Understanding Laplace Transform: Step 1 to 2 Difficulty

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SUMMARY

The discussion focuses on the challenges faced in understanding the transition from step 1 to step 2 in the application of the Laplace Transform. The user simplifies the expression e^(3-s)t to N, leading to the conclusion that the answer involves evaluating limits and derivatives. The key takeaway is that when t=0, e^{(3-s)t} equals 1, not 0, which is crucial for correctly solving the problem. This highlights the importance of careful limit evaluation in Laplace Transform calculations.

PREREQUISITES
  • Understanding of Laplace Transform fundamentals
  • Familiarity with limit evaluation techniques
  • Basic knowledge of exponential functions
  • Experience with calculus, particularly derivatives
NEXT STEPS
  • Study the properties of the Laplace Transform in detail
  • Learn about limit evaluation in calculus
  • Explore the application of exponential functions in differential equations
  • Practice solving Laplace Transform problems with varying initial conditions
USEFUL FOR

Students studying engineering or mathematics, particularly those tackling differential equations and Laplace Transforms, as well as educators looking for insights into common student misconceptions.

robertjford80
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Homework Statement



Screenshot2012-06-05at55352AM.png


The Attempt at a Solution



I can understand step 2 to 3, but I can't get step 1 to 2. For simplicity sake we'll just call e^(3-s)t = N since it will = N anyway ultimately.

I think the answer should be

[N/3-s - 1/(3-s)^2)N - (0 - 1/(3-s)^2)0

The second term is still multiplied by zero. So the answer should be infinity.
 
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Your variable is t. And its limits are from 0 to N. When t=0, you have

[tex]e^{(3-s)t} = e^0 = 1[/tex]

And not 0, as you got...
 
of course, how could i have forgotten.
 

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