The first week of a presidency is a time for symbolic communication, in which the new occupant of the White House can send out messages through public gestures without yet having to tackle the heart of the problems confronting the nation.

President Nixon devoted most of his first day in office in 1969 to meetings on Vietnam. President Carter dispensed with a limousine in favor of a tan Lincoln during his first week four years ago and went to the Justice Department to open the building's Pennsylvania Avenue doors, which had been locked since the riots of the early 1970s.

President Reagan got off to a fast start. After a transition-period profile so low it was sometimes invisible, Reagan was never far from the cameras and reporters in his first week as president. In an evident desire to capitalize on his ability to communicate on television, the president and his advisers planned a string of events that kept the networks well stocked.

Reagan promised during the campaign to revive government by the Cabinet, so there was a Cabinet meeting every day, including yesterday.

The economy was the focus of his campaign and leads Reagan's list of problems to solve, so most of each meeting was devoted to the economy.

Some have criticized Reagan for holding the reins of power too loosely and delegating too much to his staff, so during his first White House week Reagan was always at the center, always involved.

Reagan's personality, his advisers believe, is one of the great assets they have to work with. Reagan can sell things that the public might be unwilling to buy from one of the president's representatives. The early whirl of White House activity aimed at presenting the image of a strong president taking personal charge.

In the first five days of Reagan's term, the idea seemed to be that if the White House reporters were kept busy they would relay the impression that the president was busy. Reagan and his aides wanted to capitalize on the goodwill that greets all new presidents rather than let the traditional early weeks of fresh hopes slip by, soured by the impression that Reagan was not enthusiastically embracing his work.

The released hostages took some of the play away, but Reagan's symbolic goals seemed largely achieved at the week's end and the former hostages themselves were a constant reminder that times had changed and that prayers for better times don't always go unanswered.

Some symbols don't change much, however. Carter tried to do away with limousines even though he knew the dollar saving would be small. Reagan has ordered his Cabinet members not to redecorate their offices in an equally symbolic step that won't do much toward balancing the budget.

But while the Regan administration has worked to give the impression of rapid and decisive action through steps that are of marginal impact, like a highly publicized order to get offers of resignation from presidential appointees who can in fact be fired with a telephone call, there also has been a major effort to tackle the "big bucks" questions that will decide the success or failure of Reagan's economic package.

The early Cabinet meetings have amounted to what a White House official described as an "attack from the center" in which the new Cabinet officers, still unfamiliar with the pressures they will face from groups whose vital interests are affected by their departments' actions, are being asked to give their approval to rather firm targets.

In this way, the department is committed before the bureaucracy and the interest groups even know what is happening, the source said.

As they consider what they can cut from the budget, Reagan and his advisers are running into some campaign promises. A considerable sum could be saved by adjusting the cost-of-living allowance for federal employes and retirees once a year instead of twice.Reagan opposed such a change during the campaign, but the potential saving is so attractive that the idea is being given serious consideration.

A less important example is the $100 million that Carter ordered the government to spend by accelerating its purchase of automobiles to help the slumping industry. Reagan supported the accelerated-purchase plan during the campaign, and it appears likely he will not back down, one source said.

In addition to the image of a new president with a crowded schedule that has been projected in his first week, there have been a number of less formal Reagan moments.

As he sat behind his desk in the Oval Office for the first time following the news of the hostages' safe release and the excitement of his inauguration, Reagan said: "It's been a very wonderful day and I guess now I can go back to California, can't I?"

He also told some visitors, "I haven't carried money for years." Since moving into the White House, he also said, he doesn't know where his checkbook is. He won't need to find out. You don't need walking-around money in the White House.