Mathematics - iii (Differential Calculus) - Vol 1 | 4. Second Shifting Theorem by Abraham | Learn Smarter
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4. Second Shifting Theorem

The Laplace Transform is crucial for solving differential equations, especially when dealing with delayed functions through the Second Shifting Theorem. This theorem, using the Heaviside step function, enables transformations of functions that activate after a specified time. Its applications span various fields, illustrating its importance in analyzing real-world systems that exhibit delays.

Sections

  • 1

    Laplace Transforms & Applications

    The Second Shifting Theorem in Laplace Transforms facilitates the handling of functions that begin after a certain delay, essential for various applications like control systems and signal processing.

    Learning Practice

  • 1.1

    Second Shifting Theorem

    The Second Shifting Theorem in Laplace Transforms enables the handling of functions that start after a delay using the Heaviside step function.

    Learning Practice

  • 1.2

    Introduction

    The section introduces the Second Shifting Theorem and the importance of Laplace Transforms in modeling time-delayed functions.

    Learning Practice

  • 1.3

    Concept Of Heaviside Unit Step Function

    The Heaviside unit step function models functions that activate at a given time, crucial for analyzing time-delayed systems using the Laplace Transform.

    Learning Practice

  • 1.4

    Second Shifting Theorem (Time Shifting In Laplace Domain)

    The Second Shifting Theorem simplifies the analysis of delayed functions in the Laplace domain, leveraging the Heaviside step function.

    Learning Practice

  • 1.5

    Proof Of The Second Shifting Theorem

    The Second Shifting Theorem provides a method to transform delayed functions in the Laplace domain.

    Learning Practice

  • 1.6

    Important Notes

    The Second Shifting Theorem is essential for handling delayed functions in Laplace transforms using the Heaviside step function.

    Learning Practice

  • 1.7

    Graphical Representation

    The section discusses the Second Shifting Theorem, its application in transformations of delayed functions using the Heaviside step function.

    Learning Practice

  • 1.8

    Examples

    This section covers the Second Shifting Theorem in Laplace Transforms, emphasizing its application in dealing with delayed functions using the Heaviside step function.

    Learning Practice

  • 1.9

    Applications Of Second Shifting Theorem

    The Second Shifting Theorem enables the Laplace Transform to handle delayed functions, proving essential in various engineering applications including control systems and signal processing.

    Learning Practice

  • 1.10

    Summary

    The Second Shifting Theorem facilitates the transformation of time-delayed functions using the Laplace Transform and the Heaviside step function.

    Learning Practice

References

Unit 1 ch4.pdf

Class Notes

Memorization

What we have learnt

  • The Laplace Transform is es...
  • The Second Shifting Theorem...
  • The unit step function is c...

Final Test

Revision Tests