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Sumudu transform: A new integral transform to solve differential equations and control engineering problems. (English) Zbl 0768.44003
The author modifies the Laplace transform in the following form \(F(u) = (1/u)\int^ \infty_ 0 e^{-t/u}f(t)dt\), so that \(u\) and \(F(u)\) are no longer dummies but can be treated as replicas of \(t\) and \(f(t)\). It is even possible to express them in the same units as \(t\) and \(f(t)\) so that the consistency of units in a differential equation describing a physical process can be maintained even after transformation. A few properties of the modified transform are given and two applications are included as examples.

MSC:
44A15 Special integral transforms (Legendre, Hilbert, etc.)
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
44A10 Laplace transform
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References:
[1] Davis B., Integral Transforms and their Applications, Applied Mathematical Sciences 26 (1978)
[2] Sneddon I. N., The Use of Integral Transforms (1972) · Zbl 0237.44001
[3] Raven, F. H. 1977.Automatic Control Engineering, third edition, 122McGraw-Hill Kogakusha.
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