Enrollment at the University of the District of Columbia has tumbled this fall by 13 percent, the largest decline in an eight-year slide that has reduced the size of the city's public university from more than 15,000 students at its peak in 1979 to less than 10,000 now.

This fall's drop of 1,443 students -- a markedly larger decline than last year's loss of 982 students -- poses a sharp challenge to Rafael L. Cortada, who took office Thursday, as UDC's new president, its fifth in 10 years.

"We're very concerned about the enrollment decline, but I don't think it's fatal," Cortada said in an interview. "I think it's a combination of small factors rather than one big thing . . . . We'll be working to turn it around."

Over the past year UDC has lost accreditation for two of its engineering degrees and cut its faculty by about 10 percent, causing uncertainty about some of its programs. To try to increase enrollment, the university spent about $110,000 on a marketing campaign that included mailing brochures to all 253,000 households in the District.

But like a similar, even more costly campaign a year ago, the marketing failed to prevent the enrollment loss.

"We really don't know to what extent we have a problem that is part of a general {national} trend," said university trustee Peter B. Edelman, "and to what extent we have problem that is local that's retrievable by marketing, improvement in the reputation of UDC and program changes . . . . There's nothing new here, except the numbers, but they really dramatize the challenges facing Dr. Cortada."

Several trustees and other officials said the university had been harmed by a protracted controversy surrounding former president Robert L. Green, who resigned in August 1985 amid accusations of misusing college funds. The college's acting president for two years, Claude A. Ford, concentrated on staffing and administrative changes and did not have a mandate from the trustees to develop new programs.

Among the changes was a shift in the application deadline from late summer, about three weeks before the start of the fall semester, to June 1. The move was aimed at reducing confusion at the start of UDC classes.

But Cortada said that despite extensive advertising, the shift had a "terrible impact" on enrollment at the relatively low-cost, open-admissions university. He said he intends to move the application deadline much closer to the start of classes again.

"Low-income people tend to come in later," Cortada said, noting that most community colleges -- which, like UDC, accept any high school graduate -- have very late application deadlines.

He said that one of his first appointments has been a special assistant for enrollment management, who "will focus on reaching {potential} students, attracting them, and retaining them."

The job went to Clarence Hicks, who had been financial aid director at the Community College of Baltimore, where Cortada served as president for five years until 1982. Cortada later headed El Camino College in California. This fall, enrollment has stabilized at the Baltimore college after falling sharply for three years.

UDC, which received $71.4 million from the District government this last year, was formed in 1977 through a merger of the city's three public colleges, D.C. Teachers College, Federal City College and the Washington Technical Institute.

University spokesman John Britton pointed to an acceleration in the enrollment decline after 1982, when UDC began enforcing a policy on academic suspensions and probation. UDC also raised its tuition sharply in 1984 and 1986, although there was no increase this year. At $684, UDC's tuition remains by far the lowest in the area.

"I think a person could be very casual and come to the university and just dabble a little bit," Britton said. "That's changed."

After sharp decreases from 1979 to 1984, the number of graduates from D.C. public high schools, UDC's largest source of students, has fallen only slightly in three years. According to D.C. school board statistics, the proportion of graduates going to college has increased and scores on college entrance tests have risen.

"That may have had a perverse effect on UDC," trustee Edelman said. "As the D.C. schools improve somewhat, their graduates certainly have more options. We're an open enrollment institution, and it's a fact of life that if people have an array of options, some will go to other places."

In statements several months ago, Cortada urged creation of a distinct two-year community college within UDC that would offer open admissions and remedial programs. He said establishing a separate four-year college within the university would "protect the integrity" of its bachelor's degree and attract more students with a strong high school record.

Around the country, total college enrollment was almost stable from 1980 to 1986. There was a 3 percent drop at community colleges in 1985, but a recovery of about the same amount last year. No nationwide figures are available for this fall, but community colleges in the Washington suburbs have reported slight increases. Prince George's Community College showed a 4 percent increase, its first rise in five years.

Around the country, the number of black college students declined from 1980 to 1985, but this year the College Board reported a major increase in black high school seniors taking college entrance exams. Black students account for most of UDC's enrollment. At the City University of New York, which like UDC has both two-year and four-year programs, enrollment was virtually unchanged this fall.