Verification of the Solution (Mathematica Tutorial)

The solution given by DSolve can be verified using various methods. The easiest method involves substituting the solution back into the equation. If the result is True, the ...

LaplacianFilter (Built-in Mathematica Symbol)

LaplacianFilter[image, r] convolves image with a range r Laplacian kernel.LaplacianFilter[image, {r_1, r_2}] uses ranges r_i in the vertical and horizontal ...

RamanujanTauZ (Built-in Mathematica Symbol)

RamanujanTauZ[t] gives the Ramanujan tau Z-function Z(t).

WeierstrassInvariants (Built-in Mathematica Symbol)

WeierstrassInvariants[{\[Omega], \[Omega]^\[Prime]}] gives the invariants {g_2, g_3} for Weierstrass elliptic functions corresponding to the half-periods {\[Omega], ...

Exact Higher-Order Equations (Mathematica Tutorial)

A linear ordinary differential equation of order n is said to be exact if The condition of exactness can be used to reduce the problem to that of solving an equation of order ...

ObservabilityGramian (Built-in Mathematica Symbol)

ObservabilityGramian[ss] gives the observability Gramian of the StateSpaceModel object ss.

Floor (Built-in Mathematica Symbol)

Floor[x] gives the greatest integer less than or equal to x. Floor[x, a] gives the greatest multiple of a less than or equal to x.

HessenbergDecomposition (Built-in Mathematica Symbol)

HessenbergDecomposition[m] gives the Hessenberg decomposition of a matrix m.

WaveletFilterCoefficients (Built-in Mathematica Symbol)

WaveletFilterCoefficients[wave, filt] gives the filter coefficients for the symbolic wavelet wave of type filt.

Equations with Non-Rational Coefficients (Mathematica Tutorial)

The ODEs that arise in practical applications often have non-rational coefficients. In such cases, DSolve attempts to convert the equation into one with rational coefficients ...