Today is graduation day for a small hand of students who diligently took lecture notes and persistently probed professors for the special knowledge they will need when they leave Harvard University.

They had walked through Harvard Yard each day with books and tape recorders, wearing the resolute look of the earnest undergraduate - though they didn't get grades.

"We'll get our report cards from the folks back home," said Carole McClellan of Austin, Tex., one of 18 who attended a five-day intensive course in city government at the John F. Kennedy School of Government.

The 18 are newly elected mayors from all over the coutry. They were participating in a seminar on transition and leadership, featuring nuts-and-bolts advice on municipal management from polictical veterans, academics and professionals.

The crash course counseled on what a mayor needs to know about finance, management, budgeting, labor relations and collective bargaining, how to pick a police chief and how to deal with the press.

Among the professors:

Labor leader Victor Gotbaum, executive director of the municipal employees union of New York City, who told the mayors not to get too friendly wiht labor leaders: "Be friendly but don't be friends; your guard should never be fully down with us and our guard should never be fully down with you."

Lame duck Mayor Moon Landrieu of New Orleans, who advised the rookie mayors not to get frustrated "if you can't do everything you set out to do in one day." He added, "you'll develop a great love affair with your city because if you don't it will be a tremendously burdensome task."

Robert diGrazia, former Boston police commissioner and now police superintendent for Montgomery County, Md., who advised maintaining control over the police chief, making him directly accountable to the mayor with "no buffers in between."

Many of th student mayors sgreed that the course was most valuable in directing them to new sources who might someday help solve a particular municipal problem, and in providing information about federal funding for city projects.

"I came here to brain-pick some of the best minds in the United States," said the mayor-elect of Utica, N.Y., Stephen J. Pawlinga. "And I'll be going home with a piece of information that I can get $300,000 in federal funds from the Department of Labor to work with. I know a lot more about where to go to get back some of that money my people paid out in taxes."

"I have a better feeling for what my true role should be now," said the new mayor of Spokane, Wash., Ron Bair. "I thought before that in my form of city government, the city manager was the boss and I served at his pleasure. I learned that I am the boss and he serves at my pleasure."

The new mayors also agreed the course was beneficial in helping to overcome their apprehensions about taking office, by placing them with others in the same situation.

"Getting elected is like the dog that finally caught the car it was chasing - what do you do with it now?" said James Amato to Lexington, Ky.

"This has been a great opportunity to gain some confidence and see your problems are not necessarily unique."

"The realization tha tyou're alone now and you have to do all those things tou said you were going to do is a humbling experience," said Charles Royer, the new mayor of Seattle. "This seminar really helps. It knocks down your ego from that euphoric high of winning to find out you have a lot to learn."

"There's so much I have to learn, it's frightening," said Isabella Cannon, the 73-year-old mayor-elect of Raleigh, N.C., displaying the efforts of five days of feverish note-taking. "You know the only thing I ever did before this politically was to be a member of Raleigh's library advisory board. There are people here with a lot more political experience than me. But this has been fantastic. It has opened doors to all the things I need to know. I feel a lot easier now."

However, the new mayor New Orleans, Earnest Morial, said the course did not provide enough specific practical information, serving instead as a mayoral primer.

"There was a great presumption that we knew nothing when we came here, he said. "But some of us do know a few things. I mean, some of us have held elected office before."