Introduction to Ordinary Differential Equations

COURSE OBJECTIVES
Ordinary Differential Equations (ODEs) are everywhere. When we hear about "mathematical models" for forecasting weather, climate change, stock price or, even more timely, temporal evolution of pandemic outbreak, the underpinning equations are actually ODEs. The main objective of this course is therefore to make acquaintance with ODEs, and will provide a solid mathematical foundation for the successful application of ODEs in several contexts.

COURSE DESCRIPTION
The course will cover basic theory of the analysis ODEs (well-posedness, stability, linear theory) and their numerical solution (numerical schemes, convergence, stability). Several examples and applications will be covered during the course.

LEARNING METHODS
The course is composed by 13 lectures, among which: 6-7 in presence, with live video and Q&A for remote students; 3-4 flipped classroom; 3-4 only remote, with pre-recorded video material and notes. Whiteboard (virtual or real) will be preferred over slides.

EXAMINATION INFORMATION
The final grade is the combination of assignments and final oral exam. Due to restriction amid COVID-19 outbreak there will be _no_ written final. In detail, assignments will contribute for 60% of the final grade (10% per 6 assignments, one every 2 weeks), while oral exam will contribute for 40%.

RECOMMENDED COURSES

• Functional and Numerical Analysis (FOMICS block course)
• Introduction to Partial Differential Equations
• Machine Learning

REFERENCES
Each lecture is accompanied by notes thoroughly covering its content.

Additional material is the following:

• Teschl, Gerald. Ordinary Differential Equations and Dynamical Systems. Graduate Studies in Mathematics Vol. 140, AMS (2012). - Quarteroni, Alfio, Riccardo Sacco, and Fausto Saleri.
• Numerical mathematics. Vol. 37. Springer (2010). - Deuflhard, Peter, and Folkmar Bornemann.
• Scientific computing with ordinary differential equations. Vol. 42. Springer (2012).