Abstract
Methods by which physical laws can be converted into mathematical form as partial differential equations are discussed. Associated with these equations are boundary conditions, or the conditions to be applied at the interface between regions in which different regimes apply, represented by a discontinuity in some or all aspects of the variables describing the mathematical system. The manner in which the form of these conditions can be deduced is considered. The principles described are illustrated by application to some of the physical laws at the centre of laser technology.
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Notes
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Indeed, Galileo went even further. The Assayer contains his well-known statement that mathematics is the language of God (https://en.wikipedia.org/wiki/The_Assayer).
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Dowden, J. (2017). Mathematics in Laser Processing. In: Dowden, J., Schulz, W. (eds) The Theory of Laser Materials Processing. Springer Series in Materials Science, vol 119. Springer, Cham. https://doi.org/10.1007/978-3-319-56711-2_1
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DOI: https://doi.org/10.1007/978-3-319-56711-2_1
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