#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? And why was he famous?

Sir Ronald Ross was a British medical doctor known for his work on the transmission of malaria. He won a Nobel Prize.

2. Copy and paste Dr. Z’s Maple code and remove option remember. Calculate astupid of 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)

Without option remember, the evaluation takes forever.

3.Let a1:= 5th digit in Ruid
	Let a2:= 2nd digit in ruid
	Let a3:= 3rd digit in ruid
Use maple to solve differential equation 
y’(t)=a1*t^a2/y^a3,y(1)=a2

a1 := 9;
a2 := 22;
a3 := 54;
dsolve({a1*D(D(y))(t) + a2*D(y)(t) + a3*y(t), y(0) = 1, D(y)(0) = 0}, y(t));
              11     (1/2)    /  11  \    /1    (1/2)  \
       y(t) = --- 365      exp|- -- t| sin|- 365      t|
              365             \  9   /    \9           /

               /  11  \    /1    (1/2)  \
          + exp|- -- t| cos|- 365      t|
               \  9   /    \9           /



4. Let a1:= 8th digit of your RUID
	Let a2:= your age
	Let a3:= your mothers age

Solve using maple the differential equation
a1*y’’(t)+a2*y’(t)+a3*y(t), subject to y(0)=1,y’(0)=0

a1 := 9;
a2 := 22;
a3 := 54;
dsolve({a1*D(D(y))(t) + a2*D(y)(t) + a3*y(t), y(0) = 1, D(y)(0) = 0}, y(t));
              11     (1/2)    /  11  \    /1    (1/2)  \
       y(t) = --- 365      exp|- -- t| sin|- 365      t|
              365             \  9   /    \9           /

               /  11  \    /1    (1/2)  \
          + exp|- -- t| cos|- 365      t|
               \  9   /    \9           /


5. Find in floating points the second largest eigenvalue and the corresponding eigenvector.

a1 := 56;
a2 := 54;
a3 := 0;


A := Matrix([[a1, a2, a3], [a2, a3, a1], [a3, a2, a1]]);
                            [56  54  0 ]
                            [          ]
                       A := [54  0   56]
                            [          ]
                            [0   54  56]

evalf(Eigenvalues(A));
                         [    56.     ]
                         [            ]
                         [    110.    ]
                         [            ]
                         [.   -54.]

evalf(Eigenvectors(A))[1];
                         [    110.    ]
                         [            ]
                         [.   -54.]
                         [            ]
                         [    56.     ]