(a) What are Dirichlet’s conditions for convergence of Fourier Series representation? (b) Define invertiblity of a system.
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- f(x) is a periodic function with period 2π where the value of f(x) in the interval <x < is : (in pict) Use Dirichlet's theorem to find the value at which the Fourier series in (Expansion f(x) using Fourier series) converges when x = 0, x = ±π/2, x = ±π, x = ±2πI) Define Fourier Series and explain it usefulness. At what instance can a function f(x) be developed as a Fourier series. II) If f(X)=1/2*(π-x), find the Fourier series of period 2π in the interval (0,2π).A point is an ordinary point of a non-homogeneous linear second order differential equation, y"+p(x)y'+q(x)y=f(x) is p, q, f are analytic at x0. Moreover, our theorem on the existence of power series solutions extends to such differential equations, ie, we can find power series solutions of non-homogeneous linear differential equations in the same manner as we have for homogeneous equations...almost. Find the series solution to the non-homogeneous initial value problem. Note: BEWARE THE THEOREM OF EQUIVALENT SERIES!!! Find the first five nonzero terms of the series solution to: y"+2y'+y=ex, y(0)=2, y'(0)=1
