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Let f(t) and g(t) be arbitrary functions of time t with Fourier transforms. Take f(t) = F_nu^(-1)[F(nu)](t)=int_(-infty)^inftyF(nu)e^(2piinut)dnu (1) g(t) = ...

y approx m+sigmaw, (1) where w = (2) where h_1(x) = 1/6He_2(x) (3) h_2(x) = 1/(24)He_3(x) (4) h_(11)(x) = -1/(36)[2He_3(x)+He_1(x)] (5) h_3(x) = 1/(120)He_4(x) (6) h_(12)(x) ...

Critical damping is a special case of damped simple harmonic motion x^..+betax^.+omega_0^2x=0, (1) in which D=beta^2-4omega_0^2=0, (2) where beta is the damping constant. ...

A special case of Stokes' theorem in which F is a vector field and M is an oriented, compact embedded 2-manifold with boundary in R^3, and a generalization of Green's theorem ...

The divergence theorem, more commonly known especially in older literature as Gauss's theorem (e.g., Arfken 1985) and also known as the Gauss-Ostrogradsky theorem, is a ...

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 ...

The ordinary differential equation (x^py^')^'+/-x^sigmay^n=0.

Given a formula y=f(x) with an absolute error in x of dx, the absolute error is dy. The relative error is dy/y. If x=f(u,v,...), then ...

Given a subset K of a vector space X, a nonempty subset S subset K is called an extreme set of K if no point of S is an internal point of any line interval whose endpoints ...

If {f_n} is a sequence of nonnegative measurable functions, then intlim inf_(n->infty)f_ndmu<=lim inf_(n->infty)intf_ndmu. (1) An example of a sequence of functions for which ...