Using infinite series and complex numbers to derive formulas involving Laplace transforms

• Autores: David E. Dobbs
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 44, Nº. 5, 2013, págs. 752-761
• Idioma: inglés
• DOI: 10.1080/0020739x.2012.756551
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• Resumen

  • The formula for the Laplace transform of an exponential function, , can be derived with equal ease if the parameters aand sare complex numbers. This leads to formulas for the Laplace transforms of eatsin?(bt) and eatcos?(bt) (where aand bare complex) and to calculations of certain inverse Laplace transforms without the need to consider Laplace transforms of derivatives or convolutions. Simpler proofs also follow from coupling the formula , for which a simple proof is given, with the fact that the operator commutes with certain familiar infinite series.