West Germany's famous Ruhr -- the largest single industrial area in the world and the key to prosperity for many German generations -- is now struggling to stay off the welfare rolls.

More than a decade of decline in the region's massive coal-mining operations during the era of cheap oil, and the cooling of steel mill furnaces more recently as Japanese competition increases and global shipbuilding shrinks, have taken a steady toll.

The Ruhr represents a microcosm of the biggest economic and social problems confronting West Germany these days and the success of failure of local, state and federal authorities in combating them represents a high-stakes undertaking with implications for the whole country and for the special character of this region.

Since 1965, about 400,000 residents have left the Ruhr, many of them having lost their jobs in a region that is sort of a Teutonic version of Pittsburgh only much larger.

The Ruhr, astride one of the world's richest coal fields, stretches over some 1,200 square miles in northwestern West Germany, near the Belgian border. It includes a dozen major cities and 5 million people.

The unemployment rate for the region is now 5.7 percent, well above the national average of 3.8 percent. $5In this central Ruhr city, says Mayor Werner Kuhlmann, the population has dropped from 390,000 in 1959 to 315,000 today, and the 7.2 percent unemployment rate is the highest for any German city.

In a country of 60 million people and rather widespread prosperity, the Ruhr, statistically at least, is about the closest thing West Germany has to a depressed area.Yet the region hardly qualifies for that description as it might be applied in the United States or many other heavily industralized nations.

The unemployment figures, although high for West Germany, are low in comparison to many other countries. West Germany's generous social welfare system, which provides about two-thirds of net pay for the first year off the job, cushions the blow for those out of work Shopping streets are still crowded and business, the shopkeepers say, is still okay, all things considered.

In May, however, more than 100 political figures, trade union leaders and government officials gathered near here to discuss ways of alleviating the Ruhr's problems. Since then, the federal government in Bonn has agreed to pump about $800 million in long-term aid into the region and this week the government of North Rhine-Westphalia, the state in which the Ruhr is located, approved a five-year $2.8 billion aid plan.

Both plans still must gain parliamentary approval, which is no problem in the state, but which could cause problems at the federal level because it might set a precedent for other areas.

The idea, Explains State Minister Christoph Zoepel, is to subsidize the high cost to Ruhr industry of maintaining and improving environmental controls of furnaces to make the region more livable, to build new housing further away from the pits, and to spruce the place up enough to stop the population exodus and attract new industry to the region.

There is also money for new research projects aimed at turning coal into oil. Indeed, the new global interest in coal due to sharply rising oil prices and threats of oil scarcity could by itself rejuvenat the Ruhr.

Yet here in the region, while there is some hope, there is mostly a sense of waiting mixed with skepticism.

Some people fear that the recent government attention and promises are linked to the 1980 elections and that whatever has not been done by then will fade in their aftermath.

Others point out that no matter what the present interest in coal, the future will be uncertain until Bonn decides whether to resume its once-ambitious nuclear power plans. Chancellor Helmut Schmidt has made clear that he views nuclear power as indispensable. While he also has put new emphasis on coal, Schmidt has combined that with a warning that an overwhelmingly coal-based economy would pose servere environmental risks of West Germany.

Furthermore, West German coal is well below the surface and labor costs are high, making it expensive to mine. Indeed, while talk of boosting the Rurhs fortunes heat up, the West German Chamber of Commerce is calling for stepping up the importation of cheaper coal from other countries, including the United States, to feed the new coal liquefaction and gasification plans.

But the main problem, according to Manfred Weiss, a local journalist, is that there are still really no new ideas for new industry here that can get the region away from its massive dependence on coal, which still accounts for more than 40 percent of Ruhr jobs.

Trade union officials say it is increasingly difficult to get young West Germans to work in the mines. "The biggest danger" for the life of the region, says Mayor Kuhlmann, "Is that the young people are the first to leave."

The feeling among young people in the past years of decline, says local newspaper editor Harald Neumann, is that there no longer was any future in coal and it questionable whether that can be reversed now.

The shortage of such workers comes at a time when union officials say there really is a need for technically well-educated miners using new automated techniques.

Almost 120,000 foreign workers have streamed into the Ruhr in recent years, mostly from Turkey and Yugoslavia, to take the jobs West Germans no longer want. Union officials contend that language problems and lack of technical training of the foreigners means some loss in comparison to German workers.

The Ruhr reflects the nationwide tendency of relatively well-off West Germans not to take menial jobs. In this city, while there are some 12,000 unemployed, Neumann points out that there are 3,000 unfilled jobs.

Similarly, perhaps because of the Ruhr's generally poor image as a grimy industrial "coalpot," or the high percentage of foreign children in the schools, about half the teachers needed for this city's elementary schools did not show up this year.

Because of the dominance of mining, there are few white-collar jobs here for young persons, and it is a tough place for women or people not in the best of health to find a job.

The area, however, is not nearly as bad as the image that many West Germans -- in a bit of national snobbishness -- ascribe to it. Gelsenkirchen, for example, which is right in the heart of the coal district, has considerable park area, new theaters and music centers, and a clean and generally pollution-free downtown and main residential area.

Because of its working-class image, the Ruhr for generations was ignored as a place to become educated. Since 1969, however, the state has built universities in Essen, Duisburg, Dortmund and Bochum.

In the early years of World War II, Ruhr coal mines turned out 130 million metric tons of coal a year. In 1978, the figure was 67 million tons.

In 1974, Ruhr steel mills were turning out about 52 million tons of raw steel annually. Now the figure is down to about 40 million tons.

This year, there has been a slight upturn in both coal and steel production, sparking some new hope, especially for coal. But it is the long-term slide that is affecting the spirit of the region.

Still, this is a region of great historical significance that has had its ups and downs many times before.

Wars have been fought over the Ruhr's resources.It has been occupied by the French and Belgians between world wars. When passive resistance to such occupation paralyzed the Ruhr economy, the entire German economy and currency eventually collapsed. In World War II, the region and its huge energy and chemical combines were bombed into ruins.

Perhaps most importantly, however, this is a region of tough people doing hard jobs and one, as Weiss says, "with a very peculiar and specific mentality shaped by history."

The people who came here to join the locals and work the mines in the 1920s and 1930s were from Poland and the eastern parts of Germany "and they were like a pioneer generation and are not so easily defeated," he adds.

Whether their grandchildren feel the same way, whether the Turks and Yugoslavs will fit into that same pioneer mold, and whether coal makes a comeback are now the questions that will determine if the Ruhr will retain the dominant position in Europe's economy that it has held for the last 60 years.