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12: Fourier Solutions of Partial Differential Equations

Last updated

Jun 23, 2024
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- 11.3E: Fourier Series II (Exercises)
- 12.1: The Heat Equation

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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 uₜ=a²uₓₓ, which arises in problems of conduction of heat.
- 12.1E: The Heat Equation (Exercises)
12.2: The Wave Equation
This section deals with the partial differential equation uₜₜ=a²uₓₓ, which arises in the problem of the vibrating string.
- 12.2E: The Wave Equation (Exercises)
12.3: Laplace's Equation in Rectangular Coordinates
This section deals with a partial differential equation that arises in steady state problems of heat conduction and potential theory.
- 12.3E: Laplace's Equation in Rectangular Coordinates (Exercises)
12.4: Laplace's Equation in Polar Coordinates
Previously, we solved boundary value problems for Laplace’s equation over a rectangle with sides parallel to the x,y -axes. Now we’ll consider boundary value problems for Laplace’s equation over regions with boundaries best described in terms of polar coordinates.
- 12.4E: Laplace's Equation in Polar Coordinates (Exercises)

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