Shanghai — Now that President Reagan has steadied the ship of Sino-American relations, China and the United States look forward to a dynamic new era of commercial and cultural cooperation.
''Your government's policy of forging closer ties in the free exchange of knowledge has not only enlivened your economy, it has opened the way to a new convergence of Chinese and American interests,'' the President told students at Fudan University on Monday. ''You have opened the door - and let me assure you that ours is open also.''
As Mr. Reagan was ending his remarkable journey to the People's Republic, the two sides signed agreements that will foster this cooperation, including:
* A tax treaty that will encourage US companies to participate in joint ventures in China. The treaty calls for an end to double taxation on American companies.
* Extension of a cultural agreement that will expand exchanges in the arts, journalism, education, and sports.
* An agreement on commercial nuclear cooperation, initialed Monday, that will enable US firms to sell nuclear reactors and other equipment to China.
It seemed fitting that the President should spend the last two days of his trip sightseeing in Shanghai, a boisterous commercial port city. With its ebullient people, Western-style buildings, and modernizing spirit, Shanghai seems the symbol of China's new economic pragmatism in both industry and agriculture.
At the Shanghai-Foxboro Company, the President toured China's first industrial joint venture with an American firm. (The Foxboro Company of Massachusetts holds 49 percent equity in the venture.)
The potential for bilateral cooperation is enormous. More than 100 American firms already are doing business in China, pouring more than $650 million into Chinese ventures - from civil aircraft parts to athletic shoe production. This summer a US investment mission will come to China, involving an estimated 25 to 30 US firms in such areas as light manufacturing, construction, agribusiness, and electronics.
Bilateral trade with China peaked in 1981 and then dropped when China began to hold up purchases of grain. But two-way trade is expected to set a new record of more than $5.5 billion in 1984. High technology, especially, has grown by leaps and bounds now that the US has eased export controls. According to US officials, transactions could more than double in the next five years.
Economic cooperation with China has more than a dollars-and-cents purpose, say administration officials. President Reagan is prepared to help modernize China for geopolitical reasons as well.
''China does not pose a strategic threat to the US in the foreseeable future, '' said one official. ''Its main concern is the Soviet Union, and it is in the interest of the US that China not fall far behind economically.''
Administration officials concede that China is a totalitarian Marxist country and could once again turn inward. But they seem sanguine that China is on a constructive path to modernization and that the opening to the West is durable, especially given the tens of thousands of Westerners coming into the country.
''Whatever the political leadership may think and however severe its control, when you have that number of people from outside and awareness inside of what is going on outside, you can't expect anything but change,'' commented national security adviser Robert C. McFarlane in an interview from Peking with CBS. ''And I think we're going to see change in China.''
Sharing this hope, many China experts still caution that US cooperation in China's development could lead to future problems. As the Chinese economy develops, for instance, US manufacturing industries could face even stiffer foreign competition.
However, Reagan has conspicuously extolled China's efforts to introduce incentives and other market-type reforms, almost as if he felt these would lead to capitalism. Telling Fudan's students about the US and ''my own values,'' Reagan noted that Americans ''devised an economic system that rewarded individual effort.''
''We believe in the dignity of each man, woman, and child,'' he told his Chinese listeners in a speech televised live in the Shanghai area. ''Our entire system is founded on an appreciation of the special genius of each individual - and of his special right to make his own decisions and lead his own life.''
It was hard to know whether the Chinese, who are by and large irreligious, appreciated the President's talking about America's religious faith and invoking the ''Bible of Moses, who delivered a people from slavery; and the Bible of Jesus Christ, who told us to love thy neighbor as thyself.'' But the President has seemed almost imbued with a mission to speak to the Chinese about free enterprise, democracy, and religion.
''He really believes this,'' a White House aide said.