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Laplace Transform and Solving Second Order Linear Differential Equations with Applications Name Professor Subject Date Laplace Transform and Solving Second Order Linear Differential Equations with Applications Introduction This paper aims at presenting facts and derivatives of the Applications of Laplace Transform in solving Ordinary Differential Equations (ODE) with constant coefficients. Laplace Transform Function ~ K The main tool I will use to accomplish this includes the following property from differential and integral calculus (Bellman & Roth 2013).: Transform of Derivatives 50 Differentiation. Let K {f(w)} = F(z) Then according to Dyke K {f ′ (w) } = zF(z) − f(0) K { f ′′(w) } = z 2K(z) − zf(0) − f ′ (0). Now consider a second order IVP – Initial Value Problem x ′′ + px′ + qx = f(w) x(0) = x0 x′ (0) = y1………………… (i) Transform of the Second Derivative Now I want to the differential equation a= dv/dt= g-(gv/275). Question 3. A weight that hangs from a spring is pulled down 0.500 cm at t=0 and released from rest. The differential equation of motion is x" + 3.22x' + 18.5=0. Write the equation for x as a function of time. Bibliography Bellman R. & Roth R. (2013). The Laplace transform. Singapore: World Scientific. Dyke P. (2014). An Introduction to Laplace Transforms and Fourier Series. (An Introduction to Laplace Transforms and Fourier Series.) London: Springer. Gardner M. F. & Barnes J. L. (1965). Transients in linear systems: Studied by the Laplace transformation. New York. Jaeger J. C. & Newstead G. (1970). An introduction to the Laplace transformation with engineering applications. New York: Barnes & Noble. LePage W. R. (2012). Complex Variables and the Laplace Transform for Engineers. Dover Publications. Pol B & Bremmer H. (2008). Operational calculus: Based on the two-sided Laplace integral. Cambridge: Cambridge University Press. [...]
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Laplace Transform and Solving second order Linear Differential Equations with Applications The Laplace transform of a function, transform of a derivative, transform of the second derivative, transform of an integral, table of Laplace transform for simple functions, the inverse Laplace transform, solving first order linear differential equations by the Laplace transfor Applications: Damped motion of an object in a fluid [mechanical, electromechanical]
Subject Area: Mathematics
Document Type: Dissertation Proposal
