save_figs = F

# Problem 1:
#
pr = polyroot( c( 1, -2, 1 ) ) 
print(pr)


# Problem 3:
#
pr = polyroot( c( -3, -4, 4 ) ) 
print(pr)


# Problem 4:
#
pr = polyroot( c( 9, 12, 4 ) ) 
print(pr)


# Problem 5:
#
pr = polyroot( c( 10, -2, 1 ) ) 
print(pr)


# Problem 7:
#
pr = polyroot( c( 4, 17, 4 ) ) 
print(pr)


# Problem 8:
#
pr = polyroot( c( 9, 24, 16 ) ) 
print(pr)


# Problem 9:
#
pr = polyroot( c( 4, -20, 25 ) ) 
print(pr)


# Problem 10:
#
pr = polyroot( c( 1, 2, 2 ) ) 
print(pr)


# Problem 11:
#
pr = polyroot( c( 4, -12, 9 ) ) 
print(pr)


# Problem 13:
#
pr = polyroot( c( 82, 6, 9 ) )
print(pr)


# Problem 14:
#
A = matrix( c( exp(2), -exp(2), -2*exp(2), 3*exp(2) ), nrow=2, ncol=2, byrow=T )
b = c( 2, 1 )
x = solve( A, b )
print(x)

print( c( 7, 5 ) * exp(-2) )


# Problem 15:
#
polyroot( c( 9, 12, 4 ) )

ts = seq( 0, 5, length.out=100 )
ys = exp(-(3/2)*ts) - (5/2)*ts*exp(-(3/2)*ts)
plot(ts, ys, type='l', xlab='t', ylab='y(t)')
abline(v=c( 2/5, 16/15 ), col='gray')
grid()


# Problem 17:
#
polyroot( c( 1, 4, 4) )

ts = seq( 0, 5, length.out=100 )
ys = exp(-(1/2)*ts) + (5/2)*ts*exp(-(1/2)*ts)
plot(ts, ys, type='l', xlab='t', ylab='y(t)')
abline(v=8/5, col='gray')
grid()


# Problem 18:
#
polyroot( c( 4, 12, 9 ) )

ts = seq( 0, 5, length.out=100 )
ys = exp(-(1/2)*ts) + (5/2)*ts*exp(-(1/2)*ts)
plot(ts, ys, type='l', xlab='t', ylab='y(t)')
abline(v=8/5, col='gray')
grid()