If you make a definition like f[x_]:=x Sin[x], Mathematica will store the expression x Sin[x] in a form that can be evaluated for any x. Then when you give a particular value ...

Numerical sums and products. This gives a numerical approximation to ∑_(i=1)^∞((1)/(i^3+i!)). There is no exact result for this sum, so Mathematica leaves it in a symbolic ...

Sparse representations of matrices are useful because they do not store every element. If one particular value appears very frequently it can be very advantageous to use a ...

SphericalBesselY[n, z] gives the spherical Bessel function of the second kind y_n (z).

The solutions to many second-order ODEs can be expressed in terms of special functions. Solutions to certain higher-order ODEs can also be expressed using AiryAi, BesselJ, ...

EndPackage[] restores $Context and $ContextPath to their values before the preceding BeginPackage, and prepends the current context to the list $ContextPath.

Constants is an option for Dt which gives a list of objects to be taken as constants.

Mathematica provides many functions to group terms in a polynomial, extract and sort the monomials, display them in various ways, and even process them as arbitrary ...

ArcSin[z] gives the arc sine sin -1 (z) of the complex number z.

Which[test_1, value_1, test_2, value_2, ...] evaluates each of the test_i in turn, returning the value of the value_i corresponding to the first one that yields True.