Laplace Transform of Exponential Function

Explains how to calculate the Laplace Transform of an exponential.
Related videos: (see iaincollings.com)
• Laplace Transform Equation Explained: • Laplace Transform Equa...
• Laplace Transform Explained: • Laplace Transform Expl...
• Laplace Transform Region of Convergence Explained: • Laplace Transform Regi...
For a full list of Videos and accompanying Worksheets, see the associated website: iaincollings.com

[@mosman7800]

You're just a master of this subject❤

[@iain_explains]

I'm so glad you find the video helpful

[@zinhaboussi]

00:02 Laplace transform of an exponential function
01:03 Laplace transform is the integral of exponential function from negative to positive infinity.
02:17 The Fourier transform of the function times the unit step is the Laplace transform.
03:17 Laplace transform of exponential function involves a complex exponential with a growing amplitude.
04:18 Laplace transform of exponential function with different values of Sigma and a
05:21 Laplace transform is different from Fourier transform in weighting the function by an exponential with a sigma.
06:15 Laplace transform of exponential function with a negative out in front can be evaluated when the real part is positive.
07:04 Region of convergence in the S plane.
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[@adeddy8138]

I have shared your channel with everyone (especially the weak students) in my class except the topper😅

[@iain_explains]

I'm glad to hear the videos are being useful.

[@yuktikumari6042]

nice

[@Edu888777]

I get a bit confused.
Exponantial functions are always unstable right? Its growing only.
But the laplace transform of it found a region (from sigma) that it stable?

[@iain_explains]

The main feature of the Laplace Transform is that it can be done for signals that are unstable (in contrast to the Fourier transform that requires the function to have finite energy). Perhaps this video will help to explain it: "Laplace Transform Region of Convergence Explained" ua-cam.com/video/SexBL1OlhhU/v-deo.html

[@mnada72]

Please explain what do you mean by weighed function by sigma 2:55

[@iain_explains]

The "weighting" that I referred to, is the "damping" coefficient in the basis function. See this video for more details: "Laplace Transform Region of Convergence Explained" ua-cam.com/video/SexBL1OlhhU/v-deo.html