What was going on when I was born?

International Cocaine traffickers in Peru killed at least 17 people employed by a United States-financed program to destroy coca crops, the Peruvian police said. All of the slain people were identified as Peruvian employees of the Coca Reduction Organization, which is part of a $30 million program the United States is financing along the Huallaga River where most of Peru's illegal coca is grown. The slayings took place at a jungle campsite. (Page A1, Column 1.) Democracy stirred for the first time in KwaNdebele, South Africa's second smallest tribal ''homeland'' for black people, which is near Pretoria. Last week there was voting for the 16 elected places in the 72-member Legislative Assembly, the first elections ever. No votes were counted at some polling places. (A1:2.)

Past the room where the city's biggest collection of Tiffany lamps glows softly in the dimness, past the dramatic Hudson River School landscapes, the crumbling manuscripts about women in American politics, people will dance tonight at the New-York Historical Society. Music will waft by the 19th-century firemen's parade with its bouquets unfolding from upturned trumpets, the coach that may have carried George Washington to his first inauguration, the Rembrandt Peale painting of a skeptical Thomas Jefferson. A piano will tinkle New York songs in the first-floor auditorium in the society's museum on Central Park West as Nancy Donner shows slides and runs a quiz on trivia from the city's rich history. Tomorrow, the society will be 180 years old.

MONDAY, NOVEMBER 19, 1984 The Economy A proposal is nearing completion that would raise taxes for some businesses by modifying accelerated depreciation rules and reduce taxes for many other companies by lowering rates over all, according to Administration officials. However, the Treasury Department bill, which focuses on tax simplification, would have a difficult time on Capitol Hill, leading tax specialists say. (Page A1.)

Not long after Phil Simms found Lionel Manuel for the 11-yard touchdown that turned out to be the difference in the Giants' 16-10 victory over the St. Louis Cardinals yesterday, Bob Sheppard's voice was heard over the public-address system. ''Here are scores of other games,'' he announced. ''In the fourth period, Philadelphia 16, Washington 10. And in the third period, Buffalo 14, Dallas . . . (a long pause) . . . 3.''

Time was when LaVell Edwards did not have to endure this. He could put on his favorite windbreaker, hop into his Pontiac and drive down to the University Mall with his wife, Patti, and quietly enjoy an ice cream cone. Or a soda. Or he could walk round this quiet city, which is a short drive from where he was born in Orem, one of 14 children of farming parents, and raised as a devout member of the Church of Jesus Christ of Latter-day Saints. But no more. Edwards is the football coach at Brigham Young University. And for the first time in the school's history, the Cougars are in the hunt for the final No. 1 ranking in football. When the news-agency polls are released this week, the Cougars, the nation's only unbeaten major college with an 11-0 record, are likely to be No. 1 because top- ranked Nebraska and No. 2 South Carolina both lost Saturday. No wonder Edwards has become a celebrity. People who have known him for years gawk and point as he ambles by. And hoardes of pupils ask for autographs when he attends local high school games.

The 14-minute videotape sales pitch makes the mart sound irresistible. Somewhere in the yawning exhibit space, a visiting doctor or hospital official can find every imaginable health care product. A computer gives directions. If the doctor wishes to look at cough medicine, the locations of the relevant exhibits will come spewing out. There will be plenty of space-age nurturing. If the office calls, a visitor will be alerted by the blinking light of the electronic chip on his identification badge. To return the call, picturephones will be spaced about the mart. If a doctor needs to study X-rays from the office, there will be an accommodating computer back in the hotel room. Need to unwind? There will be golf, tennis and sailing. Welcome to Ecumed, the huge merchandise mart for health care products and the $2 billion vision of Tishman Speyer Properties of New York and the Crown family of Chicago. If all goes well, ground will be broken for the mart and convention center in January on 293 acres near Fort Lauderdale, Fla. The complex is slated to open about July 1988, and leases are already being mailed out for the initial tenants.

First off, the weatherman promised lots of heavy gray clouds, freezing rain and snow, with falling temperatures thrown in for good measure. Second, the team is bad, awful, horrendous, hadn't won a game all year. No matter. Jim Ryan swears he would come to see New York's last professional football team, the Buffalo Bills, even if it won a game now and then, even if it was balmy at game time.

Under capricious skies that brought rain and light by turn to places of little hope, the officials and the policeman stood before the galvanized iron hut that represented a polling booth and said, well, yes, the turnout had been sluggish. The officials numbered 7 or 8; the voters this day numbered 26, they said, from an area of shacks and barren land that is home to 5,000 people. ''Maybe it will pick up,'' one of them ventured. The others mused on this frail oracle with expressions that seemed to say: ''And maybe not.'' First Vote In Area And thus did democracy stir, for the first time, this week in KwaNdebele, South Africa's second smallest, and most improbable tribal ''homeland,'' a repository for black people wanted in white South Africa only for their labor.

The American public, its level of confidence in government rebounding after more than a decade of doubts, expects President Reagan to avoid an economic recession in his second term and to make a real effort to negotiate an arms control treaty, a New York Times/CBS News Poll shows. But at the same time, the public expects him to break his most insistent campaign promise and ask Congress to vote an increase in taxes. Fifty-seven percent of the public and 40 percent of his own voters expect him to ask for higher taxes. The poll detailed the depth and solidity of the national swing toward the Republican Party, showing Americans now about equally divided between those who identify with them and those who identify with the Democrats. 'Major Realignment' Seen This development prompted a leading Republican poll taker, Robert M. Teeter, to say, ''We are in the midst of a major political realignment in this country.'' But he said that how that shift played out would depend on how well Republicans handled themselves after Mr. Reagan left the White House, especially how they handled their own potential cleavages over social issues.

A 28-year-old mathematician at A.T.&T. Bell Laboratories has made a startling theoretical breakthrough in the solving of systems of equations that often grow too vast and complex for the most powerful computers. The discovery, which is to be formally published next month, is already circulating rapidly through the mathematical world. It has also set off a deluge of inquiries from brokerage houses, oil companies and airlines, industries with millions of dollars at stake in problems known as linear programming. These problems are fiendishly complicated systems, often with thousands of variables. They arise in a variety of commercial and government applications, ranging from allocating time on a communications satellite to routing millions of telephone calls over long distances. Linear programming is particularly useful whenever a limited, expensive resource must be spread most efficiently among competing users. And investment companies use the approach in creating portfolios with the best mix of stocks and bonds.

A band of cocaine traffickers burst into a jungle campsite and opened fire with automatic weapons, killing at least 17 people employed by a United States-financed program to destroy coca crops, the police said today. All those killed in the attack, which took place early Saturday, were identified as Peruvian employees of the Coca Reduction Organization. The group is taking part in a $30 million program that the United States is financing to cut the production of coca along the Huallaga River, where most of the illegal coca in Peru is grown.

After years of urging investors to take a stake in American business, a great many Wall Street firms have decided to follow their own advice. Increasingly, investment bankers in the United States are acting like their merchant banking counterparts abroad. They are investing their firms' capital in the leveraged buyouts of established companies. They are funnelling seed money into venture capital fledglings. And they are becoming real estate tycoons in their own right. Indeed, large firms such as Merrill Lynch & Company, the First Boston Corporation, Morgan Stanley & Company and Drexel Burnham Lambert Inc., as well as a fast-growing number of smaller outfits, are going well beyond the traditional risk-taking of market making and underwriting, where, if firms buy a company's shares, they do not hold them long.