I would start with something like...
Code:
update  courses c
set     c.exp_date = (select  n.exp_date
                      from    new_courses n
                      where   c.user_id    =  n.user_id
                      and     c.course_id  =  n.course_id
                      and     c.start_date =  n.start_date
                      and     c.exp_date   <> n.exp_date)
;