I advise you to not to stay illegal after expiration of your visa, and check the prompt visa options for you by the Internal Affairs ministry - or the Police Administration -Emniyet Müdürlüğü- of your city. 2 months sounds not a big deal, however the visa and residence regulations of Turkey are being modified and, for some cases there is prosecution charge, which may cause trouble to you.... I advise to find the most convenient way, such as an extension letter of your school or touristic reasons....