L{f;je*sin(t- t)dr}.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Find the Laplace Transform. Given solution: 1/(s-1) * 1/(s^2+1)
![The image displays the following mathematical expression:
\[ \mathcal{L} \left\{ \int_{0}^{t} e^{\tau} \sin(t - \tau) \, d\tau \right\}. \]
This expression represents the Laplace transform of the integral of the function \( e^{\tau} \sin(t - \tau) \) with respect to \( \tau \) over the interval from 0 to \( t \).
- \(\mathcal{L}\{\}\) denotes the Laplace transform operator.
- \(\int_{0}^{t}\) signifies the definite integral from 0 to \( t \).
- \( e^{\tau} \) and \(\sin(t - \tau)\) are the exponential and sine functions, respectively, as part of the integrand.
This type of expression is often encountered in the analysis of linear time-invariant systems and differential equations. It involves both convolution and transformation techniques, which are fundamental concepts in engineering and applied mathematics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F64800780-3a27-40b8-a11a-6cbcd87af243%2F32018f9f-b489-4796-ad6d-80ab605f7d87%2Fdwpldj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image displays the following mathematical expression:
\[ \mathcal{L} \left\{ \int_{0}^{t} e^{\tau} \sin(t - \tau) \, d\tau \right\}. \]
This expression represents the Laplace transform of the integral of the function \( e^{\tau} \sin(t - \tau) \) with respect to \( \tau \) over the interval from 0 to \( t \).
- \(\mathcal{L}\{\}\) denotes the Laplace transform operator.
- \(\int_{0}^{t}\) signifies the definite integral from 0 to \( t \).
- \( e^{\tau} \) and \(\sin(t - \tau)\) are the exponential and sine functions, respectively, as part of the integrand.
This type of expression is often encountered in the analysis of linear time-invariant systems and differential equations. It involves both convolution and transformation techniques, which are fundamental concepts in engineering and applied mathematics.
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Advanced Engineering Mathematics](https://www.bartleby.com/isbn_cover_images/9780470458365/9780470458365_smallCoverImage.gif)
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
![Numerical Methods for Engineers](https://www.bartleby.com/isbn_cover_images/9780073397924/9780073397924_smallCoverImage.gif)
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
![Introductory Mathematics for Engineering Applicat…](https://www.bartleby.com/isbn_cover_images/9781118141809/9781118141809_smallCoverImage.gif)
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
![Mathematics For Machine Technology](https://www.bartleby.com/isbn_cover_images/9781337798310/9781337798310_smallCoverImage.jpg)
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
![Basic Technical Mathematics](https://www.bartleby.com/isbn_cover_images/9780134437705/9780134437705_smallCoverImage.gif)
![Topology](https://www.bartleby.com/isbn_cover_images/9780134689517/9780134689517_smallCoverImage.gif)