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).

NSolve gives you a general way to find numerical approximations to the solutions of polynomial equations. Finding numerical solutions to more general equations, however, can ...

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 ...

Throughout any computation, Mathematica maintains an evaluation stack containing the expressions it is currently evaluating. You can use the function Stack to look at the ...