The map, in modern terms, includes parts of Jordan and Egypt. When 18th- and 19th-century mapmakers wrote "Palestine" or "Filastin," they were often referring to a geographic region analogous to:
"Syria,"
"Arabia,"
"Mesopotamia,"
"Anatolia,"
rather than a territory with internationally recognized borders.
In fact, the Ottoman Empire formally called the area (which it divided into 3 sections): Kudüs Mutasarrıflığı (Mutasarrifate of Jerusalem), Nablus Sancağı (Nablus District), and Akka Sancağı (Acre District).
If someone in 1800 asked an Ottoman official, "What province am I standing in?", he would likely respond with one of these areas: Kudüs Sancağı, Akka Sancağı, Nablus Sancağı, Şam Eyaleti, or Sayda Eyaleti. Rather than "Filistin Vilayeti" (Province of Palestine), because there generally was no standard Ottoman province officially bearing that name.
You didn't say if you actually got that Ph.D but if you did, was it from the University of Gaza?