Just noticed your date is in the correct format. In your DATE_ADD Function, you are missing the comma after the first c.
$SQL = "SELECT *, curdate() AS c,
dayofweek(curdate()) AS d FROM $table_name
WHERE date BETWEEN date_sub(c, INTERVAL (d -1) DAY)
AND date_add(c, INTERVAL (7-c) DAY) ";
--ETA: This code doesn't work because c and d aren't recognized in the functions after 'WHERE'.... I'm working on remembering now...