There are many situations where one wants to find a formula that best fits a given set of data. One way to do this in Mathematica is to use Fit. Basic linear fitting. Here is ...

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 ...

An Abel ODE is a first-order equation of the form This equation arose in the context of the studies of Niels Henrik Abel on the theory of elliptic functions, and represents a ...

Here is an example of an exact ODE. This verifies the solution. Here is a contour plot of the solution.

The simplest type of linear second-order ODE is one with constant coefficients. This linear second-order ODE has constant coefficients. Notice that the general solution is 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 ...

One-dimensional Laplace transforms. The Laplace transform of a function f(t) is given by ∫_0^∞f(t)e^-stt. The inverse Laplace transform of F(s) is given for suitable γ by ( ...

You can use the keyboard to move the cursor forward or backward one character or one word at a time. You can also delete the character or word to the right or the left of the ...

Numerical root finding. NSolve gives you numerical approximations to all the roots of a polynomial equation. You can also use NSolve to solve sets of simultaneous equations ...

Mathematica represents matrices and vectors using lists. Anything that is not a list Mathematica considers as a scalar. A vector in Mathematica consists of a list of scalars. ...