zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
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 $F(u) = (1/u)\int\sp \infty\sb 0 e\sp{-t/u}f(t)dt$, 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.

44A15Special transforms (Legendre, Hilbert, etc.)
34A25Analytical theory of ODE (series, transformations, transforms, operational calculus, etc.)
44A10Laplace transform
Full Text: DOI