We are here with you hands in hands to facilitate your learning & don't appreciate the idea of copying or replicating solutions. Read More>>

www.vustudents.ning.com

 www.bit.ly/vucodes + Link For Assignments, GDBs & Online Quizzes Solution www.bit.ly/papersvu + Link For Past Papers, Solved MCQs, Short Notes & More

Dear Students! Share your Assignments / GDBs / Quizzes files as you receive in your LMS, So it can be discussed/solved timely. Add Discussion

# Mth 301 GDB

Only idea

+ How to Join Subject Study Groups & Get Helping Material?

+ How to become Top Reputation, Angels, Intellectual, Featured Members & Moderators?

+ VU Students Reserves The Right to Delete Your Profile, If?

Views: 372

.

+ http://bit.ly/vucodes (Link for Assignments, GDBs & Online Quizzes Solution)

+ http://bit.ly/papersvu (Link for Past Papers, Solved MCQs, Short Notes & More)

Attachments:

### Replies to This Discussion

Innocent Genious Thanks for sharing ur idea

Note for All Members: You don’t need to go any other site for this assignment/GDB/Online Quiz solution, Because All discussed data of our members in this discussion are going from here to other sites. You can judge this at other sites yourself. So don’t waste your precious time with different links.

MTH301 GDB SOLUTION 1 FALL2012

What are the algebraic advantageous applications of Laplace and Fourier Transforms? Give just one example with proper explanation.

solution:

The Laplace transform is a widely used integral transform with many applications in physics and engineering. Denoted , it is a linear operator of a function f(t) with a real argument t (t ≥ 0) that transforms it to a function F(s) with a complex argument s. This transformation is essentially bijective for the majority of practical uses; the respective pairs of f(t) and F(s) are matched in tables. The Laplace transform has the useful property that many relationships and operations over the originals f(t) correspond to simpler relationships and operations over the images F(s).[1] It is named after Pierre-Simon Laplace, who introduced the transform in his work on probability theory.

The Laplace transform is related to the Fourier transform, but whereas the Fourier transform expresses a function or signal as a series of modes of vibration (frequencies), the Laplace transform resolves a function into its moments. Like the Fourier transform, the Laplace transform is used for solving differential and integral equations. In physics and engineering it is used for analysis of linear time-invariant systems such as electrical circuits, harmonic oscillators, optical devices, and mechanical systems. In such analyses, the Laplace transform is often interpreted as a transformation from the time-domain, in which inputs and outputs are functions of time, to the frequency-domain, where the same inputs and outputs are functions of complex angular frequency, in radians per unit time.
Given a simple mathematical or functional description of an input or output to a system, the Laplace transform provides an alternative functional description that often simplifies the process of analyzing the behavior of the system, or in synthesizing a new system based on a set of specifications.

MTH301 GDB SOLUTION 1 FALL2012

The Laplace transform is related to the Fourier transform but whereas the Fourier transform expresses a function or signal as a series of modes of vibration (frequencies), the Laplace transform resolves a function into its moments. Like the Fourier transform, the Laplace transform is used for solving differential and integral equations. In physics and engineering it is used for analysis of linear time-invariant systems such as electrical circuits, harmonic oscillators, optical devices, and mechanical systems. In such analyses, the Laplace transform is often interpreted as a transformation from the time-domain, in which inputs and outputs are functions of time, to the frequency domain, where the same inputs and outputs are functions of complex angular frequency, in radians per unit time. Given a simple mathematical or functional description of an input or output to a system, the Laplace transform provides an alternative functional description that often simplifies the process of analyzing the behavior of the system, or in synthesizing a new system based on a set of specifications.

MTH301 GDB SOLUTION 1 FALL2012

Fourier Transforms and Laplace Transforms are both frequency space transforms, but one has an imaginary argument and the other a real one. They're associated with different physical situations that dictate where they are used. Fourier Transforms are useful if you want to see the frequency spectrum makeup of a signal -- something you don't get from the Laplace Transform. Laplace Transforms, on the other hand, are useful in solving rate equations. They come in useful if you're taking a course in Diff Q's (Differential Equations).

Fourier is a subset of Laplace. Laplace is a more generalized transform.

Fourier is used primarily for steady state signal analysis, while Laplace is used for transient signal analysis. Laplace is good at looking for the response to pulses, step functions, delta functions, while Fourier is good for continuous signals.

Transforms are used because the time-domain mathematical models of systems are generally complex differential equations. Transforming these complex differential equations into simpler algebraic expressions makes them much easier to solve. Once the solution to the algebraic expression is found, the inverse transform will give you the time-domain response.

The Laplace transform is a widely used integral transform with many applications in physics and engineering. Denoted , it is a linear operator of a function f(t) with a real argument t (t ≥ 0) that transforms it to a function F(s) with a complex argument s. This transformation is essentially bijective for the majority of practical uses; the respective pairs of f(t) and F(s) are matched in tables. The Laplace transform has the useful property that many relationships and operations over the originals f(t) correspond to simpler relationships and operations over the images F(s).[1] It is named after Pierre-Simon Laplace, who introduced the transform in his work on probability theory.

The Laplace transform is related to the Fourier transform, but whereas the Fourier transform expresses a function or signal as a series of modes of vibration (frequencies), the Laplace transform resolves a function into its moments. Like the Fourier transform, the Laplace transform is used for solving differential and integral equations. In physics and engineering it is used for analysis of linear time-invariant systems such as electrical circuits, harmonic oscillators, optical devices, and mechanical systems. In such analyses, the Laplace transform is often interpreted as a transformation from the time-domain, in which inputs and outputs are functions of time, to the frequency-domain, where the same inputs and outputs are functions of complex angular frequency, in radians per unit time.
Given a simple mathematical or functional description of an input or output to a system, the Laplace transform provides an alternative functional description that often simplifies the process of analyzing the behavior of the system, or in synthesizing a new system based on a set of specifications.

## Latest Activity

+ ! ! ! ! ! cr@zy giRl updated their profile
6 minutes ago
59 minutes ago
NOORI and Haroon Bahadar are now friends
1 hour ago
zohaib iftikhar left a comment for NOORI
1 hour ago
NOORI left a comment for zohaib iftikhar
1 hour ago
3 hours ago
Ayesha posted a blog post

### Golden Words

3 hours ago
3 hours ago
3 hours ago
3 hours ago
♦_"Tooba"_♦ liked shan's discussion what will be the future of PAKISTAN?
3 hours ago

1