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Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![The image contains a mathematical equation and exercises related to the Laplace transform. The focus is on transforming functions and understanding the concept using exercises:
## Transcription
---
**Mathematical Equation:**
\[
F(s) = \frac{1}{s - 2} e^{-3s}
\]
**Explanation under the Equation:**
The highlighted section mentions, "right signals the switching property. We know from the..."
---
**Exercises:**
The exercises contain many examples of illustrating the preceding concepts and extending the Laplace transformation to additional functions.
**EXERCISES**
1. Use the definition of the Laplace transform to compute the transform of the square pulse function \( x(t) = 1, \; 1 \leq t \leq 2; \; x(t) = 0, \) otherwise. Plot \( x(t) \) on \( t \geq 0, \) and plot its transform \( X(s). \)
---
This content serves as an educational guide to understanding the application of Laplace transforms through practical exercises.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc10cce41-ef51-4545-a724-9736e236d3b7%2Fc05de677-b48a-4061-9329-832f17ee77e4%2F3gc5xep_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains a mathematical equation and exercises related to the Laplace transform. The focus is on transforming functions and understanding the concept using exercises:
## Transcription
---
**Mathematical Equation:**
\[
F(s) = \frac{1}{s - 2} e^{-3s}
\]
**Explanation under the Equation:**
The highlighted section mentions, "right signals the switching property. We know from the..."
---
**Exercises:**
The exercises contain many examples of illustrating the preceding concepts and extending the Laplace transformation to additional functions.
**EXERCISES**
1. Use the definition of the Laplace transform to compute the transform of the square pulse function \( x(t) = 1, \; 1 \leq t \leq 2; \; x(t) = 0, \) otherwise. Plot \( x(t) \) on \( t \geq 0, \) and plot its transform \( X(s). \)
---
This content serves as an educational guide to understanding the application of Laplace transforms through practical exercises.
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