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Maxwell's equations are the system of partial differential equations describing classical electromagnetism and therefore of central importance in physics. In the so-called ...

The maximum and minimum of the normal curvature kappa_1 and kappa_2 at a given point on a surface are called the principal curvatures. The principal curvatures measure the ...

The torsion of a space curve, sometimes also called the "second curvature" (Kreyszig 1991, p. 47), is the rate of change of the curve's osculating plane. The torsion tau is ...

The term "total curvature" is used in two different ways in differential geometry. The total curvature, also called the third curvature, of a space curve with line elements ...

Determinants are mathematical objects that are very useful in the analysis and solution of systems of linear equations. As shown by Cramer's rule, a nonhomogeneous system of ...

The spherical harmonics can be generalized to vector spherical harmonics by looking for a scalar function psi and a constant vector c such that M = del x(cpsi) (1) = psi(del ...

(x^2)/(a^2-lambda)+(y^2)/(b^2-lambda)=z-lambda (1) (x^2)/(a^2-mu)+(y^2)/(b^2-mu)=z-mu (2) (x^2)/(a^2-nu)+(y^2)/(b^2-nu)=z-nu, (3) where lambda in (-infty,b^2), mu in ...

There are several different definitions of conical coordinates defined by Morse and Feshbach (1953), Byerly (1959), Arfken (1970), and Moon and Spencer (1988). The ...

The v coordinates are the asymptotic angle of confocal hyperbolic cylinders symmetrical about the x-axis. The u coordinates are confocal elliptic cylinders centered on the ...

A predictor-corrector method for solution of ordinary differential equations. The third-order equations for predictor and corrector are y_(n+1) = ...