Laplace's Transform for Solving System of Ordinary Differential Equations

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الملخص

The idea of the Laplace’s transform has a profound influence over the development of mathematical analysis. It also plays a significant role in mathematical applications. More generally, the overall theory of transforms has become an important part of modern mathematics. Anotherway of looking at the Laplace transform is as mapping from points in the T domain to points is the S domain. Two aspects of Laplace transform are: the variable S often has to take complex values. This means that f(s) is a function of a complex variable. The Laplace transform has many interesting and useful properties, the most fundamental of which is linearity. It is linearity that enables researchers to add results together to deduce more complicated ones. Another important property is the shift rules of the Laplace transform that do not involve in calculus. The first of these takes the form of another theorem because of its generality. The Laplace transform of functions of exponential order was considered like the hyperbolic functions sinh(pt), cosh(pt) and the trigonometric functions sin(pt) and cos(pt). The Laplace transform of the other trigonometric functions tan, cat, sec, cosec, does not exist as they all have singularities for finite t.Also the Laplace transform was considered to be a special function like Dirac delta function δ(f) and Heaviside function H(t). An important resultwas that the Laplace transform of derivatives of functions, since every differential equation involves some derivatives. Laplace transform was used here for solving linear differential equations and a system of linear differential equations coupled by taking Laplace transform to the differential equation and then taking the inverse of Laplace transforms to find the solution of the differential equations. Theresidue theorem was also applied to evaluate the inverse of Laplace transforms for some functions. We recommend that to apply Laplace transform to systems of more than two coupled differential equations.

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f3bc41de-7808-4a05-8e2a-5ac719d4dedc

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0

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Crawler

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الرسائل العلمية

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رسائل ماجيستير

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pdf text

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73176_1.pdf

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[{"name_ar":"عبد الله بشير موسى","title_ar":"اشراف","title_en":"Supervision"},{"name_ar":"عمر الصديق بشير الزين","title_ar":"اعداد","title_en":"Preparation"},{"name_ar":"محمد حسن محمد خبير","title_ar":"اشراف","title_en":"Supervision"}]

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English

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اسم المصدر

Laplace's Transform for Solving System of Ordinary Differential Equations

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عبد الله بشير موسى, محمد حسن محمد خبير

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عمر الصديق بشير الزين

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