Mathematics - iii (Differential Calculus) - Vol 2 | 9. Non-Homogeneous Linear PDEs by Abraham | Learn Smarter
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9. Non-Homogeneous Linear PDEs

Non-Homogeneous Linear Partial Differential Equations (PDEs) feature a non-zero function on their right-hand side, essential for modeling physical phenomena under external forces. The general solution combines the complementary function (CF) of the homogeneous equation with a particular integral (PI). Various solving techniques include the operator method, method of undetermined coefficients, and variation of parameters, which are crucial for tackling advanced engineering problems.

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Sections

  • 9

    Partial Differential Equations

    This section covers Non-Homogeneous Linear Partial Differential Equations (PDEs), emphasizing their definition, solution structure, and solving methods.

    Learning Practice

  • 9.1

    Definition And Standard Form

    This section introduces Non-Homogeneous Linear Partial Differential Equations (PDEs), highlighting their significance, definition, and standard form.

    Learning Practice

  • 9.2

    Solution Structure

    This section outlines the structure of solutions to non-homogeneous linear partial differential equations, emphasizing the roles of the complementary function and particular integral.

    Learning Practice

  • 9.3

    Methods Of Solving Non-Homogeneous Linear Pdes

    This section outlines various methods for solving non-homogeneous linear partial differential equations, including the operator method, the method of undetermined coefficients, and variation of parameters.

    Learning Practice

  • 9.4

    Example Problems

    This section presents example problems for solving non-homogeneous linear partial differential equations (PDEs).

    Learning Practice

  • 9.5

    Applications

    This section explores the diverse applications of non-homogeneous linear partial differential equations in various fields including engineering and biological sciences.

    Learning Practice

References

Unit_2_ch9.pdf

Class Notes

Memorization

What we have learnt

  • Non-Homogeneous Linear PDEs...
  • The general solution is der...
  • Key solving techniques incl...

Final Test

Revision Tests