July 24, 1984

The Federal Deposit Insurance Corporation is planning to make a $4.5 billion investment in the Continental Illinois National Bank and Trust Company to keep the giant Chicago bank from failing, sources in the banking industry said yesterday. The plan, emerging in advance of the official announcement, which is expected today or tomorrow, was in line with industry expectations and closely followed a proposal made weeks ago by the bank's own investment banker, Goldman, Sachs & Company. It appeared to reflect the F.D.I.C.'s conclusion that the cheapest way to maintain an independent Continental was for the Federal agency to become the bank's financial backbone. Some Aspects of the Plan Under the F.D.I.C. plan, Continental's shareholders would immediately lose about $1 billion, or half the equity they have in the company, and they would be liable for any future losses that might be incurred by the Federal agency. Ultimately, they could be wiped out if more loans than expected prove uncollectable.

ONE reason many new schoolteachers quickly leave the profession, according to experts, is that they feel overwhelmingly isolated, receiving only the most minimal help as they struggle to cope with the rigor and unpredictability of the classroom. Confounded by an inability to get each student to understand every lesson, angered by youths who are disruptive and stymied by the difficulty of organizing the school day, novice teachers often despair and quit within a few weeks after starting. Now, in an effort to deal with this problem, the New York City Board of Education is preparing a cadre of recently retired teachers to act as mentors who will offer support to at least a small number of new teachers. The pilot program is seen as a possible model for handling a situation that plagues school districts around the country.

The nation's economy grew at a surprisingly strong 7.5 percent annual rate in the second quarter, the Commerce Department announced today, and inflation eased when it might have been expected to increase. Inflation for the entire economy fell to a 3.2 percent annual rate in the second quarter from 4.4 percent in the first quarter, the department reported. ''I don't know how you can write a script for a better recovery than we're seeing right now,'' said Commerce Secretary Malcolm Baldrige, who led the Administration's exultation about the continued good economic news. Democrats have acknowledged that the economy's strong performance was a big advantage for President Reagan's re-election bid and that his Democratic challenger, Walter F. Mondale, has yet to discover a potent economic theme for the campaign.

For legions of law school graduates, Harcourt Brace Jovanovich Inc. provided essential help at a critical moment. Faced with state bar examinations that had to be passed before they could become licensed attorneys, they turned to the company's special bar exam cram courses. But the company, many felt, tried to keep too much of the booming business in bar exam preparation courses and a number of lawyers did what lawyers often do: They filed suit. Harcourt Brace recently settled the seven-year-old antitrust case and this month began notifying the plaintiffs, more than 150,000 lawyers in 23 states who took the company's bar review course between 1973 and February 1984. The plaintiffs will share nearly $2 million in cash and receive discounts on the company's books and professional courses.

THE first symptom of heart disease is sometimes sudden death. Never was that fact made clearer than in the ironic death last week of James Fixx, whose best-selling book ''The Complete Book of Running'' led tens of thousands to take up jogging and made him a guru of the running world. Mr. Fixx, whose transition from a heavy young man who smoked two packs of cigarettes a day into a trimmer, middle-aged nonsmoking athlete seemed to insure a healthy life, died at the age of 52 while jogging in Vermont. Friends described him as being in fine physical condition and said he had not complained of any symptoms while running 10 miles a day and pursuing other vigorous physical activity. He had trounced his sister, Kitty Fixx Bower, in a tennis match on Cape Cod the day before his death. His former wife, Alice Kasman Fixx, said, ''He never had any warning.''