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38626 results in Cambridge Textbooks

Page 1844 of 1932

  • Appendix on Notation

  • Harold Jeffreys, University of Cambridge and St John's College, Cambridge, Bertha Jeffreys, Girton College, Cambridge
  • Book:
    Methods of Mathematical Physics
    Published online:
    12 September 2018
    Print publication:
    18 November 1999, pp 706-710

  • Summary

    The difficulty of learning mathematical physics is much increased by confusion of notation, especially the overworking of certain letters and the introduction of awkward sign conventions. The only criterion usually recognized is conformity with ‘standard practice’. Unfortunately standard practice is not unique and students are put to much unnecessary trouble by having to accustom themselves to work with different conventions in rapid succession. Research workers in border-line subjects are also inconvenienced by finding the usual symbols in one subject pre-empted for different meanings in another.

    The following principles are important in choosing conventions:

  • (1) Complications should be reduced to a minimum. Negative signs should not be introduced without good reason.

  • (2) Genuine physical differences should be recognized as such and not disguised as conventions; attempts to disguise them always lead to later difficulties that should have been forestalled.

  • (3) Where a mathematical theory has applications in several subjects the notation should be such that it can be carried over into those subjects unchanged; so far as possible it should not use symbols already used with other meanings in those subjects.

    • The outstanding difficulty of notation at present is the ambiguous use of Y and φ. V is used for potential energy, which is a property of a complete system, but also for the various potential functions, which are functions of position within the system. It is also used for Hamilton's characteristic function, and, in hydrodynamics, for a component of the velocity at a great distance.

Page 1844 of 1932