BSplineBasis (Built-in Mathematica Symbol)

BSplineBasis[d, x] gives the zeroth uniform B-spline basis function of degree d at x.BSplineBasis[d, n, x] gives the n\[Null]^th uniform B-spline basis function of degree ...

Sparse Arrays (Mathematica Guide)

Mathematica has special sparse-array technology for efficiently handling arrays with literally astronomical numbers of elements when only a small fraction of the elements are ...

Reducing Expressions to Their Standard ... (Mathematica Tutorial)

The built-in functions in Mathematica operate in a wide variety of ways. But many of the mathematical functions share an important approach: they are set up so as to reduce ...

CDFWavelet (Built-in Mathematica Symbol)

CDFWavelet[] represents a Cohen\[Dash]Daubechies\[Dash]Feauveau wavelet of type "9/7". CDFWavelet["type"] represents a Cohen\[Dash]Daubechies\[Dash]Feauveau wavelet of type " ...

BiorthogonalSplineWavelet (Built-in Mathematica Symbol)

BiorthogonalSplineWavelet[] represents a biorthogonal spline wavelet of order 4 and dual order 2.BiorthogonalSplineWavelet[n, m] represents a biorthogonal spline wavelet of ...

ReverseBiorthogonalSplineWavelet (Built-in Mathematica Symbol)

ReverseBiorthogonalSplineWavelet[] represents a reverse biorthogonal spline wavelet of order 4 and dual order 2.ReverseBiorthogonalSplineWavelet[n, m] represents a reverse ...

Integrate (Built-in Mathematica Symbol)

Integrate[f, x] gives the indefinite integral \[Integral]f d x. Integrate[f, {x, x_min, x_max}] gives the definite integral \[Integral]_x_min^x_max\ f\ d x. Integrate[f, {x, ...

Matrices and Linear Algebra (Mathematica Guide)

Mathematica automatically handles both numeric and symbolic matrices, seamlessly switching among large numbers of highly-optimized algorithms. Using many original methods, ...

References (Mathematica Tutorial)

[AB04] Abell, M. L. and J. P. Braselton. Differential Equations with Mathematica. (3rd ed.) Elsevier Academic Press, 2004. [A89] Abramov, S. A. "Rational Solutions of Linear ...

CountRoots (Built-in Mathematica Symbol)

CountRoots[poly, x] gives the number of real roots of the polynomial poly in x.CountRoots[poly, {x, a, b}] gives the number of roots between a and b.