Sumif using date range

I want to take sum of values in one column depending on dates in another column. Can anyone please help me do it.
In the attached sheet I have dates in column A and values in column B.
In cell E3, I want the sum of all values in column that fall in month of Jan08.
Similatly in cell E4 i want sum of values for month of Feb08 and so on.
Thanks,

Taher

=SUMPRODUCT(($A$3:$A$31>=D3)*($A$3:$A$31<DATE(YEAR(D3),MONTH(D3)+1,1))*($B$3:$B$31))

Does that help?

Regards

Dav

Both the formulas worked great!
Thanks a lot.