Mathematics - iii (Differential Calculus) - Vol 2 | 7. Method of Separation of Variables 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
7. Method of Separation of Variables

The Method of Separation of Variables is an essential technique for solving linear partial differential equations (PDEs) by transforming them into simpler ordinary differential equations (ODEs). This method relies on the assumption that solutions can be expressed as a product of functions, each depending on a single variable. It requires appropriate boundary conditions and can effectively address problems such as the heat and wave equations through Fourier series and superposition principles.

Sections

  • 7

    Partial Differential Equations

    The Method of Separation of Variables simplifies partial differential equations into separate ordinary differential equations for easier solving.

    Learning Practice

  • 7.1.1

    What Is The Method Of Separation Of Variables?

    The Method of Separation of Variables is a technique for solving linear PDEs by expressing the solution as a product of functions, each dependent on a single variable.

    Learning Practice

  • 7.1.2

    Application To Standard Pdes

    This section describes the application of the Method of Separation of Variables to solve standard partial differential equations (PDEs), particularly focusing on heat and wave equations.

    Learning Practice

  • 7.1.3

    General Steps For The Method

    The General Steps for the Method outline how to apply the Method of Separation of Variables to solve partial differential equations.

    Learning Practice

  • 7.1.4

    Types Of Boundary Conditions

    The section discusses the different types of boundary conditions—Dirichlet, Neumann, and Mixed—essential for successfully applying the Method of Separation of Variables in solving partial differential equations.

    Learning Practice

  • 7.1.5

    Fourier Series And Superposition

    This section covers the use of Fourier series in expanding initial conditions for solutions of partial differential equations, emphasizing superposition of eigenfunctions.

    Learning Practice

  • 7.1.6

    Limitations Of The Method

    The Method of Separation of Variables has specific applicability limitations, only being effective for linear PDEs under homogeneous boundary conditions.

    Learning Practice

  • 7.1.2

    Method Of Separation Of Variables

    The Method of Separation of Variables is a technique used to solve linear partial differential equations (PDEs) by reducing them to simpler ordinary differential equations (ODEs).

    Learning Practice

  • 7.2.1

    Introduction

    This section introduces Partial Differential Equations (PDEs) and the Method of Separation of Variables, a technique for solving linear PDEs.

    Learning Practice

  • 7.3

    Summary

    The Method of Separation of Variables simplifies solving partial differential equations (PDEs) by expressing solutions as products of functions of individual variables.

    Learning Practice

References

Unit_2_ch7.pdf

Class Notes

Memorization

What we have learnt

  • The Method of Separation of...
  • The process includes assumi...
  • It is primarily applicable ...

Final Test

Revision Tests