RootSum[f, form] represents the sum of form[x] for all x that satisfy the polynomial equation f[x] == 0.

TruncatedDistribution[{x_min, x_max}, dist] represents the distribution obtained by truncating the values of dist to lie between x_min and ...

WeierstrassP[u, {g_2, g_3}] gives the Weierstrass elliptic function \[WeierstrassP](u; g_2, g_3).

WeierstrassSigma[u, {g_2, g_3}] gives the Weierstrass sigma function \[Sigma](u; g_2, g_3).

Definitions such as f[x_]=x^2 specify values for functions. Sometimes, however, you need to specify general properties of functions, without necessarily giving explicit ...

The Mathematica function DSolve finds symbolic solutions to differential equations. (The Mathematica function NDSolve, on the other hand, is a general numerical differential ...

First-order PDEs are usually classified as linear, quasi-linear, or nonlinear. The first two types are discussed in this tutorial. A first-order PDE for an unknown function ...

The differential equations that arise in practice are of two types. Here is an example of the first type. Here is an example of the second type. This equation has a symbolic ...

Minimization and maximization. Minimize and Maximize yield lists giving the value attained at the minimum or maximum, together with rules specifying where the minimum or ...

Implicit Runge–Kutta methods have a number of desirable properties. The Gauss–Legendre methods, for example, are self-adjoint, meaning that they provide the same solution ...