Say that your first table will contain the maximum date from the second table, and that there is a one-to-many relationship: field t1id in the second table refers to field id in the first table. Here's the SQL to update all max_date fields in the first table:
UPDATE t1 JOIN ( SELECT t2.t1id, MAX(t2.thedate) maxdate FROM t2 GROUP BY t2.t1id ) AS agg ON t1.id=agg.t1id SET t1.max_date=agg.maxdate
I hope that this proves useful; let me know if it does!
Disclaimer: I won't be help responsible for any loss of data or time you suffer as a result of following my advice!