A table of federal spending estimates in the March 11 Washington Post incorrectly identified the year for which the estimates of former president Carter were made. The column of figures showing spending by function should have been headed Carter 1982.

President Reagan sent his final fiscal 1982 budget proposals to Congress yesterday with a reminder of "the mandate for change" that elected him and a declaration that only "politics-as-usual" stands in the way of reduced inflation and a return to prosperity.

Reagan's additional budget revisions bring to $46 billion the cuts in nondefense spending proposed for fiscal 1982 by slicing into almost 300 federal spending programs and reducing government loans and loan guarantees by $21 billion.

The net spending reduction is $1.2 billilon, however, because the administration is adding $3.6 billion to the defense budget and $1. 2 billion to other programs.

Together with his proposed 30 percent cut in income tax rates over three years and accelerated depreciation write-offs for business, the spending cuts are central to Reagan's program for balancing the budget in 1984. For 1982, the budget is estimated at $695.3 billion and the deficit at $45 billion.

Most of the $13.8 billion new cuts detailed yesterday had leaked out in recent days. They strike particularly hard at regulatory agencies. The Occupational Safety and Health Administration, for example, would lose 9,000 of its 70,000 inspectors; the Federal Trade Commission, Consumer Product Safety Commission and Equal Employment Opportunity Commission also were on the cuts list.

Reagan also proposed a change under which most welfare recipients would have to work to keep their benefits, recommended further cuts in housing assistance for the poor and chopped nutrition programs below the levels set in the first round of proposed cuts on Feb. 18.

Under the "workfare" proposal, a mother with a child under three or with children three to six and no available day care, would not have to work. But other welfare mothers would.

The budget also would eliminate a further benefit under Social Security: the $255 burial payment, which will no longer be given if there are no survivors. This would save $150 million in 1982.

But there were also some winners besides the Defense Department -- programs that managed to hold their own or even grow fatter in these lean times.

Owners of private planes warded off the 20 percent tax on aviation fuel that Reagan advisers had sought to impose. Instead, the tax seems likely to be raised only a penny a gallon, to 8 cents.

Charles Spence of the Aircraft Owners and Pilots Association said, "We're delighted that they realized they had been misinformed." Airline passengers also got a break; a proposed 9 percent airline ticket tax was reduced to 6.5 percent.

In a victory for Hispanic groups, the bilingual education program was kept separate from a proposed block grant for education.

The Clinch River breeder, which the Carter administration had sought to halt, was allocated $222 million in 1982, as part of the Reagan administration's commit >TO> funds included for design studies for a large commercial breeder reactor. Most non-nuclear energy programs were cut sharply. The strategic petroleum reserve escaped, however.

Another winner was a surprise: the tiny U.S. Travel Service, which spends $8 million to encourage foreigners to take their vacations in the United States. The Carter Administration planned to reduce its spending to $3 million as a step toward wiping it out.

Earlier administrations have argued that the service duplicates work done by the private tourism industry. That would seem an argument in line with Reagan's philosophy, but the travel service has bounced back with a budget nearly $4 million fatter than Carter intended.

The maritime industry lost a little, however, as shipbuilding subsidies were shaved slightly. The administration also proposed a new system of block grants for Indians, and recommend cuts in Small Business Administration loan programs.

The administration issued its final revisions with a plea that they be approved without exception.

"One exception logically leads to many other exceptions and to erosion of the plan and of its long-term benefits for the economy and for all Americans," the budget document said.

Almost every proposed budget cut requires approval of Congress. If the proposals are approved, federal spending would grow by 6.1 percent in 1982, almost half the growth rate forecast in the last Carter budget.

But the short- and long-term difficulties of trying to control the federal budget are evident in the budget revisions Reagan made public yesterday.

Since Feb. 18, the budget cutters led by Office of Management and Budget Director David A. Stockman had to find close to $7 billion to cut in order to make up for an underestimate of federal spending discovered only after the first set of proposals was made public.

The long-term uncertainties are indicated by the widening of the gap still to be closed to balance the budget in 1984. On Feb. 18, Reagan said that further spending reductions totaling $21.2 billion in 1983 and $30.7 billion in 1984 would have to be found. Now, because of reestimates, $29.8 billion will be needed in 1983 and $44.2 billion, almost as much as the administration found to cut this year, will be needed in 1984.

The budget document gives only a vague outline of where the Reagan administration intends to look for these future cuts. The outline was "carefully crafted so that no one could identify precisely any of the programs likely to come under the knife," one OMB official said.

Stockman defended the lack of precision by saying that the administration had identified a large number of cuts in only six weeks in office. "I would suggest that we can achieve the rest in a relatively brief period of time," Stockman said in briefing reporters on the budget.

Further cuts, according to the budget program, will be in such areas as development of fundamental and comprehensive health care financing reforms, more efficient delivery of veterans health services, reevaluation of housing subsidies, reconsideration of federal annuities so as not unduly to reward those who work for the government only a few years at high salary levels, examination of federal stock-piles and imposition of further user charges.

All of the Reagan effort to balance the budget hangs on the economic assumptions made by the OMB, which foresee inflation being reduced quickly. Interest rates are also assumed to be falling sharply during 1982, resulting in a saving to the government of $7.4 billion over the more modest savings from interest rate declines predicted by the Carter administration.

One example of the unpredictable way in which assumptions can change is the administration's calculation of corporate profits subject to taxes in the future.

Corporate profits are seen now as several billion dollars a year larger than they were expected to be in the assumptions of Feb. 18. In 1984, the year the budget will be balanced under the Reagan program, corporate profits have grown from $363 billion to $367 billion.

When Reagan told Stockman and other budget planners that he would not approve a proposal for a 2-cent-a-gallon gasoline tax that would have raised $2 billion in revenue in 1984, according to well-informed sources, OMB officials asked the Treasury Department to alter its revenue forecasts to make up for the absence of the gasoline tax.

Treasury officials refused. OMB officials then made up the $2 billion difference by raising the estimates of corporate profits, which will be taxed at a 46 percent rate.

Other new cuts would come in science. Television programs like NOVA and 3-2-1 Contact would be damaged or killed as a result of cuts in the National Science Foundation budget. Programs to train women and minorities would be wiped out as would almost all social science and behavioral science research such as the famous Minnesota "twins" study that has shown the importance of genes as opposed to environment.