On Generalizations of the Initial and Terminal Value Theorems.
Palavras-chave:Initial and Terminal Value Theorems, Laplace Transform, Differential Equations.
The Initial and Terminal Value Theorems provide information about the limiting values of applications whose Laplace Transform is known. Such theorems, in addition to being relevant in their original form, are susceptible to generalizations that are also important. This article demonstrates the Initial and Terminal Value Theorems and their generalizations, studying these results for possible applications in Engineering and Physics. The novelty of this study is mainly in the presentation of the results. Despite being a review article, it presents proofs of theorems that are uncommon to be found in the literature. Therefore, this work contributes in the form of a complementary material for the study of the Laplace Transform and its applications.
I. V. L. Costa. “processos estocásticos: difusão e crescimento.” PhD thesis. UNB, 2006.
G. Doetsch and W. Nader. Introduction to the Theory and Application of the Laplace Transformation. New York: Springer-Verlag, 1974. isbn: 978-3540064077.
S. Haykin and B. Van Veen. Signals and Systems. John Wiley & Sons, 1998. isbn: 978- 0471138204.
D. J. Irwin and R. M. Nelms. Basic Engineering Circuit Analysis. Wiley, 2015. isbn: 978-1118539293.
B. P. Lathi. Signals, Systems and Communication. Wiley, 1966. isbn: 9780471518358.
A. V. Oppenheim, S. Hamid, and A. S. Willsky. Signals and Systems. Prentice Hall, 1996. isbn: 978-0138147570.
J. L. Schiff. The Laplace Transform: Theory and Applications. New York: Springer Science & Business Media, 1999. isbn: 0-387-98698-7.
M. R. Spiegel. Laplace Transforms. Schaum’s Outlines. New York: McGraw-Hill, 1965. isbn: 978-0070602311