The Laplace transform is a wonderful tool for solving ordinary and partial differential equations, and has enjoyed much success in this realm. But with its success, a certain casualness has been bred concerning its application, without much regard for hypotheses and when they are valid. In the present text, the author brings to the subject a certain amount of mathematical correctness and makes it accessi ble to undergraduates. To this end the text addresses a number of issues which are rarely considered. Special features of the book include a justification of the Laplace Transform method for solving linear ODEs, sufficient conditions for taking the Laplace Transform of an infinite series, steady-state solutions, and a rigorous approach to the Complex Inversion Formula, to name but a few.

Preliminary Text. Do not use. The Laplace transform is a wonderful tool for solving ordinary and partial differential equations, and has enjoyed much success in this realm. But with its success, a certain casualness has been bred concerning its application, without much regard for hypotheses and when they are valid. In the present text, the author brings to the subject a certain amount of mathematical correctness and makes it accessible to undergraduates.

Autorentext

Joel L. Schiff has a PhD in Mathematics from the University of California Los Angeles (UCLA). He has spent his career at the University of Auckland, Auckland, New Zealand and written eight books on mathematical and scientific subjects including astronomy. With colleague Wayne Walker, he helped developed the Arithmetic Fourier Transform used in signal processing. The author was also the founder publisher of the international journal Meteorite, and in 1999, he and his wife discovered a new asteroid from their backyard observatory. They named it after notable New Zealand meteorite scientist, Brian Mason. As well, the author has for years done astrometrical observations of Near-Earth Asteroids that are sent to the database maintained by the Center for Astrophysics/Harvard & Smithsonian.

Zusammenfassung
For instance, when we apply the Laplace trans form method to a linear ordinary differential equation with constant coefficients, any(n) + an-lY(n-l) + * * * + aoy = f(t), why is it justified to take the Laplace transform of both sides of the equation (Theorem A.

Inhalt
1 Basic Principles.- 2 Applications and Properties.- 3 Complex Variable Theory.- 4 Complex Inversion Formula.- 5 Partial Differential Equations.- References.- Tables.- Laplace Transform Operations.- Table of Laplace Transforms.- Answers to Exercises.