ReplacePart[expr, i -> new] yields an expression in which the i\[Null]\[Null]^th part of expr is replaced by new. ReplacePart[expr, {i_1 -> new_1, i_2 -> new_2, ...}] ...

Roots[lhs == rhs, var] yields a disjunction of equations which represent the roots of a polynomial equation.

SechDistribution[\[Mu], \[Sigma]] represents the hyperbolic secant distribution with location parameter \[Mu] and scale parameter \[Sigma].

SumConvergence[f, n] gives conditions for the sum \[Sum]_n^\[Infinity] f to be convergent.SumConvergence[f, {n_1, n_2, ...}] gives conditions for the multiple sum \[Sum]_n ...

Around 1870, Marius Sophus Lie realized that many of the methods for solving differential equations could be unified using group theory. Lie symmetry methods are central to ...

To begin, consider an initial value problem for a linear first-order ODE. This is a linear first-order ODE. Notice that the general solution is a linear function of the ...

The following is the sequence of steps that Mathematica follows in evaluating an expression like h[e_1,e_2…]. Every time the expression changes, Mathematica effectively ...

You can use lists as tables of values. You can generate the tables, for example, by evaluating an expression for a sequence of different parameter values. This gives a table ...

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 ...

All textual and graphical forms in Mathematica are ultimately represented in terms of nested collections of boxes. Typically the elements of these boxes correspond to objects ...