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Titlebook: Differential Equations: Methods and Applications; Belkacem Said-Houari Textbook 2015 Springer International Publishing Switzerland 2015 Fi

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https://doi.org/10.1007/978-3-319-25735-8First order differential equations; Second order differential equations; Laplace transform; Power serie
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978-3-319-25734-1Springer International Publishing Switzerland 2015
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Differential Equations: Methods and Applications978-3-319-25735-8Series ISSN 2296-4568 Series E-ISSN 2296-455X
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Modelling and Definitions,mple applications of differential equations..An object of mass . is released from a certain height . above the ground and falls under the force of gravity . We want to write a mathematical model that describe the change of the height . with respect to time .. We assume that at time . = ., we know th
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Laplace Transforms,al differential equation into an algebraic expression which can then simply be transformed once again using the inverse Laplace transform into the solution of the original problem..Before entering into the details, let us first make a connection between the Laplace transform and the power series. We
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Power Series Solution,aracteristic equation. There is no similar procedure for solving linear differential equation with variable coefficients. The Laplace transform method that we studied in 4 can be an effective tool for some special cases, but as we have seen for the Laplace transform method, it is not always easy to
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Qualitative Theory,f solving general differential equations, we do not know the explicit solutions of many important differential equations or sometimes we need just to know some information about the solutions like their behavior when . (the independent variable) becomes very large. Furthermore, maybe it is not worth
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