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Also known as the total curvature. The linear element of the indicatrix ds_P=sqrt(ds_T^2+ds_B^2).

A pair of linear operators L and A associated with a given partial differential equation which can be used to solve the equation. However, it turns out to be very difficult ...

A Gröbner basis G for a system of polynomials A is an equivalence system that possesses useful properties, for example, that another polynomial f is a combination of those in ...

In bispherical coordinates, Laplace's equation becomes (1) Attempt separation of variables by plugging in the trial solution f(u,v,phi)=sqrt(coshv-cosu)U(u)V(v)Psi(psi), (2) ...

Clairaut's difference equation is a special case of Lagrange's equation (Sokolnikoff and Redheffer 1958) defined by u_k=kDeltau_k+F(Deltau_k), (1) or in "x notation," ...

A congruence of the form ax^2+bx+c=0 (mod m), (1) where a, b, and c are integers. A general quadratic congruence can be reduced to the congruence x^2=q (mod p) (2) and can be ...

A matrix is a concise and useful way of uniquely representing and working with linear transformations. In particular, every linear transformation can be represented by a ...

To solve the heat conduction equation on a two-dimensional disk of radius a=1, try to separate the equation using U(r,theta,t)=R(r)Theta(theta)T(t). (1) Writing the theta and ...

Unlike quadratic, cubic, and quartic polynomials, the general quintic cannot be solved algebraically in terms of a finite number of additions, subtractions, multiplications, ...

In conical coordinates, Laplace's equation can be written ...