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Laplace equation:
in 3D U_xx+U_yy+U_zz=0
Or in 2D U_xx+U_yy=0 where U is a function of the spatial variables x,y,z in 3D and x,y in 2D.Also, U_xx is the second order partial derivative of u with respect to x, same for y and z.
Laplace transform:
L(f(t))=integral of (e^(-s*t))*f(t) dt as t goes from 0 to infinity. Laplace transform is more like an operator rather than an equation.
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The Laplace transform of sin3t?
find Laplace transform? f(t)=sin3t
What is the difference between Fourier transform and Laplace transform and z transform?
Fourier transform and Laplace transform are similar. Laplace transforms map a function to a new function on the complex plane, while Fourier maps a function to a new function on the real line. You can view Fourier as the Laplace transform on the circle, that is |z|=1. z transform is the discrete version of Laplace transform.
What is the difference between the fourier laplace transform?
They are similar. In many problems, both methods can be used. You can view Fourier transform is the Laplace transform on the circle, that is |z|=1. When you do Fourier transform, you don't need to worry about the convergence region. However, you need to find the convergence region for each Laplace transform. The discrete version of Fourier transform is discrete Fourier transform, and the discrete version of Laplace transform is Z-transform.
What kind of response is given by laplace transform analysis?
The type of response given by Laplace transform analysis is the frequency response.
Can a discontinuous function have a laplace transform?
Sure! The definition of Laplace transform involves the integral of a function, which always makes discontinuous continuous.
