The Laplace Transformation (Lectures on Applied Mathematics, Volume 1) - ISBN:B0007F2FYM

The Laplace Transformation (Lectures on Applied Mathematics, Volume 1)

Date: 21 April 2011, 00:06

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ASIN: B0007F2FYM
This book is based on lectures, given at the Applied Mathematics Laboratory
of the David Taylor Model Basin. It ill devoted to the Laplace Transformation
and its application to linear ordinary differential equations with
variable coefficients, to linear partial differential equations, with two independent
variables and constant coefficients, and to the determination of
asymptotic series. The treatment of the Laplace Transformation is baaed
on the Fourier Integral Theorem and the ordinary different equations selected for
detailed treatment are those of Laguerre and Bessel. The
partial differential equation governing thc motion of a tightly stretched
vibrating string and a generalization of thia equation are fully treated.
Asymptotic series for the integral from p to infinity of exp (-z**2) dz and for the modified
Bessel function I_n(p), absolute value of arg p < (pi/2), are obtained by means of the
Laplace Transformation and finally, aymptotic series useful in the calculation
of the ordinary Bessel functions J_n(t) are treated.
Care has been taken to make the treatment self-contained, and details
of the proofs of the basic mathematical theorems are given.
Washington, D. C.
April 1962

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