In mathematics and physics, nonlinear partial differential equations are (as their name suggests) partial differential equations with nonlinear terms. They describe many different physical systems, ranging from gravitation to fluid dynamics, and have been used in mathematics to solve problems such as the Poincaré conjecture and the Calabi conjecture. They are difficult to study: there are almost no general techniques that work for all such equations, and usually each individual equation has to be studied as a separate problem.
Famous quotes containing the words list of, list, partial and/or differential:
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Went down the list of the dead.
Officers, seamen, gunners, marines,
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The bearded man and the lad in his teens,
Carpenters, coal-passers—all.”
—Joseph I. C. Clarke (1846–1925)
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—Lawrence Kutner (20th century)
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—J. Robert Oppenheimer (1904–1967)
“But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
—Antonin Artaud (1896–1948)