The Laplace transform is an extremely versatile technique for solving differential equations, both ordinary and partial. It con 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-Stiellies integral, yet of a level an undergraduate student can appreciate. When it comes to the deepest part of the theory, the complex inversion formula, knowledge of pales, residues, and contour integration of meromorphic functions is required. To this end, on entire chapter is devoted to the fundamentals of complex analysis. In addition to all the theoretical considerations, there ore numerous worked examples drown 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.