First year calculus and linear algebra
Fundamentals of measure theory, integration, L^p spaces. Hilbert spaces and orthonormal bases. Fourier series. Distributions. Fourier transform and applications. Jordan form and matrix exponential. Introduction to ODEs. Fundamentals of probability theory.
This course couples a rich (altough elementary) study of the theoretical elements of the program, with the applications of aforementioned theories to problems, mostly coming from effective experimental models.
Gerald Teschl , Ordinary Differential Equations and Dynamical Systems
AMS graduate studies in math 140 ; versione 27 Giugno 2012