InverseFunction (Built-in Mathematica Symbol)

InverseFunction[f] represents the inverse of the function f, defined so that InverseFunction[f][y] gives the value of x for which f[x] is equal to y. InverseFunction[f, n, ...

SpheroidalS2Prime (Built-in Mathematica Symbol)

SpheroidalS2Prime[n, m, \[Gamma], z] gives the derivative with respect to z of the radial spheroidal function S_n^m, (2)(\[Gamma], z) of the second kind.

Classification of Differential Equations (Mathematica Tutorial)

While differential equations have three basic types—ordinary (ODEs), partial (PDEs), or differential-algebraic (DAEs), they can be further described by attributes such as ...

The Secant Method (Mathematica Tutorial)

When derivatives cannot be computed symbolically, "Newton's" method will be used, but with a finite difference approximation to the Jacobian. This can have costs in terms of ...

InterpolatingPolynomial (Built-in Mathematica Symbol)

InterpolatingPolynomial[{f_1, f_2, ...}, x] constructs an interpolating polynomial in x which reproduces the function values f_i at successive integer values 1, 2, ... of x. ...

Vector Analysis Package (Vector Analysis Package Guide)

Frequently, physical systems exhibit special symmetries or structures that make a particular coordinate system especially useful. In a mathematically elegant solution to ...

ArcLengthFactor (Vector Analysis Package Symbol)

ArcLengthFactor[{f_1, f_2, f_3}, t] gives the derivative of the arc length of the curve described by the parametrized curve coordinates {f_1, f_2, f_3} with respect to the ...

ND (Numerical Calculus Package Symbol)

ND[expr, x, x_0] gives a numerical approximation to the derivative of expr with respect to x at the point x_0.ND[expr, {x, n}, x_0] gives a numerical approximation to the ...

LerchPhi (Built-in Mathematica Symbol)

LerchPhi[z, s, a] gives the Lerch transcendent \[CapitalPhi] (z, s, a).

Norms in NDSolve (Mathematica Tutorial)

NDSolve uses norms of error estimates to determine when solutions satisfy error tolerances. In nearly all cases the norm has been weighted, or scaled, such that it is less ...