Titlebook: Ordinary Differential Equations; William A. Adkins,Mark G. Davidson Textbook 2012 Springer Science+Business Media, LLC, part of Springer N

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https://doi.org/10.1007/978-1-4614-3618-8Laplace transform; discontinuous functions; existence theorem; first order differential equations; gener

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First Order Differential Equations,ic current, etc.) as a function of time. Frequently, the scientific laws governing such quantities are best expressed as equations that involve the rate at which that quantity changes over time. Such laws give rise to differential equations.

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The Laplace Transform,r μ(.) = e. chosen so that the left-hand side of the resulting equation becomes a perfect derivative (μ(.).).. Then the unknown function .(.) can be retrieved by integration. When .(.) = . is a constant, μ(.) = e. is an exponential function. Unfortunately, for higher order linear equations, there is not a corresponding type of integrating factor.

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Matrices,simultaneous system of linear equations. In this chapter, we will give a review of matrices, systems of linear equations, inverses, determinants, and eigenvectors and eigenvalues. The next chapter will apply what is learned here to linear systems of differential equations.

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978-1-4899-8767-9Springer Science+Business Media, LLC, part of Springer Nature 2012

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Ordinary Differential Equations978-1-4614-3618-8Series ISSN 0172-6056 Series E-ISSN 2197-5604

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William A. Adkins,Mark G. DavidsonContains numerous helpful examples and exercises that provide motivation for the reader.Presents the Laplace transform early in the text and uses it to motivate and develop solution methods for differ

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Second Order Constant Coefficient Linear Differential Equations,This chapter begins our study of second order linear differential equations, which are equations of the form . where .(.), .(.), .(.), called the ., and .(.), known as the ., are all defined on a common interval .. Equation (1) is frequently made into an . by imposing .: .(..) = .. and .(..) = .., where .. ∈ ..