My problem is attached as jpg file.
To What Function does the Fourier Series of a Give Function Converge?
Please see the attached file for the fully formatted problems.
Fourier Series - Heat Equation - Differential Equation
Please see the attached file for the fully formatted problems. 6. Consider an insulated bar of length pi. Let u(x,t) be its temperature at time t at position x, where 0 < x < pi. Suppose that u(x, y) satisfies the heat equation ... subject to the boundary conditions u(0. 1) = 10 and t(r, t) = 20. for all time t and the init ...continues
Fourier Series for periodic functions
Find the Fourier series as well as the first three partial sums of the Fourier series.
F(x)=x-x^2 if -1
Solve using Fourier transforms and residue calculus
3. The nefarious Evil Corp is dumping radioactive pollutant into a river moving with speed c. Define x to be the downstream coordinate, with the pollutant being injected at x=0... (see attachment for rest of question)
Use the Fourier transform to solve the one-dimensional wave equation. See attached file for full problem description.
Calculating the inverse fourier transform
Calculate the inverse Fourier transform of 1/(w^2+2iw-2) in two ways: using the definition and using partial fractions.
Steady state deflection differential equation
The steady state deflection is given by: y''''+c^4*y=f(x) calculate and plot the deflection for a load: f = 1 for |x|<10, f=0 everywhere else. using Fourier transform. Plot the deflection for various values of c.
Suppose f(t) and g(t) are 2π periodic functions with Fourier series representations {see attachment}. Find the Fourier series of {see attachment}.
Finding a Polynomial whose Fourier Representation has Decaying Coefficients
Please see the attached file for the fully formatted problem. Problem: Find a polynomial whose Fourier representation on 0 ≤ x ≤ 2π has coefficients that decay like 1/n3. Solution: There is a hint which says:
