The general solution to a differential equation contains undetermined coefficients that are labeled C[1], C[2], and so on. This example has one undetermined parameter, C[1]. ...

$MessageList is a global variable that gives a list of the names of messages generated during the evaluation of the current input line.

Goto[tag] scans for Label[tag], and transfers control to that point.

Compile[{x_1, x_2, ...}, expr] creates a compiled function that evaluates expr assuming numerical values of the x_i. Compile[{{x_1, t_1}, ...}, expr] assumes that x_i is of a ...

CompilationTarget is an option for Compile that specifies the target runtime for the compiled function.

Symbol["name"] refers to a symbol with the specified name.

"Introduction to Manipulate" and "Introduction to Dynamic" provide most of the information you need to use Mathematica's interactive features accessible through the functions ...

CheckAbort[expr, failexpr] evaluates expr, returning failexpr if an abort occurs.

SynchronousInitialization is an option for Manipulate, DynamicModule, and related functions that specifies whether or not to evaluate the expression given as the setting for ...

Parallelization is an option for Compile that specifies whether it should create a compiled function that could run in parallel.