For these questions one can use melody finders.
There are many of them. See: WikiHow
http://www.wikihow.com/Identify-Songs-Using-Melody
So far I could not find the first melody.
The second (start of a) melody I first tried in Themefinder
http://www.themefinder.org/ with 7 results (only classical)
Than I tried the same query in the MelodyCatcher
http://www.melodycatcher.com/ with 10 results. partly classical.
You can play the query on a virtual keyboard or copy (Ctrl-C) and Past (Ctrl-V) the query as A2 G2 F2 E2 D2 C2 C2 in the Notename field.
You can see if the wanted melody is among these results and if not try a longer query.