ENV E 558 Lecture 1: Introduction and History

Let
H = {f : R → R | f(x) = ax + b; a, b ∈ R; a > 0}.
H1 = {f : R → R | f(x) = ax; a ∈ R; a > 0}.
H2 = {f : R → R | f(x) = x + b; b ∈ R}.
(a) Prove that H1 and H2 are subgroups of H.
(b) Determine whether each is a normal subgroup of H.

A bandpass filter passes signals with frequencies that are within a certain range.In this filter the ratio of the magnitudes of the voltages is given by:
RV=V0/Vi=wRC/sqrt(1-w^2LC)^2+(wRC)^2 where w is the frequency of the input signal.Given R=1000ohm,L=11mH and C=8µF,determine the frequency range that corresponds to RV>=0.87.
Using MATLAB:
a) First plot the graph
b)Use matlab to construct a script for the Bisection method and Newton's method to find one of the possible roots.