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 ...

On most computer systems, you can execute external programs or commands from within Mathematica. Often you will want to take expressions you have generated in Mathematica, ...

Functions that are specified by simple algebraic formulas tend to be such that when their input is changed only slightly, their output also changes only slightly. But ...

Some integer functions. The remainder on dividing 17 by 3. The integer part of 17/3.

Evaluating integrals is much more difficult than evaluating derivatives. For derivatives, there is a systematic procedure based on the chain rule that effectively allows any ...

With the default option setting Lighting->Automatic, Mathematica uses a simulated lighting model to determine how to color polygons in three-dimensional graphics. Mathematica ...

Mathematica expressions provide a very general way to handle all kinds of data, and you may sometimes want to use such expressions inside your external programs. A language ...

A Mathematica script is simply a file containing Mathematica commands that you would normally evaluate sequentially in a Mathematica session. Writing a script is useful if ...

When a differential system has a certain structure, it is advantageous if a numerical integration method preserves the structure. In certain situations it is useful to solve ...

NDSolve uses norms of error estimates to determine when solutions satisfy error tolerances. In nearly all cases the norm has been weighted, or scaled, such that it is less ...