68356 - Laboratory In Mathematics

Course Unit Page

Academic Year 2018/2019

Learning outcomes

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.

Course contents

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

Readings/Bibliography

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.

Teaching methods

Lectures.

Assessment methods

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

Links to further information

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

Office hours

See the website of Luca Ferrari