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The Laplace transform: Theory and applications. (English) Zbl 0934.44001
Undergraduate Texts in Mathematics. New York, NY: Springer. xiv, 233 p. DM 79.00; öS 577.00; sFr. 72.00; £ 27.00; $ 39.95 (1999).
This remarkable textbook for students of either mathematics or engineering deals with a rigorous, but well readable, treatment of the basic properties of the Laplace transform and its applications to various types of equations up to partial differential equations, in particular to those stemming from physics and engineering. The necessary mathematical remedies are explained in detail, e.g. the elements of the theory of analytical functions and those of the Riemann-Stieltjes integral in order to have a rigorous basis for the treatment of the complex inversion formula and the Dirac delta function, respectively. The book contains several exercises with solutions and a table of the usual Laplace transforms. Let us mention that $s^{-1}\log s$ on p. 156 does satisfy (4.8), and that the complicated conditions of Theorem 4.3 are equivalent to the requirement that $F(s)$ is a proper rational function.

44A10Laplace transform
44-01Textbooks (integral transforms)
35A22Transform methods (PDE)
00A06Mathematics for non-mathematicians