#ATTENDANCE QUIZ FOR LECTURE 2 of Dr. Z.'s Math336 Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p2
#with an attachment called
#p2FirstLast.txt
#(e.g. p2DoronZeilberger.txt)

#Right after attending the lecture  but no later than  Tue., Sept. 7, 4:00pm, 2021, 4:00pm

LIST ALL THE ATTENDANCE QUESTIONS FOLLOWED BY THEIR ANSWERS


#1 Who was Sir Ronald Ross? What was his claim to fame?
 
Ronald Ross discovered transmission of malaria by mosquitoes and became the first British Nobel Laureate.


#2 Delete option remember in the recurrence relation from ÒGetting to know youÓ and compute astupid(100).

astupid := proc(n):
if n = 0 then 
0:
elif n = 1 then 
1:
elif n = 2 then 
4:
else 
3*astupid(n - 1) - 3*astupid(n - 2) + astupid(n - 3):
fi:
end:
astupid(100)

This took too long. 



#3 Let a1 := 5th digit in your RUID, a2 := 2nd digit, a3 := 3rd digit. Solve yÕ(t) = a1*t^a2/y(t)^a3

a1 = 1
a2 = 9
a3 = 3

dsolve({D(y)(t)= t^9/y(t)^3, y(1)=9}, y(t));

y(t) = sqrt(5)*(10*t^10 + 164015)^(1/4)/5




#4 What was Hilda HudsonÕs middle name? 

Phoebe


#5 Let a1 := 8th digit of RUID, a2 := your age, a3 := motherÕs age. Solve a1yÕÕ + a2yÕ + a3y = 0, y(0) = 1, yÕ(0) = 0

a1 = 1
a2 = 20
a3 = 57


dsolve({D(D(y))(t)+2*D(y)(t) + 57*y(t)=0, y(0)=1, D(y)(0)=0}, y(t));

y(t) = -(59*exp(t/2)*sin(sqrt(227)*t/2)*sqrt(227))/12939 + (59*exp(t/2)*cos(sqrt(227)*t/2))/57 - 2/57




#5 Let a1 := fatherÕs age, a2 := motherÕs age, a3 := younger siblingÕs age, A:= [[a1, a2, a3], [a2, a3, a1], [a3, a2, a1]]. Find the second largest eigenvalue and corresponding eigenvector. 


A = [[61, 57, 20], [57, 20, 61], [20, 57, 61]]


with(LinearAlgebra)
A := Matrix([[61, 57, 20], [57, 20, 61], [20, 57, 61]]);

evalf(Eigenvalues(A));

                   [138., -37., 41.]

(second smallest 41)

evalf(Eigenvectors(A))[2]

 [[-1.062142273, 1., 1.], [0.02180430635, 1., -2.070175439], [1., 1., 1.]]