Università Roma Tre

Under the general title of this Course, we consider both, asymptotic and
numerical methods mostly to handle ordinary differential equations and systems,
and possibly some partial differential equations, and applications. Among the
asymptotic methods, the so-called ``singular perturbations'' are addressed.
These two subjects, which represent basic techniques of Applied Mathematics,
are usually taught separately. In this course we will use both, at the same
time, in the same problems.

Asymptotic Methods:

Introduction to Asymptotic Analysis. Asymptotic series. Regular and singular
perturbations of ordinary differential equations and systems.

Numerical Methods:

Numerical solution, using several algorithms, of ordinary differential
equations and systems. This will be mostly done in the computing laboratory.

Robert E. O'malley,
Singular Perturbation Methods for Ordinary Differential Equations,
Springer-Verlag, Applied Mathematical Sciences, 89, New York, 1991.

John K. Hunter,
Asymptotic Analysis and Singular Perturbation Theory,
Lecture Notes, https://www.math.ucdavis.edu/~hunter/notes/asy.pdf,
2004