Partial Differential Equations : Ideal Gas Law
According to the ideal gas law, the pressure, the temperature and the volume of a gas are related by PV = kT (k is a constant). Show the following: (attached)
Please use: 1.) LaPlace Transform and 2.) Fourier Transforms methods and 3.) our old friend separation of variables with eigenvalues expansion to solve each problem. It is not necessary to evaluate an inverse transform. Where convenient, show any solution as a convolution of two functions and indicate how these functions are det ...continues
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Suppose U is a positive harmonic function which is defined everywhere in the plane. Show that U must be a constant function. This is a question regarding Poisson Integral Formula in PDE. I need to find it using the Harnak's inequalities.
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Partial Differential Equations : Eigenvalue Expansion
Solve the Boundary value problem PDF: Ut = Uxx + 7sin(5x/2) b. C. U(0,t) = 3 Ux(Pi,t) = 0 i. c. U(x,0) = 3 + 6sin(7x/2)
Solving Differential Equations
Solve the following differential equation: df(t)/dt + 2f(t) = 6 Numerically for f(0)=100
Fourier Integrals, Heat Kernels and a One-Dimensional Heat Equation
I am having difficulty computing u(x,t), also interpretation when e -> 0 See attached file for full problem description.
PDE Utt = Uxx+sin(3x) 0
Suppose f(x) has the Fourier transform F(ω). If a ≠ 0 show that f(ax) has the Fourier Transform 1/|a| F (ω/a). Please see the attached file for the fully formatted problems.
