Differential Equations

a dynamical system is the description of how a system evolves in time

Since we don't even know whether these solutions exist, our understanding is at a very primitive level. Standard methods from PDE appear inadequate to settle the problem.

allows one to bound a function that is known to satisfy a certain differential or integral inequality

integral relation satisfied by stationary localized solutions to a nonlinear Schrödinger equation or nonlinear Klein-Gordon equation

Papers of 1836 - 1837 by Sturm and Liouville on differential equations involved expansions of functions in series

Pfaff did important work in analysis working on partial differential equations, special functions and the theory of series.

was a French mathematician, who worked on both partial differential equations and algebraic topology

His contributions include work in harmonic analysis and differential equations

his papers covered number theory, special functions, operational calculus and nonlinear differential equations

was a Soviet mathematician working in mathematical analysis and partial differential equations

contributed to the theory of partial differential equations

Some of his major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equations, number theory, and signal processing.

worked in the fields of special functions, differential equations, and difference equations

published about 100 papers on differential equations

Lax made contributions to the theory of hyperbolic partial differential equations.

a French mathematician and politician working primarily on partial differential equations, Riemannian geometry and mathematical physics

One of Korkin's major contributions was to the development of partial differential equations.

a technique for uniformly approximating periodic solutions to ordinary differential equations when regular perturbation approaches fail

Almost all Van Vleck's research papers were in the fields of function theory and differential equations.

his work on the theory of differential equations from the algebraic viewpoint, which he called differential algebra

among the greatest pioneers of differential algebra and symbolic computation for systems of partial differential equations

specializing in differential equations, determinants, and mathematical physics

specializing in differential geometry, partial differential equations and their applications

His main contributions relate to conformal mappings and partial differential equations.

partial differential equations and mechanics

Painlevé's mathematical work on differential equations

contributed significantly to the study of differential equations

important contributions to the field of linear differential equations

differential equations of the string oscillations

who invented a new technique for solving differential equations

to the theory of ordinary differential equations

in recognition of his contributions to partial differential equations

who worked on partial differential equations, fluid dynamics

the foremost contributor to the modern theory of linear partial differential equations

teoria delle equazioni differenziali

ordinary differential equations, partial differential equations, harmonic analysis, mathematical biology and the history of mathematics

In a 1638 letter to Descartes, de Beaune posed a problem that can be reformulated in modern notation as solving the differential equation dydx=αy−x now seen as the first example of the inverse tangent method of deducing properties of a curve from its tangents.

Jacopo Francesco Riccati (28 May 1676-15 April 1754) was a Venetian mathematician and jurist from Venice, known for his widely influential work on solving differential equations.

phenomenon of zodiacal light, for his "push" or "shadow" theory of gravitation, for inventing the integrating factor as a method for solving ordinary differential equations, for his close association with both Christiaan Huygens and Isaac Newton,

In 1716 he obtained the Galileo-chair at the University of Padua, where he worked on differential equations and geometry.

Nicolaus worked mostly on curves, differential equations, and probability.

In the theory of ordinary differential equations (ODEs), Lyapunov functions, named after Aleksandr Lyapunov, are scalar functions

tence and uniqueness theorem for analytic partial differential equations associated with Cauchy initial value problems.

Kac, establishes a link between parabolic partial differential equations and stochastic processes.

differential equations

differential equations

partial differential equations

partial differential operators

worked on differential equations and singularity theory

He made numerous contributions to differential equations and partial differential equations

Other topics included optics, calculus, trigonometry and partial differential equations in mathematics. == See also == Cotes's spiral == References == == External links == Samuel Earnshaw Archived 12 April 2016 at the Wayback Machine

He was awarded the Fields Medal in 2006 for his contributions to partial differential equations, combinatorics, harmonic analysis, and additive number theory.

In mathematics, the Grothendieck-Katz p-curvature conjecture is a local-global principle for linear ordinary differential equations, related to differential Galois theory and in a loose sense analogous to the result in the Chebotarev density theorem considered as the polynomial case.

The Duffing equation (or Duffing oscillator), named after Georg Duffing (1861-1944), is a non-linear second-order differential equation used to model certain damped and driven oscillators.

In fact, the Airy equation is the simplest second-order linear differential equation with a turning point (a point where the character of the solutions changes from oscillatory to exponential).

They are often employed in solving partial differential equations in many scientific fields.

In mathematics, a Lamé function, or ellipsoidal harmonic function, is a solution of Lamé's equation, a second-order ordinary differential equation.

From the parabolic partial differential equation in the model, known as the Black-Scholes equation, one can deduce the Black-Scholes formula, which gives a theoretical estimate of the price of European-style options and shows that the option has a unique price given the risk of the security and its expected return (instead replacing the security's expected return with the risk-neutral rate).

In mathematics, Abel's identity (also called Abel's formula or Abel's differential equation identity) is an equation that expresses the Wronskian of two solutions of a homogeneous second-order linear ordinary differential equation in terms of a coefficient of the original differential equation.

Calculus and Analysis Differential Equations

Calculus and Analysis Differential Equations

Kurt Friedrichs was a German American mathematician who worked on many aspects of partial differential equations.

Marcel Riesz was a Hungarian-born mathematician who worked on summation methods, potential theory and other parts of analysis, as well as number theory and partial differential equations.

Sergei Bernstein was a Ukrainian mathematician who made important contributions to partial differential equations, differential geometry, probability theory and approximation theory.

Vladimir Arnold is a Ukrainian-born mathematician who won a Wolf prize for his work on dynamical systems, differential equations and singularity theory.