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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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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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2012
The method for solving a first order linear differential equation \(y^{\prime} + p(t)y = f(t)\) (Algorithm 3 of Sect. 5) involves multiplying the equation by an integrating factor μ(t) = e∫p(t) dt chosen so that the left-hand side of the resulting equation becomes a perfect derivative (μ(t)y)′.
William A. Adkins, Mark G. Davidson
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The method for solving a first order linear differential equation \(y^{\prime} + p(t)y = f(t)\) (Algorithm 3 of Sect. 5) involves multiplying the equation by an integrating factor μ(t) = e∫p(t) dt chosen so that the left-hand side of the resulting equation becomes a perfect derivative (μ(t)y)′.
William A. Adkins, Mark G. Davidson
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The Mathematical Gazette, 1963
In technical colleges one is often called upon to introduce advanced mathematical techniques to students whose background is not very extensive. Such a method is the use of the Laplace Transform for the solution of linear differential equations with constant coefficients.
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In technical colleges one is often called upon to introduce advanced mathematical techniques to students whose background is not very extensive. Such a method is the use of the Laplace Transform for the solution of linear differential equations with constant coefficients.
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