- Worcester, United States
Siddhant Pandey
Worcester Polytechnic Institute, Physics, Undergraduate
This pedagogical article discusses the existence of the Inverse Laplace Transform. To prove that the Inverse Laplace Transform exists, it needs to be proven that the Laplace Transform is bijective. To this end, it needs to be proven that... more
This pedagogical article discusses the existence of the Inverse Laplace Transform. To prove that the Inverse Laplace Transform exists, it needs to be proven that the Laplace Transform is bijective. To this end, it needs to be proven that the Transform is injective and surjective. Surjectivity of the Laplace Transform can be achieved by limiting our co-domain to the set of functions which are the Laplace Transforms of some well-behaved functions. The only thing left to prove then is the injectivity of the Laplace Transform.
Research Interests:
We will use FEM to convert a one-dimensional Poisson-like second order ODE into a matrix equation, which can be further solved numerically.
Research Interests:
A brief reference to the functional derivative.