The Quarterly Journal of Mechanics and Applied Mathematics · 1959 · 28 citations · 0 references
Natural SciencesMathematicsDifferential EquationsIntegral Equation FormulationsIntegral EquationsLaplace Transform MethodsMethod Of MomentsSystems Of Differential EquationsLaplace TransformLaplace Transform AnalysisLaplace Transforms Of Differential EquationsLinear Time-invariant System ResponseSystem Response Analysis
For cases when the functions x(t) and y(t) have rational Laplace transforms, simple methods are presented for the evaluation of the integrals ∫0∞xy dt and ∫0∞x2 dt in terms of the transform coefficients. The results are extended to the moment integrals ∫0∞trxy dt and ∫0∞trx2 dt, Where r = 1,2,…