Mathematics - iii (Differential Calculus) - Vol 2 | 18. Eigenfunction Expansion Method by Abraham | Learn Smarter
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18. Eigenfunction Expansion Method

The Eigenfunction Expansion Method provides a systematic approach for solving linear partial differential equations (PDEs) by utilizing the properties of eigenfunctions from Sturm–Liouville problems. It allows the representation of solutions as infinite series, connecting concepts from linear algebra, differential equations, and Fourier analysis. This method is particularly effective for boundary value problems, enabling efficient solution derivation under various conditions.

Sections

  • 18

    Partial Differential Equations

    The Eigenfunction Expansion Method provides a systematic approach to solve linear partial differential equations using eigenfunctions.

    Learning Practice

  • 18.1

    Basic Concept

    The Eigenfunction Expansion Method forms a framework for solving linear partial differential equations through the use of eigenfunctions and coefficients, enabling efficient solutions to complex problems.

    Learning Practice

  • 18.2

    Sturm–liouville Problems And Eigenfunctions

    This section introduces Sturm–Liouville problems and their significance in deriving eigenfunctions essential for solving partial differential equations (PDEs).

    Learning Practice

  • 18.3

    General Steps In The Eigenfunction Expansion Method

    The Eigenfunction Expansion Method provides a systematic approach for solving linear PDEs through the use of eigenfunctions derived from Sturm–Liouville theory.

    Learning Practice

  • 18.5

    Properties Of Eigenfunction Expansions

    Eigenfunction expansions offer enhanced techniques for solving partial differential equations by leveraging orthogonality and completeness.

    Learning Practice

  • 18.6

    Applications

    The Eigenfunction Expansion Method is widely applicable in solving various linear partial differential equations in fields like heat conduction, vibrations, and quantum mechanics.

    Learning Practice

References

Unit_2_ch18.pdf

Class Notes

Memorization

What we have learnt

  • The Eigenfunction Expansion...
  • Eigenfunctions derived from...
  • Separating variables to for...

Final Test

Revision Tests