Lars Hormander, 81, a Swedish mathematician who received the highest honors in his field for his work on the equations that describe many of the most important natural phenomena, from snowstorms to supernovas, died Nov. 25. Sweden’s Lund University, where he spent much of his career, reported his death, which occurred in Lund.

No cause was disclosed.

Dr. Hormander’s reputation as one of the world’s foremost mathematicians derived from his efforts to create firm theoretical underpinnings for one of the most important mathematical tools used by scientists and engineers: linear partial differential equations.

These equations, often extremely difficult to solve, can provide the answers to important questions about the physical behavior of the real world, including weather, electromagnetism and the flow of fluids of all sorts.

In their power to enhance the understanding of physical reality, partial differential equations provide a big step up from the equations of basic algebra. Basic algebraic equations include terms that show how the size of one quantity is related to the size of another.

Differential equations, which are more general, include terms that describe the rate at which one quantity changes with respect to another. Partial differential equations make mathematical statements of broader applicability.

Dr. Hormander “laid much of the foundations for the modern theory of partial differential equations,” Terence Tao, a mathematician at the University of California at Los Angeles, wrote in an e-mail.

Before Dr. Hormander, Tao wrote, “one could try to solve each such equations separately by an ad hoc collection of tricks.”

But, with Dr. Hormander’s theory, he wrote, it was possible to analyze “large classes of such equations simultaneously and rapidly.”

Described as the foremost modern contributor to the modern theory of linear partial differential equations, Dr. Hormander received the Fields Medal in 1962 and the Wolf Prize in 1988. He was elected to the National Academy of Sciences in 1976.

In a citation accompanying the award of the 2006 Steele prize for exposition, another major mathematical honor, the American Mathematical Society lauded Dr. Hormander’s four-volume work titled “The Analysis of Linear Partial Differential Operators.”

According to the award committee, almost all of the “exciting developments” connected to the theory of such equations in the period from 1960 to 1985 could be found in Dr. Hormander’s work, which has been described as a mathematical masterpiece.

Moreover, the committee wrote, “one is hard-pressed to find any comparable ‘expository’ work that covers so much material and with such depth and understanding of such a broad area of mathematics.”

His much-admired mathematical compendium, Dr. Hormander wrote, began in the 1950s with “modest lecture notes” intended for his students in Sweden.

Another of his works renowned among mathematicians is “An Introduction to Complex Analysis in Several Variables.”

Lars Valter Hormander was born Jan. 24, 1931, in Mjallby, a fishing village in southern Sweden, where his father was a teacher. He did his undergraduate and graduate work at Lund University and obtained a PhD in 1955.

He spent several years at major academic research centers in the United States, including the University of Chicago, Stanford University and the Institute for Advanced Study in Princeton, N.J. He also worked at the Courant Institute of Mathematical Sciences at New York University.

Most of his career was spent at Lund, where he was a professor from 1968 through his retirement in 1996.

Information about survivors could not be confirmed.