This chapter provides a compact, self-contained introduction to the Laplace transform, a powerful technique that can be applied with ease to a wide variety of time-dependent problems. Rather than strive for the greatest generality, this introduction addresses only those simplest properties that are most useful for the solution of diffusion problems. Only elementary methods of calculus are used, and integration in the complex plane is avoided altogether. It follows that questions regarding analyticity, the inversion integral, and asymptotic behavior cannot be completely answered, although some such properties will be demonstrated.N1
KeywordsDiffusion Equation Image Space Original Function Image Function Laplace Transform
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- 1.M. R. Spiegel, Theory and Problems of Laplace Transforms (Schaum Publishing Co., New York, 1965).Google Scholar