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

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.

11 sections

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Sections

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  1. 15
    Laplace Transforms & Applications

    The Final Value Theorem allows for the determination of a function's...

  2. 15.1
    Final Value Theorem

    The Final Value Theorem (FVT) allows us to determine the steady-state value...

  3. 15.2
    Introduction

    The Final Value Theorem (FVT) allows for efficient determination of a...

  4. 15.3
    Theoretical Background

    The Final Value Theorem (FVT) is a method to determine the steady-state...

  5. 15.3.1
    Definition Of Final Value Theorem (Fvt)

    The Final Value Theorem is a mathematical tool that helps determine the...

  6. 15.3.2
    Conditions For Applying Final Value Theorem

    The Final Value Theorem (FVT) provides a method for determining the...

  7. 15.4
    Step-By-Step Process

    The Final Value Theorem (FVT) provides a method to find the steady-state...

  8. 15.5

    The section discusses the Final Value Theorem and its applications in...

  9. 15.5.2
    Example 2: Non-Converging Function (Invalid Case)

    This section discusses the limitations of the Final Value Theorem (FVT),...

  10. 15.6
    Applications Of Final Value Theorem

    The Final Value Theorem (FVT) is a powerful mathematical tool that allows...

  11. 15.7
    Important Notes

    The section provides crucial insights regarding the application and...

What we have learnt

  • The Final Value Theorem can determine the steady-state value of a function using its Laplace transform.
  • FVT is applicable only if the poles of sF(s) lie in the left half of the complex plane and the function converges to a finite value.
  • FVT is commonly used in control systems and electrical circuits to find final values without needing a complete inverse Laplace transform.

Key Concepts

-- Final Value Theorem (FVT)
A theorem used to find the steady-state value of a time-domain function in the Laplace transform domain.
-- Laplace Transform
A technique for converting a time-domain function into a frequency-domain representation.
-- Poles
Values of s where the function sF(s) becomes infinite, which affect the applicability of the FVT.
-- Convergence
The behavior of a function approaching a limit value as time approaches infinity.

Additional Learning Materials

Supplementary resources to enhance your learning experience.