Normalize[v] gives the normalized form of a vector v. Normalize[z] gives the normalized form of a complex number z.Normalize[expr, f] normalizes with respect to the norm ...

[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 ...

The Lotka–Volterra system arises in mathematical biology and models the growth of animal species. Consider two species where Y_1(T) denotes the number of predators and Y_2(T) ...

HermiteH[n, x] gives the Hermite polynomial H_n (x).

Mathematica contains the world's largest collection of number theoretic functions, many based on specially developed algorithms.

Packing a large number of sophisticated algorithms—many recent and original—into a powerful collection of functions, Mathematica draws on almost every major result in number ...

Piecewise[{{val_1, cond_1}, {val_2, cond_2}, ...}] represents a piecewise function with values val_i in the regions defined by the conditions cond_i. Piecewise[{{val_1, ...

Orthogonal polynomials. Legendre polynomials LegendreP[n,x] arise in studies of systems with three-dimensional spherical symmetry. They satisfy the differential equation ...

NDSolve returns solutions as InterpolatingFunction objects. Most of the time, simply using these as functions does what is needed, but occasionally it is useful to access the ...

Limit[expr, x -> x_0] finds the limiting value of expr when x approaches x_0.