Rosh Codesh (Hebrew רֹאשׁ קֹדֶש), the "Head of the New (Moon)" ="Head of the Month," is the term for the first day of the month in Jewish Talmudic Calendar. It is the day after the observation of the New Moon at the time of sunset, which in Israel is 18:00 Jerusalem time (16:00 Universal Time).
The time of the New Moons can be calculated today accurately to 10000 years before or after now. The further it is from today, the bigger is the Delta T, the uncertainty in converting Dynamical Time to Universal Time.
While most astronomical programs used the Julian Calendar, it is better to sense the season by converting to Gregorian Calendar, since the Equinoxes and Solstices are more fixed in the latter. A convenient program to find the Gregorian dates as well as the week days is CalMaster2000.
While this article is about the astronomically determined Rosh Codesh, Jewish religious rules often allows postponements (Dehioth) of the "head of the month."  There is a similar article on the same issue with a different pronunciation Rosh Chodesh, written more from Jewish religious aspect.
- A. O. Scheffler and P. P. Scheffler, Calmaster2000: Dates, Holidays, Astronomical Events (Pittsburgh, PA: Zephyr Services).
- Arthur Spier, The Comprehensive Hebrew Calendar: Its Structure, History, and One Hundred Years of Corresponding Dates, 5660-5760, 1900-2000 (New York: Behrman House, Inc., Publishers, 1952)