Synopses & Reviews
The Laplace transform is an extremely versatile technique for solving differential equations, both ordinary and partial. It can also be used to solve difference equations. The present text, while mathematically rigorous, is readily accessible to students of either mathematics or engineering. Even the Dirac delta function, which is normally covered in a heuristic fashion, is given a completely justifiable treatment in the context of the Riemann-Stieltjes integral, yet at a level an undergraduate student can appreciate. When it comes to the deepest part of the theory, the Complex Inversion Formula, a knowledge of poles, residues, and contour integration of meromorphic functions is required. To this end, an entire chapter is devoted to the fundamentals of complex analysis. In addition to all the theoretical considerations, there are numerous worked examples drawn from engineering and physics. When applying the Laplace transform, it is important to have a good understanding of the theory underlying it, rather than just a cursory knowledge of its application. This text provides that understanding.
"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. ZENTRALBLATT MATH"
"The book contains plenty of examples, exercises (with answers at the end) and a table of transforms. The book is certainly a handsome introduction to the Laplae transform, by its clear representation well-suited for self-study." Nieuw Archief voor Wiskunde, March 2001 "This clearly written undergraduate textbook can be recommended to students and teachers of this subject, both in a mathematial and engineering context." Newsletter of the EMS, issue 42, December 2001
Includes bibliographical references (p. 207-208) and index.
Table of Contents
Basic Principles.- Applications and Properties.- Complex Variable Theory.- Complex Inversion Formula.- Partial Differential Equations.- Appendix.- References.