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

With careful standardization of argument conventions, Mathematica provides full coverage of elliptic integrals, with arbitrary-precision numerical evaluation for complex ...

Differentiation Total Derivatives Derivatives of Unknown Functions

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 ...

Even more so than for other special functions, you need to be very careful about the arguments you give to elliptic integrals and elliptic functions. There are several ...

In calculus even more than other areas, Mathematica packs centuries of mathematical development into a small number of exceptionally powerful functions. Continually enhanced ...

To control how a 3D surface responds to simulated light, set its reflection properties. Mathematica lets you control the diffuse reflection of light on a matte surface and ...

Now that we have introduced the basic features of patterns in Mathematica, we can use them to give a more or less complete example. We will show how you could define your own ...

Numerical sums, products and integrals. Here is a numerical approximation to ∑_(i=1)^∞((1)/(i^3)). NIntegrate can handle singularities in the integration region.

This does an integral over the interior of the unit circle. Here is an equivalent form. Even though an integral may be straightforward over a simple rectangular region, it ...