The evalhf command, which evaluates an expression to a numerical value using the floating-point hardware of the underlying system, has been extended to handle complex numbers.  In addition, a number of common commands like map, zip, and basic Matrix arithmetic are now also handled directly by evalhf.

The new fdiff command has been added for computing numerical derivatives. Alternatively, numerical differentiation can be invoked using evalf and D. This feature is particularly useful for mathematical functions for which no symbolic derivative is known.

Examples

fdiff(exp(x),x=1);

$2.718281828$

fdiff(BesselJ(v,x),[v],[v=1,x=2]) = evalf(D[1](BesselJ)(1,2));

$\mathrm{-0.05618076074}=\mathrm{-0.05618076074}$

Support for the numerical evaluation of several new mathematical functions has been added. The functions are: Wrightomega, SphericalY (spherical harmonics), and the five Heun functions HeunG, HeunC, HeunB, HeunD, and HeunT.

For more details on this function, see Enhancements to Symbolic Capabilities in Maple 10.

Special code has been added to RootFinding[Analytic] to detect multiple roots. For more details, see Efficiency Improvements in Maple 10.