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...ints'' by Jean E. Taylor|title=Differential Geometry: Partial Differential Equations on Manifolds|chapter-url=https://books.google.com/books?id=ulgECAAAQBAJ&pg= ** {{cite journal|title=Nonlinear partial differential equations and applications: Crystalline variational methods|journal=Proceedings of th ...

[[File:Maxwell's equations for electromagnetism.jpg|thumb|Maxwell's equations for electromagnetism]] ...agnetic phenomenon, based upon deriving of the [[speed of light]] from his equations. ...

...s. In the calculus of variations they appear as surfaces of least area, in differential geometry as surfaces of vanishing mean curvature. In gas dynamics the equat ...nt aerodynamical literature. In the general theory of partial differential equations, finally, equation (1) appears as the the simplest nonlinear equation of el ...

...kt:qualitative|qualitative]] analysis of systems described by differential equations. If no self-contained formula for the solution is available, many computer * Almost all of fluid dynamics follows from a differential equation called the [[w:Navier-Stokes equation|Navier-Stokes equation]]. Bu ...

...Lagrangian mechanics|Lagrangian]], [[w:Hamiltonian mechanics|Hamiltonian]] equations of motion, and even General [[Theory of relativity|Relativity]]. It was his ...ry of the rotation of a body around a fixed point, established the general equations of motion of a free body, and the general equation of hydrodynamics. He sol ...

...if the dimensions match on either side of the equality. Fourier's partial differential equation for conductive diffusion of heat is now taught to every student of ...onstrations analogous to... the theorems... of statics and dynamics. These equations... receive a different form, when they express the distribution of luminous ...

* The general equations are next applied to the case of a magnetic disturbance propagated through a ...he ideas as expressed in symbols had ever quite found their way out of the equations of their minds. ...

...g surfaces is required. The general problem is that of solving the general equations with arbitrary conditions at any given boundaries. In discussing this probl ...discovery of {{w|Hooke's Law}} in 1660, and the formulation of the general equations by [[w:Claude-Louis Navier|Navier]] in 1821.'''<!-- p. 2--> ...

...as endured to this day... known as ''[[Maxwell's equations|Maxwell's field equations]]''. Based on [[Michael Faraday|Faraday]]'s earlier work, Maxwell stressed ...is colleague [[James Clerk Maxwell|Maxwell]]; and [[w:History of Maxwell's equations|one of the most astonishing theories]] of science, eclipsed only in recent ...

...ume the burden of Newton's action at a distance. ...[O]ne set of Maxwell's equations is to the effect that, in the presence of a magnetic field which changes in ...in, or justify, these equations by intellectual constructions. But... the equations alone appeared as the essential thing and the strength of the fields as the ...

...ve its birth in 1821, when [[w:Claude-Louis Navier|Navier]] first gave the equations for the equilibrium and motion of elastic solids, but some of the problems ...is that <math>\frac{\partial u}{u}</math> is proportional to <math>\frac{\partial x}{x^2}</math>. Hence '''according to Riccati we should have instead of Hoo ...

* The analytical equations, unknown to the ancient geometers, which [[René Descartes|Descartes]] was t ...he developed it... it constituted a part of a work entitled ''Analyse des equations determines'' (1831), which was in press when death overtook him. This work ...

...n Hamilton|Hamilton]] and [[Hermann Grassmann|Grassman]] in the 1840s, for partial [[w:Arithmetization of analysis|arithmetization]] in the second and third d ...mphasized, his theory is not intended to be a practical method for solving equations. But, as stated by [[David Hilbert|Hilbert]], the {{w|Galois theory}} and t ...

...ty#Einstein.27s equations|metric function]] through the [[w:Einstein field equations|field equation]]. ...In this approach, gravity is the structure of spacetim ...pace dimension, Kaluza... derived the new equations. ...Kaluza found extra equations... those Maxwell had written down in the 1880s for deriving the electromagn ...

...ger, is introduced to derive a simplified set of nonlinear... differential equations. ...plates or shells was first attacked from the point of view of the general equations of Elasticity by [[w:Hermann Aron|H. Aron]]. He expressed the geometry of t ...

...[[w:Principle of relativity|principle of general relativity]] was to write equations for physics that were valid for all observers, independently of the [[w:Coo ...struck Einstein as absurd. He therefore tried to sidestep the logic of his equations, and modified them by adding... a "[[cosmological constant]]." The term rep ...

...and Origin of The Differential Calculus (1714)|''History and Origin of The Differential Calculus'' (1714)]]<br />[[#The Analyst (1734)|''The Analyst'' (1734)]]<br ...ometry it would have been impossible to describe graphs using mathematical equations, and hence, except perhaps as a pure theory, the calculus would be complete ...

...ation of the whole of mathematics]], that every system which you devise is partial and suffers from one great shortcoming. If it is [[Consistency|consistent]] ...tting. He can do long division like the ancient Egyptians, solve quadratic equations like the Babylonians, and study geometry just as the student in [[Euclid|Eu ...

...was an English clergyman and [[w:Mathematics|mathematician]] who is given partial credit for the development of [[w:infinitesimal calculus|infinitesimal calc ...ections of the cone but then proceeded to derive their properties from the equations, "without the embranglings of the cone," as he put it. ...

...w:Cubic equation|cubic]] and [[w:Quartic equation|quartic]] and through... partial... symbolism; and trigonometry had become an independent discipline. The ti ...usa) published in 820 an algebraic treatise which went as far as quadratic equations: translated into Latin in the sixteenth century, it became a primer for the ...