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, ...

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 ...

Patterns are used throughout Mathematica to represent classes of expressions. A simple example of a pattern is the expression f[x_]. This pattern represents the class of ...

Minimization and maximization. Minimize and Maximize yield lists giving the value attained at the minimum or maximum, together with rules specifying where the minimum or ...

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 ...

Many differential equations exhibit some form of stiffness, which restricts the step size and hence effectiveness of explicit solution methods. A number of implicit methods ...

Numerical integration functions. This finds a numerical approximation to the integral ∫_(0)^∞ e^-x^3 x. Here is the numerical value of the double integral ∫_(-1)^1 dx ...

Mathematica provides a compact way of representing boxes in terms of strings. This is particularly convenient when you want to import or export specifications of boxes as ...

CUDAImageAdd[img, x] adds an amount x to each channel value in img.CUDAImageAdd[mem, x] adds an amount x to each channel value in mem.CUDAImageAdd[img 1, img 2] gives an ...

CUDAImageMultiply[img, x] multiplies an amount x to each channel value in img.CUDAImageMultiply[mem, x] multiplies an amount x to each channel value in ...