September 15, 1984

P. W. Botha was sworn into office today as South Africa's first President under a new Constitution that gives him potentially authoritarian powers. As he was inaugurated at a ceremony in Cape Town, the police fired tear gas and rubber bullets at protesters outside the city and in Soweto, the black township outside Johannesburg. In Durban, six prominent political fugitives remained in the British Consulate to press demands for the annulment of Government orders for their detention without trial. There was a perception here that the violence and the Government's continuing confrontation with opponents of the Constitution were undermining Mr. Botha's new authority as well as the visions of the Afrikaner role in Africa that were evoked at the inauguration.

Tentative agreement has been reached for two debates in October between President Reagan and his Democratic challenger, Walter F. Mondale, officials in both camps said today. They said there would also be a debate between Vice President Bush and Geraldine A. Ferraro, his Democratic rival. An Administration official said that no final agreement on details of the televised confrontations was likely until early next week, but that the Presidential debates were likely to be two weeks apart, probably Oct. 7 and 21, with the Vice-Presidential debate in between, possibly Oct. 11. Series of Private Talks Officials said the first debate would probably be held in Louisville, Ky., and the second in Kansas City, Mo., with Philadelphia a possible site for the Vice-Presidential match. But they said those plans could change.

Mario Cuomo's lecture at Notre Dame masterly stated a thoughtful politician's analysis of how his private religion guides his public life. He can be devout without imposing religious beliefs on others - not only can but must. Roman Catholics especially know from their history that ''to assure our freedom, we must allow others the same freedom.'' To employ the law to force one's religious conviction on others runs the risk that ''they might someday force theirs on us.''

The Federal Reserve announced today that the nation's industrial production rose only two-tenths of 1 percent in August. Economists said the report was the clearest evidence to date that the economy's strongest performance in more than 40 years had abated and had settled into the slowdown long sought by the Reagan Administration. Economic slowdowns, the history of the business cycle shows, often portend recessions, but few analysts see anything so ominous for the balance of this year or next. ''Recession? No,'' said Francis H. Schott, economist at the Equitable Life Assurance Society of the United States. ''I'm just completely convinced that the expansion has quite a way to go.''

After a blunt late-night meeting Wednesday in a motel suite in Tupelo, Miss., at which Walter F. Mondale voiced concern about his troubled campaign, the Democratic Presidential candidate has decided to change his tactics and shake up his staff. In the tactical changes, Mondale aides say, the candidate decided to drop most ''visual'' events, such as shaking hands outside factory gates before television cameras, and focus instead on rallies and speeches. ''Mondale made it clear that at every event he wants a forum for substance,'' said James A. Johnson, the chairman of the campaign. ''He wants to do events, meetings, where he has a real chance to make his case. He wants to be as substantive as possible, to appeal to voters in a way that's as compelling as possible.''