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2 results

  • 8 - Partial-Differential Equations

  • from Part II - Mathematical Methods
  • Steven R. Pride, University of California, Berkeley
  • Book:
    An Introduction to Continuum Physics
    Published online:
    06 February 2025
    Print publication:
    13 February 2025, pp 459-488

  • Summary

    In this first chapter of Part II of the book on the mathematical methods of continuum physics, the continuum governing equations in Part I are related to three simple partial-differential equations that are analyzed throughout Part II: (1) the scalar wave equation, (2) the scalar diffusion equation, and (3) the scalar Poisson (or Laplace) equation. The nature of the boundary and initial conditions required in specifying well-posed boundary-value problems for each type of partial-differential equation is derived. The three types of equations are then solved using the method of separation of variables. In so doing, the most essential things to remember about the nature of the solution to wave, diffusion, and potential boundary-value problems are presented.