Protect[s_1, s_2, ...] sets the attribute Protected for the symbols s_i. Protect["form_1", "form_2", ...] protects all symbols whose names match any of the string patterns ...

QGamma[z, q] gives the q-gamma function \[CapitalGamma]_q (z).

If you make a definition such as f[x_]:=value, Mathematica will use the value you give for any f function it encounters. In some cases, however, you may want to define a ...

The general solution to this equation is found by separation of variables. Even when variables can be separated, the final solution might be accompanied by a warning message ...

Functions to pick out pieces of polynomials. Here is an algebraic expression. This gives the coefficient of x in e.

A partial differential equation (PDE) is a relationship between an unknown function u(x_1,x_2,…,x_n) and its derivatives with respect to the variables x_1,x_2,…,x_n. Here is ...

JacobiAmplitude[u, m] gives the amplitude am(u \[VerticalSeparator] m) for Jacobi elliptic functions.

Mathematica can be used to make plots of functions. You give Mathematica a function, and it builds up a curve or surface by evaluating the function at many different points. ...

NorlundB[n, a] gives Nørlund polynomials B_n^(a) of degree n in a.NorlundB[n, a, x] gives generalized Bernoulli polynomials B_n^(a)(x).

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 ...