THUMB through the technicolor promotional brochure on the St. Louis area - prepared for prospective businesses by the Fantus Company - and you'll find each urban asset described in glowing detail. Everything worth bragging about is there. But, like similar brochures of other large industrial cities, any sales pitch for the city's public school system is conspicuously absent. Private and parochial schools net the high marks.
As federal education funds are cut back and the exodus to the suburbs continues, older city school systems are increasingly dependent on a shrinking real estate tax base. Many city schools have few science and advanced-math teachers. Even inner-city valedictorians are finding it harder to get into good universities.
For years desegregating schools has been widely viewed as a partial answer to the problem of quality. But as the white population in city schools has dwindled , traditional strategies have had to be revamped.
Despite the 1954 Supreme Court ruling that racially separate schools are ''inherently unequal,'' there has been a push in recent years, supported by many black parents, to solve the problem by pumping more resources into city schools. The enrichment is often combined with voluntary desegregation measures such as establishment of magnet schools and open-enrollment policies.
Still, 1 of every 3 black students nationwide attends a school that is at least 90 percent black.
Some experts, such as Gary Orfield, a University of Chicago political scientist, say the best overall solution is to merge city and suburban school districts into metropolitan systems. He concedes that suburban resistance is strong. But he notes that countywide systems are common in the South and that courts have ordered such areawide solutions in Wilmington, Del.; Louisville, Ky.; and Indianapolis.
''With education desegregation in the North, we're either going to have to go forward or backward - we can't stand still,'' Professor Orfield says.
''We've either got to do it with cities and suburbs - or operate black, white , and Hispanic school systems separately. (The latter) would lead to a stratification of the whole socialization process. I think that's fatal.''
The St. Louis public schools, which are 80 percent black, are trying an innovative city- and state-financed plan which, if it works, could become something of a national model.
Under a voluntary arrangement - with the threat of a trial acting as a spur - 23 largely white suburban school districts in St. Louis County and the city's public schools agreed last summer to an areawide desegregation program.
''The beauty of it is that the parties worked out the solution instead of the judge - they deserve tremendous credit for their courage,'' says D. Bruce LaPierre, the Washington University law professor appointed a special master by the court to negotiate a settlement.
Under the plan, 15,000 inner-city students would attend suburban schools within the next five years, and several thousand suburbanites would commute to St. Louis schools. City schools would be improved across the board, with funding to achieve lower student-teacher ratios, larger arts staffs, and all-day kindergartens.
''The plan concerns itself less with who sits beside whom than with development of a quality system that would attract a diverse student population, '' St. Louis school superintendent Jerome B. Jones said in an interview. ''We're talking not just about a race issue but a class issue.''
What troubles him most now, he says, is the question of how an increasingly older and poorer urban population can be made to support public schools. He notes that St. Louis voters have turned down 22 bond issues in as many years.
''The kind of constituency we need to support the schools doesn't exist,'' he says. ''Increasingly, urban school districts are going to be forced to turn to the courts to get state bodies or voters to meet their responsibilities.''
''There are negative costs if we don't support and sustain our schools,'' warns Carl Holman, president of the National Urban Coalition. ''The youngsters getting the least education are going to cost society more.''
Aware of the crunch ahead, public school systems are reaching out for broader support. Businesses and foundations have responded with gifts of money, equipment, time, and even lobbying on bond issues.
A meeting held recently in the Academic and Athletic Academy, one of the St. Louis magnet schools, underscores the breadth of the new outreach. Realtors gathered in the school library to hear how the new areawide plan will work. They were clearly hungry for every positive detail.
''Tell us,'' one pleaded, ''how we can dispel the notion that the public schools are not a draw.''
Superintendent Jones acknowledges that such get-togethers are new for educators, who until now have largely kept to themselves.
''I think we recognize that we're all dependent on each other. . . ,'' he says. ''Only when people believe that the streets are safe and the schools are good are they going to come back into the city.''