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The partial differential equation (1+f_y^2)f_(xx)-2f_xf_yf_(xy)+(1+f_x^2)f_(yy)=0 (Gray 1997, p. 399), whose solutions are called minimal surfaces. This corresponds to the ...

A linear equation is an algebraic equation of the form y=mx+b involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. The ...

A determinant used to determine in which coordinate systems the Helmholtz differential equation is separable (Morse and Feshbach 1953). A determinant S=|Phi_(mn)|=|Phi_(11) ...

When A and B are self-adjoint operators, e^(t(A+B))=lim_(n->infty)(e^(tA/n)e^(tB/n))^n.

The term "characteristic" has many different uses in mathematics. In general, it refers to some property that inherently describes a given mathematical object, for example ...

An equation involving a function f(x) and integrals of that function to solved for f(x). If the limits of the integral are fixed, an integral equation is called a Fredholm ...

The partial differential equation u_t+u_(xxxxx)+30uu_(xxx)+30u_xu_(xx)+180u^2u_x=0.

A differential equation is an equation that involves the derivatives of a function as well as the function itself. If partial derivatives are involved, the equation is called ...

An equation of the form f(x,y,...)=0, where f contains a finite number of independent variables, known functions, and unknown functions which are to be solved for. Many ...

For the hyperbolic partial differential equation u_(xy) = F(x,y,u,p,q) (1) p = u_x (2) q = u_y (3) on a domain Omega, Goursat's problem asks to find a solution u(x,y) of (3) ...