Application of Laplace Transform

The temperature distribution in a semi-infinite bar that is heated at one end is described by the solution of the following problem  

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Other applications of Laplace transforms are given under Differential Equations. ... 

Let us first state a few important points about the application of Laplace transform in solving differential equations (Fig. 2.1). After we have formulated a model in terms of a linear or linearized differential equation, dy/dt = f(y), we can solve for y(t). Alternatively, we can transform the equation into an algebraic problem as represented by the function G(s) in the Laplace domain and solve for Y(s). The time domain solution y(t) can be obtained with an inverse transform, but we rarely do so in control analysis. 

Applications of Laplace Transforms for Drug Degradation and Biotransformation... 

We can illustrate the application of Laplace transforms by using them to solve the simple differential equation that we have used to describe the singlecompartment model (Equation 2.7). Starting with this equation/... 

By his application of Laplace transforms to the transient response of electrical circuits, Oliver Heaviside created the foimdation for impedance spectroscopy. Heaviside coined the words inductance, capacitance, and impedance and introduced these concepts to the treatment of electrical circuits. His papers on the subject, published in The Electrician beginning in 1872, were compiled by Heaviside in book form in 1894.6/7 pj-om the perspective of the application to physical systems, however, the history of impedance spectroscopy begins in 1894 with the work of Nemst. ... 

Applications of Laplace Transforms for Solutions of ODE 369 The dynamic material balance for constant volumetric flow is... 

In safety studies, linear first-order differential equations are sometime solved. Laplace transforms are a useful tool for solving a set of linear first-order differential equations. The application of Laplace transforms to solve a set of linear first-order differential equations describing a patient safety problem in a health care facility is demonstrated through the following example. 

In this chapter we have considered the application of Laplace transform techniques to solve linear differential equations. Although this material may be a review for some readers, an attempt has been made to concentrate on the important properties of the Laplace transform and its inverse, and to point out the techniques that make manipulation of transforms easier and less prone to error. 

The application of Laplace transforms to the analytical solution of complicated differential kinetic laws is simplified significantly on the basis of three of its fundamental... 

As an example of application of Laplace transforms to complex reaction schemes, consider the consecntive first-order reversible reactions... 

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