#ATTENDANCE QUIZ FOR LECTURE 3 of Dr. Z.'s Math336 Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p3
#with an attachment called
#p3FirstLast.txt
#(e.g. p3DoronZeilberger.txt)

#Right after attending the lecture, but no later than 4:00pm that day

Name: Anusha Nagar

LIST ALL THE ATTENDANCE QUESTIONS FOLLOWED (IF YOU KNOW THEM) BY THE ANSWERS

Attendance Question 1: Is the SIR model named after Sir Ronald Ross, or is it named after someone else?

Answer 1: The SIR model stands for Susceptible, Infected, and Recovered (or Removed) model. I can't find anything that indicates it is named after Sir Ronald Ross. 

Attendance Question 2: Why is this property not true for y'(t)=y(t)^2; 

Answer 2: Because the equation is non-linear, and the property is only valid for linear diff eq.

Attendance Question 3: 
a1:= the fifth digit of your RUID (if it is 0 make it 1)
a2:=the first digit of your RUID
a3:= second digit of RUID
My RUID: 185007365
Solve by maple the diff eq
a1*y''(t)-a2*y'(t)+a3*y(t)=0, y(0) = 0, y'(0)=0


Answer 3: dsolve({D(D(y))(t) - D(y)(t) + 8*y(t) = 0, y(0) = 0, D(y)(0) = 1}, y(t));
                 2    (1/2)    /1  \    /1   (1/2)  \
          y(t) = -- 31      exp|- t| sin|- 31      t|
                 31            \2  /    \2          /

The syntax didn't turn out well when I pasted it, so here is the answere:
y(t)=2*sqrt(31)*e^(t/2)*sin(sqrt(31)*t/2)/31

Attendance Question 4: (EXTRA CREDIT 5 POINTS):
What did professor do wrong (syntax)?

Answer 4: 

Attendance Question 5:
Why is the property that if a(n) is a solution so is C*a(n) not valid for the non-linear recurrance?
a(n)=a(n-1)^2

Answer 5: I'm not completely sure - I will review the lecture recording once it is posted again. I think it's similar to the idea with differential equations.