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main equations: the heat equation, Laplace's equation and the wave equa- In the preceding examples, the boundary conditions where either fixed. In this chapter we present an elementary discussion on partial differential equations including one dimensional heat and wave equations. In this section we consider a general method of separation of variables and its applications to solving heat equation and wave equation on a finite interval (a1I will consider the heat equations, but basically no change must be made to solve the wave equation. 22.1 Solving the Dirichlet problem for the heat equation in 3.3 Some examples; importance of the interval . which are the heat equation, wave equation and the Poisson equation, respectively. Note. and compare the propagation of waves to conduction of heat. We have already seen that u given by (4) solves the heat equation, due to the invariance Derivation of Wave Equation and Heat Equation. Ang M.S.. 2011-10-7. Wave Equation. For one Dimensional Wave. Y = y(x, t). The net upward force is.