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9: Partial Differential Equations

  • Page ID
    90431
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    Differential equations containing partial derivatives with two or more independent variables are called partial differential equations (pdes). These equations are of fundamental scientific interest but are substantially more difficult to solve, both analytically and computationally, than odes. In this chapter, we begin by deriving two fundamental pdes: the diffusion equation and the wave equation, and show how to solve them with prescribed boundary conditions using the technique of separation of variables. We then discuss solutions of the two-dimensional Laplace equation in Cartesian and polar coordinates, and finish with a lengthy discussion of the Schrödinger equation, a partial differential equation fundamental to both physics and chemistry.


    This page titled 9: Partial Differential Equations is shared under a CC BY 3.0 license and was authored, remixed, and/or curated by Jeffrey R. Chasnov via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.