Mathematics - iii (Differential Calculus) - Vol 1 | 5. Laplace Transform of Derivatives 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
5. Laplace Transform of Derivatives

The Laplace Transform serves as a crucial tool for solving differential equations, converting them into algebraic equations for easier manipulation. This chapter explains the Laplace Transform of derivatives and provides the essential formulas for first and higher-order derivatives. The application of these transforms to solve differential equations, particularly in Initial Value Problems (IVPs) in engineering contexts, is also highlighted.

Sections

  • 1

    Laplace Transforms & Applications

    The Laplace Transform is a crucial method for transforming differential equations into algebraic equations, especially focusing on derivatives.

    Learning Practice

  • 1.1

    Laplace Transform Of Derivatives

    The Laplace Transform is instrumental in solving differential equations, allowing for the conversion of derivatives into manageable algebraic expressions.

    Learning Practice

  • 1.1.1

    Introduction

    The Laplace Transform is a crucial method for solving differential equations, particularly in engineering and physical sciences.

    Learning Practice

  • 1.1.2

    Preliminaries

    This section introduces Laplace Transforms, focusing on the transforms of derivatives, which simplify solving differential equations.

    Learning Practice

  • 1.1.3

    Laplace Transform Of The First Derivative

    The Laplace Transform of the first derivative allows us to transform differential equations into algebraic equations, simplifying their solutions.

    Learning Practice

  • 1.1.4

    Proof Of First Derivative

    This section covers the Laplace Transform of derivatives, specifically the first derivative, and provides proofs and applications.

    Learning Practice

  • 1.1.5

    Laplace Transform Of The Second Derivative

    The section explains how to compute the Laplace Transform of the second derivative of a function, building upon the first derivative's transformation.

    Learning Practice

  • 1.1.6

    Proof Of Second Derivative

    This section discusses the Laplace transform of the second derivative, outlining key formulas and their significance in solving differential equations.

    Learning Practice

  • 1.1.7

    Laplace Transform Of The N-Th Derivative

    This section discusses the Laplace Transform of the n-th derivative, demonstrating how to convert higher-order derivatives into algebraic expressions for more manageable computations.

    Learning Practice

  • 1.1.8

    General Formula

    This section outlines the general formula for the Laplace Transform of derivatives, illustrating its crucial role in solving differential equations.

    Learning Practice

  • 1.2

    Applications

    This section discusses the applications of the Laplace Transform, particularly in solving differential equations.

    Learning Practice

  • 1.2.1

    Solving Differential Equations

    This section introduces the Laplace Transform and its application in solving differential equations, particularly focusing on derivatives.

    Learning Practice

  • 1.2.1.1

    Example Problems

    This section discusses the Laplace Transform of derivatives, illustrating how it can be applied to solve differential equations.

    Learning Practice

  • 1.3

    Summary

    This section focuses on the Laplace Transform of derivatives, providing formulas and applications for solving differential equations.

    Learning Practice

References

Unit 1 ch5.pdf

Class Notes

Memorization

What we have learnt

  • The Laplace Transform of de...
  • The key formulas for the La...
  • Laplace Transforms are wide...

Final Test

Revision Tests