A Turing computable function is a function of an integral variable or a real or computable variable, computable predicates that can be computed by a Turing machine.  Turing machines are discussed in the mathematical an logical portion of article.

polynomial is a mathematical expression of one or more algebraic terms each of which consists of a constant multiplied by one or more variables raised to a nonnegative integral power.  The general form of a polynomial is a + bn +cn2.   For example, the function Babbage computed for the royal society was 41 + n+n2.

The term 'difference' came about from the principle used to evaluate such expressions: a mathematical technique called the Method of Differences, on which Babbage had carried out important work. By this technique all polynomial evaluation could, in principle, be reduced to addition.

Subroutines are sets of instructions for computing commonly used functions that can be called by the main program in the course of its execution.

Loops are repeated applications of a series of instructions.

Jumps are conditional branches of a program that allow it to move to another section of instructions when the if clause (antecedent) is satisfied.

Harmonic analysis is a mathematical procedure using integration to split up a complex waveform into several simple waveforms of which it is composed.

The term Isomorphic applies to mappings from one model to another model or set of objects as well as one system to another such that all of the relevant relations are preserved by the mapping.  Isomorphic state changes are changes that preserve a structure mapping from one thing to another across state changes.