PrimeQ[expr] yields True if expr is a prime number, and yields False otherwise.

ReflectionMatrix[v] gives the matrix that represents reflection of points in a mirror normal to the vector v.

SphericalHarmonicY[l, m, \[Theta], \[Phi]] gives the spherical harmonic Y_l^m(\[Theta], \[Phi]).

ArcCosh[z] gives the inverse hyperbolic cosine cosh -1 (z) of the complex number z.

Min[x_1, x_2, ...] yields the numerically smallest of the x_i. Min[{x_1, x_2, ...}, {y_1, ...}, ...] yields the smallest element of any of the lists.

e_1 || e_2 || ... is the logical OR function. It evaluates its arguments in order, giving True immediately if any of them are True, and False if they are all False.

The general form of a linear second-order PDE is Here uu(x,y), and a, b, c, d, e, f, and g are functions of x and y only—they do not depend on u. If g0, the equation is ...

This is a simple homogeneous DAE with constant coefficients. This finds the general solution. It has only one arbitrary constant because the second equation in the system ...

Around 1870, Marius Sophus Lie realized that many of the methods for solving differential equations could be unified using group theory. Lie symmetry methods are central to ...

A differential system can sometimes be solved by analytic means. The function DSolve implements many of the known algorithmic techniques. However, differential systems that ...