/tü ā fərst ə-präk-sə-mā-shən/

1. [techspeak] When one is doing certain numerical computations, an approximate solution may be computed by any of several heuristic methods, then refined to a final value. By using the starting point of a first approximation of the answer, one can write an algorithm that converges more quickly to the correct result.

2. In jargon, a preface to any comment that
indicates that the comment is only approximately true. The remark
"*To a first approximation, I feel good*" might indicate that
deeper questioning would reveal that not all is perfect (e.g., a
nagging cough still remains after an illness).