Math 267 Assignment 3 1. (a) Given an integer k , nd the constant dk for which yk (t) = dk eikt is a particular solution of the DE y (t) + 2y (t) + 3y (t) = eikt . (b) Suppose that f (t) has a Fourier series expansion f (t) =
ck eitk .
Using the resul
Math 267 Assignment 1 - Solutions 1. Find the general solution of the following DEs. (a) y + 5y = 0, (b) y + 6y + 13y = 0, (c) 25y 20y + 4y = 0. Solution. (a) The characteristic equation of the given ODE is r2 + 5r = r(r + 5) = 0 So, the general solution
Math 267 Assignment 4 1. In each case below, sketch the graph of the function f (t) and nd the (complex) Fourier series of f (t). (a) f (t) is periodic with period 4 , and 1 if 2 t < 1 if t < f (t) = 1 if t < 2 (b) f (t) is periodic with period 2, and f (