12: Fourier Solutions of Partial Differential Equations
- Page ID
- 9473
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In this chapter, we use the series discussed in Chapter 11 to solve partial differential equations that arise in problems of mathematical physics.
- 12.1: The Heat Equation
- This section deals with the partial differential equation \(u_t = a^2u_{xx}\), which arises in problems of conduction of heat
- 12.2: The Wave Equation
- This section deals with the partial differential equation \(u_{tt} = a^2u_{xx}\), which arises in the problem of the vibrating string.
- 12.3: Laplace's Equation in Rectangular Coordinates
- This section deals with the partial differential equation \(u_{xx} + u_{yy} = 0\), which arises in steady state problems of heat conduction and potential theory.
- 12.4: Laplace's Equation in Polar Coordinates
- This section deals with the partial differential equation \(u_{rr} + 1/r u_r + 1 r^2 u_{θθ} = 0\), which is the equivalent to the equation studied in Section 1.3 when the independent variables are polar coordinates.