ISem23

Dear Participants of ISem 23,

We have just uploaded the fourth lecture, which you can find at the following link

https://www.mat.tuhh.de/veranstaltungen/isem23/_media/lecture_04.pdf

or in the forum.

This lecture is devoted to a first application of the developed concepts. We will provide a solution theory for ordinary differential equations in Hilbert spaces.

We provide an abstract solution theory, which works globally in time and then specialise to particular situations such as the classical Picard–Lindelöf theorem or differential equations additionally depending on the history of the unknown.

In passing, we introduce the concept of causality, which will – in one way or another – accompany us throughout the whole remaining lecture course.

The provided theorems and proofs of this week's lecture might seem to be a bit technical. However, they will always be elementary in the sense that no difficult theory needs to be invoked. We genuinely hope that you can still enjoy the material as it proves to be rather versatile, when it comes to particular applications.

We really appreciate the participation in the forum and value all the comments posted there. We are looking forward to our future discussions.

We have received several solutions to the exercises. This is really great and we encourage to continue sending us solutions to the exercises, as this is also valuable feedback for us as to how well we did in getting our ideas across. Hence, we welcome contributions to the exercises by any team and we particularly ask the team from Delhi to take note of the exercises and to provide `official' solutions for us to upload.

With the best regards,

the virtual lecturers