We will discuss transseries, Ecalle Borel summability, application to generic ODEs, the principle of transasymptotic matching, general singularities of ODEs, existence and uniqueness in PDEs, formation of singularities in PDEs, integrability of ODEs and difference equations and other topics according to the students' interests. I will post course notes as we progress.
I will assign weekly homework, the end of each
week, due at the end of the following week.I will give a
take home final exam at the end of the quarter.