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Introduction to the Laplace Transform
1993Publisher Summary This chapter provides an overview of the Laplace transform. It presents a list of Laplace transforms of frequently used functions. The Laplace transform has many operational properties. Apart from these operational properties, the chapter highlights additional frequently used properties of the Laplace transform as well.
Martha L. Abell, James P. Braselton
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New identities for the Wright and the Mittag-Leffler functions using the Laplace transform
, 2014In this paper, we state three theorems for the inverse Laplace transform and using these theorems we obtain new integral identities involving the products of the Wright and Mittag-Leffler functions. The relationships of these integral identities with the
A. Ansari, A. Sheikhani
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1965
In Part I we confined our attention to the use of the Laplace transform to continuous functions. We now consider discontinuous functions.
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In Part I we confined our attention to the use of the Laplace transform to continuous functions. We now consider discontinuous functions.
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2009
Although the Fourier transform has been shown to be a useful tool in a variety of applications, there are others for which it is not particularly well suited. Generally these other applications involve initial value problems for which the auxiliary data are prescribed at t=0 .
Bhimsen K. Shivamoggi, Larry C. Andrews
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Although the Fourier transform has been shown to be a useful tool in a variety of applications, there are others for which it is not particularly well suited. Generally these other applications involve initial value problems for which the auxiliary data are prescribed at t=0 .
Bhimsen K. Shivamoggi, Larry C. Andrews
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2010
This chapter presents the main properties and applications of the Laplace transform. One important applicative strength of the Laplace method is the conversion of linear ordinary differential equations (ODE) into algebraic equations by means of the direct Laplace transform, which enables calculation of the transformed solution with relative ease ...
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This chapter presents the main properties and applications of the Laplace transform. One important applicative strength of the Laplace method is the conversion of linear ordinary differential equations (ODE) into algebraic equations by means of the direct Laplace transform, which enables calculation of the transformed solution with relative ease ...
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1995
Publisher Summary This chapter focuses on Laplace transformation. The chapter defines the Laplace transform and reviews its basic properties. The Dirac delta function δ(x) and the Laplace transform pairs are also reviewed. The Dirac delta function δ(x) is particularly useful when working with the Laplace transform.
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Publisher Summary This chapter focuses on Laplace transformation. The chapter defines the Laplace transform and reviews its basic properties. The Dirac delta function δ(x) and the Laplace transform pairs are also reviewed. The Dirac delta function δ(x) is particularly useful when working with the Laplace transform.
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Nature, 1957
Handbuch der Laplace-Transformation Von Prof. Gustav Doetsch. Band 2: Anwendungen der Laplace-Transformation. 1 Abteilung. (Lehrbucher und Monographien aus dem Gebiete der Exakten Wissenschaften. Mathematische Reihe, Band 15.) Pp. 436. (Basel und Stuttgart: Birkhauser Verlag, 1955.) 56.15 Swiss francs; 56.15 D. marks.
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Handbuch der Laplace-Transformation Von Prof. Gustav Doetsch. Band 2: Anwendungen der Laplace-Transformation. 1 Abteilung. (Lehrbucher und Monographien aus dem Gebiete der Exakten Wissenschaften. Mathematische Reihe, Band 15.) Pp. 436. (Basel und Stuttgart: Birkhauser Verlag, 1955.) 56.15 Swiss francs; 56.15 D. marks.
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, 2002 In this chapter, we give the definition of the Laplace transform and derive some of its more important properties, including a result on its asymptotic behavior known as Watson’s lemma. The results given in this chapter may be found in many places. Some classic books are Ditkin and Prudnikov [20], Doetsch [22], and Widder [73].
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2011
In this chapter we begin the use of transformations for the representation and analysis of continuous-time signals and systems. The Laplace transform is obtained when applying complex exponentials or eigenfunctions to linear time-invariant (LTI) systems.
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In this chapter we begin the use of transformations for the representation and analysis of continuous-time signals and systems. The Laplace transform is obtained when applying complex exponentials or eigenfunctions to linear time-invariant (LTI) systems.
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2006
With the advent of television and radar during the Second World War, the behavior of wideband amplifiers in the time domain has become very important [Ref. 1.1]. In today’s digital world this is even more the case. It is a paradox that designers and troubleshooters of digital equipment still depend on oscilloscopes, which — at least in their fast and ...
Peter Starič, Erik Margan
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With the advent of television and radar during the Second World War, the behavior of wideband amplifiers in the time domain has become very important [Ref. 1.1]. In today’s digital world this is even more the case. It is a paradox that designers and troubleshooters of digital equipment still depend on oscilloscopes, which — at least in their fast and ...
Peter Starič, Erik Margan
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