Mathematics - iii (Differential Calculus) - Vol 1 | 15. Final Value Theorem by Abraham | Learn Smarter
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15. Final Value Theorem

The chapter discusses the Final Value Theorem (FVT), a mathematical tool used in the analysis of systems to determine the steady-state behavior of responses without fully performing an inverse Laplace transform. It outlines the theorem's conditions, provides examples of its application, and emphasizes common errors regarding its use. The applications of FVT span various fields, including control systems, electrical circuits, and mechanical systems.

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Sections

  • 15

    Laplace Transforms & Applications

    The Final Value Theorem allows for the determination of a function's steady-state value using Laplace transforms without needing to compute the full inverse transform.

    Learning Practice

  • 15.1

    Final Value Theorem

    The Final Value Theorem (FVT) allows us to determine the steady-state value of a system's response as time approaches infinity without the need for a full inverse Laplace transform.

    Learning Practice

  • 15.2

    Introduction

    The Final Value Theorem (FVT) allows for efficient determination of a system's steady-state behavior without needing the inverse Laplace transform.

    Learning Practice

  • 15.3

    Theoretical Background

    The Final Value Theorem (FVT) is a method to determine the steady-state value of a system's response in engineering via Laplace transforms.

    Learning Practice

  • 15.3.1

    Definition Of Final Value Theorem (Fvt)

    The Final Value Theorem is a mathematical tool that helps determine the steady-state value of a time-domain function using its Laplace transform, relevant in various engineering fields.

    Learning Practice

  • 15.3.2

    Conditions For Applying Final Value Theorem

    The Final Value Theorem (FVT) provides a method for determining the steady-state value of a function using Laplace transforms, under specific conditions.

    Learning Practice

  • 15.4

    Step-By-Step Process

    The Final Value Theorem (FVT) provides a method to find the steady-state behavior of a system's response in engineering without the need for the full inverse Laplace transform.

    Learning Practice

  • 15.5

    Examples

    The section discusses the Final Value Theorem and its applications in determining the steady-state value of a function using Laplace transforms.

    Learning Practice

  • 15.5.2

    Example 2: Non-Converging Function (Invalid Case)

    This section discusses the limitations of the Final Value Theorem (FVT), specifically highlighting scenarios where it cannot be applied, such as oscillatory functions.

    Learning Practice

  • 15.6

    Applications Of Final Value Theorem

    The Final Value Theorem (FVT) is a powerful mathematical tool that allows for the determination of a system's steady-state behavior without necessitating the full inverse Laplace transform.

    Learning Practice

  • 15.7

    Important Notes

    The section provides crucial insights regarding the application and limitations of the Final Value Theorem (FVT) within system analysis.

    Learning Practice

References

Unit 1 ch15.pdf

Class Notes

Memorization

What we have learnt

  • The Final Value Theorem can...
  • FVT is applicable only if t...
  • FVT is commonly used in con...

Final Test

Revision Tests