- Docente: Luca Ferrari
- Language: English
- Teaching Mode: Traditional lectures
- Campus: Bologna
- Corso: Second cycle degree programme (LM) in Quantitative Finance (cod. 8854)
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