It started out as a kind of dignified Oval Office campaign that kept President Reagan above the partisan fray. Now there is a visible change. With Democratic contender Walter Mondale shaving the President's leads in the polls, anxious Reagan strategists have gone on the attack and altered the Reagan style, making for a more rough-and-tumble campaign. Political experts note that:
* On the hustings the President has become a slugger, pointedly hitting at Mondale by name for the first time instead of ignoring him to show how desperate Mr. Mondale is.
* Mr. Reagan has not distanced himself from disparaging comments made by George Bush and his wife about Geraldine Ferraro, reflecting the feistier line of attack.
* On the campaign trail, Reagan is conspicuously showing himself to be fit and vigorous in an effort to counter any doubts about his age.
From the outset Reagan-Bush campaign planners expected Reagan's lead to narrow by the time of the election, but they did not count on such a marked setback as a result of the first presidential debate. The tightening has come sooner than anticipated.
According to the latest Harris Survey (a Democratic poll), Mondale trails Reagan by 53 to 44 percent - only 9 points - nationally. This compares with a 54 -to-42-percent lead before the debate.
Meantime, the Des Moines Sunday Register reports that the Democratic challenger, who was behind 58 to 35 percent in Iowa in September, now trails by only 51 to 43 percent.
Reagan campaign officials say their own polls show the President ahead nationwide by 16 points. But they do not deny that they are under pressure for a sharper, more intensified campaign and that the second presidential debate will be extremely important.
''We see ourselves in a competitive race,'' says John Buckley, deputy spokesman of the Reagan-Bush reelection committee. ''We anticipated it would close up. There is a margin of comfort at this point, but we will have to work as hard as we can in the field and be as hard-hitting as we can in the paid media and in getting across the presidential message.''
Jubilant Democratic strategists, for their part, suggest that the Reagan reelection effort is coming unstuck. Mondale campaign chairman Jim Johnson said this week that ''they have been living in a cocoon of good news for so long that they were not ready for it'' and that a ''frantic quality'' now marks the Republican campaign.
If that is normal campaign hyperbole, it is nonetheless true that the Reagan campaign has shifted its strategy. Before the debate the campaign was laying plans to go all out for the House and Senate races, but instead the campaign is continuing to focus on those states which the President himself must win.
Reagan is likely, for instance, to make a second trip to California, where Mondale arrived Tuesday, hoping to capitalize on his improved ratings enough to capture the state's 47 electoral votes on Nov. 6. Last August, Reagan's campaign manager had said the President would travel there only if he were slipping.
Although experts still see Reagan winning the election (a Los Angeles Times poll published Tuesday indicated no shift in voter preferences, despite an improved public image of Mondale), they note that a large share of his support comes from Democrats and independents without deep ties to him. So there is room for erosion.
''Earlier polls showing that Gary Hart might win over Reagan tell us that there is not an unshakable majority for Reagan,'' says political scientist Norman Ornstein of the American Enterprise Institute. ''So the President is getting on the offensive, throwing darts at Mondale, and showing that he is aggressive.''
In Georgia this week the President accused Mondale of playing ''Russian roulette'' with the economy and of being ''confused'' by Soviet behavior. ''So much baffles him,'' said Reagan. 'He promises us Camelot, but he'd give us a Reign of Error.''
Reagan campaign officials do not deny that the campaign had a bad week after the first presidential debate, when the White House issued a medical report on the President's health and Sen. Paul Laxalt (R) of Nevada lambasted the President's White House aides for mishandling his preparation for the debate.
But officials say that after a bad week following the first presidential debate, the campaign is back in stride, especially with Vice-President Bush's ''decisive victory'' in the face-off with Ms. Ferraro and the President's recent campaign trips, including the successful one-day train tour through western Ohio.