#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: Shreya Ghosh

Q1. Is the SIR model named after Sir Ronald Ross or something else?

A1. The SIR model is not named after Is Ronald Ross. It is actually named after the three compartments that compose the model: the susceptible, the infected, and the recovered.

Q2. Why is this property not true for y'(t)= y(t)^2? (non homogeneous equations)

A2. The solutions cannot be added because in linear homogenous equations, the derivative of the addition of a sum of functions is the same as the sum of the derivatives of the individual functions, however, this is not the case for non homogenous equations, as the functions are part of greater functions.

Q3. a1:= fifth digit RUID, a2:=first digit RUID, a3:= second digit RUID. solve by maple and by hand: a1*y''(t) - a2*y'(t) + a3*y(t) = 0, y(0) = 0, y'(0) = 0

A3. dsolve({D(D(y))(t) - D(y)(t) + 8*y(t) = 0, y(0) = 0, D(y)(0) = 0}, y(t));
                            y(t) = 0


Q4. Why is the property that is a(n) is a solution so is C*a(n) not valid for non-linear recurrences?
 
A4. The coefficient does not remain constant in the recurrence so it cannot be factored out like in linear solutions.