Mathematics - iii (Differential Calculus) - Vol 1 | 3. Topic 3: First Shifting Theorem by Abraham | Learn Smarter
K12 Students

Academics

AI-Powered learning for Grades 8–12, aligned with major Indian and international curricula.

Academics

Grades

Grade 8 Grade 9 Grade 10 Grade 11 Grade 12

Curriculum

CBSE ICSE IB
Professionals

Professional Courses

Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.

Professional Courses
Games

Interactive Games

Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.

games
Typing
Memory
Math
English Adventures
Knowledge
3. Topic 3: First Shifting Theorem

The chapter explores the First Shifting Theorem within Laplace Transforms, highlighting its utility in solving linear differential equations and its application in various engineering fields. It addresses how this theorem facilitates the handling of functions multiplied by exponential terms in the time domain, allowing for shifts in the Laplace domain. Additionally, it includes proofs, applications, common mistakes, and provides exercises to reinforce understanding.

Sections

  • 1

    Unit 1: Laplace Transforms & Applications

    The First Shifting Theorem is a critical property of the Laplace Transform that facilitates the analysis of systems with exponential functions.

    Learning Practice

  • 1.1

    Topic 3: First Shifting Theorem

    The First Shifting Theorem simplifies the process of working with Laplace Transforms of functions multiplied by exponential terms.

    Learning Practice

  • 1.2

    Introduction

    The First Shifting Theorem in Laplace Transforms simplifies solving linear differential equations involving exponential functions.

    Learning Practice

  • 1.3

    First Shifting Theorem (Laplace Domain Shift)

    The First Shifting Theorem allows for the simplification of Laplace Transforms of functions multiplied by exponential terms, which is critical in engineering applications.

    Learning Practice

  • 1.4

    Theorem Statement

    The First Shifting Theorem in Laplace Transforms facilitates the handling of exponential factors in time-domain functions by simplifying transformations in the Laplace domain.

    Learning Practice

  • 1.5

    Meaning

    The First Shifting Theorem is a key concept in Laplace Transforms that facilitates the analysis of systems affected by exponential factors in the time domain.

    Learning Practice

  • 1.6

    Proof Of The First Shifting Theorem

    The First Shifting Theorem in Laplace Transforms provides a method to handle time-domain functions multiplied by exponential terms by shifting their Laplace transform in the s-domain.

    Learning Practice

  • 1.7

    Application Scenarios

    This section discusses the application of the First Shifting Theorem in solving engineering problems involving differential equations with exponential terms.

    Learning Practice

  • 1.8.1

    Example 3

    The section discusses the First Shifting Theorem in Laplace Transforms, highlighting its significance in solving engineering problems involving exponential terms.

    Learning Practice

  • 1.9

    Common Mistakes To Avoid

    This section outlines common errors encountered when using the First Shifting Theorem in Laplace Transforms.

    Learning Practice

  • 1.10

    Summary

    The First Shifting Theorem in Laplace Transforms allows for handling exponential functions in the time domain by shifting functions in the Laplace domain.

    Learning Practice

  • 1.11

    Additional Exercise (Practice)

    This section emphasizes the application of the First Shifting Theorem in finding Laplace Transforms of functions involving exponential terms.

    Learning Practice

References

Unit 1 ch3.pdf

Class Notes

Memorization

What we have learnt

  • The First Shifting Theorem ...
  • Applications of the theorem...
  • Attention to conditions suc...

Final Test

Revision Tests