# An Evolutionary Introduction to Laplace Transforms

## Related Articles

- Functional calculus via Laplace transform and equations with infinitely many derivatives. Górka, P.; Prado, H.; Reyes, E. G. // Journal of Mathematical Physics;Oct2010, Vol. 51 Issue 10, p103512
We study nonlocal linear equations of the form f(âˆ‚t)[lowercase_phi_synonym]=J(t), tâ‰¥0, in which f is an entire function. We develop an appropriate functional calculus via Laplace transform, we solve the aforementioned equation completely in the space of exponentially bounded...

- LAPLACE TRANSFORM AND GENERALIZED HYERS-ULAM STABILITY OF LINEAR DIFFERENTIAL EQUATIONS. ALQIFIARY, QUSUAY H.; SOON-MO JUNG // Electronic Journal of Differential Equations;2014, Vol. 2014, p1
By applying the Laplace transform method, we prove that the linear differential equation ... has the generalized Hyers-Ulam stability, where Î±k is a scalar, y and f are n times continuously differentiable and of exponential order.

- Increasing smoothness of solutions to a hyperbolic system on the plane with delay in the boundary conditions. Lyul'ko, N. A. // Siberian Mathematical Journal;Nov2008, Vol. 49 Issue 6, p1062
Under consideration is a mixed problem in the half-strip Î = {( x, t): 0 < x < 1, t > 0} for a first order homogeneous linear hyperbolic system with delay in t in the boundary conditions. We study the behavior of the Laplace transform of a solution to this problem for the large values of the...

- SKEW LAPLACE DISTRIBUTIONS. I. THEIR ORIGINS AND INTER-RELATIONS. Kozubowski, Tomasz J.; Podgorski, Krzysztof // Mathematical Scientist;Jun2008, Vol. 33 Issue 1, p22
There are numerous asymmetric extensions of the classical Laplace distribution scattered in the literature. In this survey we discuss their origins and inter-relations. In particular, we point out which types of skew Laplace distributions are essentially the same, described in different, albeit...

- PRETRIGONOMETRIC AND PREHYPERBOLIC FUNCTIONS VIA LAPLACE TRANSFORMS. Khandeparkar, Ramkrishna B. // Neural, Parallel & Scientific Computations;Sep-Dec2010, Vol. 18 Issue 3/4, p423
The article presents a study that examines Laplace transforms of pretrigonometric, prehyperbolic and extended pretrigonometric and prehyperbolic functions. It uses Laplace transform method to solve initial value problems for second order non-homogenous differential equation and to solve matrix...

- Limit Lognormal Multifractal as an Exponential Functional. Ostrovsky, Dmitry // Journal of Statistical Physics;Sep2004, Vol. 116 Issue 5/6, p1491
The limiting distribution of the limit lognormal multifractal, first introduced by Mandelbrot (Statistical Models and Turbulence, M. Rosenblatt and C. Van Atta, eds., Lecture Notes in Physics 12, Springer, New York, 1972, p. 333) and constructed explicitly by Bacry et al. (Phys. Rev. E 64,...

- Laplace-Type Semi-Invariants for a System of Two Linear Hyperbolic Equations by Complex Methods. Mahomed, F. M.; Qadir, A.; Ramnarain, A. // Mathematical Problems in Engineering;2011, Vol. 2011, Special section p1
In 1773 Laplace obtained two fundamental semi-invariants, called Laplace invariants, for scalar linear hyperbolic partial differential equations (PDEs) in two independent variables. He utilized this in his integration theory for such equations. Recently, Tsaousi and Sophocleous studied...

- Two-sided Laplace transform over Cayley-Dickson algebras and its applications. Ludkovsky, S. // Journal of Mathematical Sciences;Jul2008, Vol. 151 Issue 5, p3372
The article presents the role of the classical Laplace transform in complex analysis and its various applications, including differential equations. It mentions a noncommutative analog of the classical Laplace transform and its new types over the Cayley-Dickson algebra. Moreover, results on the...

- A new Mathematical Equation for Pressure Transient Analysis of Naturally Fractured Vuggy Reservoirs. Lijun Zhang; Shiqing Cheng; Junling Wang // AIP Conference Proceedings;5/21/2010, Vol. 1233 Issue 1, p1630
For the existence of certain large size vugs and fractures in some reservoirs such as Tahe oilfield and the fact that the fluid flow in these mediums is inconsistent with Darcy-flow, new pressure transient models are established for these reservoirs. The numerical inversion method in Laplace...