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


#Email  ShaloshBEkhad@gmail.com 
#Subject: p3
#with an attachment called
#p3NikitaJohn.txt

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

Name: Nikita John

1. Is the SIR model of epidemics named after Ronald Ross or is it named 
after something else?
	The SIR model of epidemics is not actually named after Sir Ronald
	Ross. SIR stands for Susceptible, Infected, and Removed, which 
	denotes the three distinct populations that are tracked in the 
	epidemic model.

2. Why is this property (property 1 from the notes) not true for 
y'(t) = y(t)^2?
	Property 1 is not true for this given differential equation because
	the given differential equation is not homogenous. This property
	only applies to homogeneous differential equations because they only
	have a general solution which is a linear combination of all 
	linearly independent solutions. Nonhomogeneous diff eq solutions have
	a combination of a general and specific solution, the specific
	solution coming from the nonzero right hand side of the equation, and
	multiplying that portion by a constant would change the solution to 
	the equation. 
	
3. a1:= the fifth digit of your RUID (if 0, make 1)
   a2:= the first digit of your RUID
   a3:= the second digit of your RUID
   Solve by hand (if possible) and Maple, the diff. eq 
   a1*y''(t)-a2*y'(t)+a3*y(t) = 0, y(0) = 0, y'(0) = 0
	Both doing it by hand and by Maple gave a very sad solution:
	y(t) = 0

4. Why is the property that if a(n) is a solution so is c*a(n) not valid
for the NON-LINEAR RECURRENCE a(n) = a(n-1)^2?
	The property stated above is not valid for the non-linear recurrence
	listed above because the nonlinear portion of the recurrence will
	have a specific solution, not a general one, so multiplying the 
	specific solution by c has the possibility of changing the solution
	entirely.