of Q in R

Nested intervals

Sequences and their limits

Bounded and monotone sequences

Subsequences

Neighbourhood of a point

Interior, boundary, cluster and isolated points

Open and closed sets

Compact sets

Continuous functions

Infinite series


Differential equations: an introduction

Separable equations

First-order linear equations

Initial value problems

Testi/Bibliografia

Robert G. Bartle and Donald R. Sherbert, Introduction to Real Analysis, Wiley & Sons.

J. David Logan, A first course in differential equations, Springer.

David C. Lay, Linear algebra and its applications, Addison-Wesley.

Many exercises are available on IOL.

Metodi didattici

Lectures.

Modalità di verifica dell'apprendimento

Final test at the end of the course. The test is optional but strongly recommended.

Link ad altre eventuali informazioni

https://iol.unibo.it/course/view.php?id=22808

Orario di ricevimento

Consulta il sito web di Luca Ferrari