2
votes
2answers
183 views

Prove that the Laplace trasform is a Linear trasformation

Could you help me prove that the Laplace Trasform is a Linear trasformation? Thank you.
6
votes
2answers
237 views

Usage of inverse Laplace transform

At my current study level in college, use of inverse Laplace transform is not mentioned well - textbooks say "use tables." So, can anyone show me how to use inverse Lapalce transform? And also proof? ...
0
votes
0answers
42 views

Invers laplace transform of resolvant using residues

I got that the inverse laplace of $\frac{1}{(s-λ)}$ is $e^{λt}$. Does this look correct?
2
votes
1answer
489 views

Fundamental matrix and exponential of matrix using Laplace Transform

I'm trying to work out how to find $$\exp(At)$$ for a system of linear differential equations $$x'=Ax.$$ I know that the solution is a fundamental matrix of the system such that $$\exp(At)=I$$ at ...
2
votes
1answer
173 views

laplace form and matrix exponential

Given the matrix $(I-A)^{-1}$ and $B$, can we compute $e^{A+B}$, where $e^X$ is defined to be $\sum_{i=0}^{\infty} \frac{X^i}{i!}$. (Note that $A$ and $B$ do not commute, and hence $e^A \cdot e^B ...