Re[z] gives the real part of the complex number z.

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, ...}] ...

lhs := rhs assigns rhs to be the delayed value of lhs. rhs is maintained in an unevaluated form. When lhs appears, it is replaced by rhs, evaluated afresh each time.

Sort[list] sorts the elements of list into canonical order. Sort[list, p] sorts using the ordering function p.

StringSplit["string"] splits " string" into a list of substrings separated by whitespace. StringSplit["string", patt] splits into substrings separated by delimiters matching ...

Applying transformation rules. The replacement operator /. (pronounced "slash-dot") applies rules to expressions. You can give a list of rules to apply. Each rule will be ...

When you make a definition in the form f[args]=rhs or f[args]:=rhs, Mathematica associates your definition with the object f. This means, for example, that such definitions ...

It is always a good idea to give variables and functions names that are as explicit as possible. Sometimes, however, such names may get inconveniently long. In Mathematica, ...

While differential equations have three basic types—ordinary (ODEs), partial (PDEs), or differential-algebraic (DAEs), they can be further described by attributes such as ...

NDSolve returns solutions as InterpolatingFunction objects. Most of the time, simply using these as functions does what is needed, but occasionally it is useful to access the ...