Mathematical Biology 4010/6010 Fall 2012
Research Project: Smallpox Max points: 100 Due Tuesday, November 27
Name:
An outbreak of smallpox in Abakaliki in southeastern Nigeria in 1967 was reported by
1. a. (10 points) Use a Riemann sum (midpoint formula) with n : 3 partitions to approximate the area
. 7 1
under the curve f (x) = x2 on the mterval [1, 7]. answer: Ax = T = 2, ana1 so
area under curv
A. Find the area of R.
Answer:
The picture looks like this:
The points of intersection of the two curves are (0,1) and (1,0).
The top curve is the parabola y : 1 3:2 and the bottom curve is the line
No calculators allowed. Show your work.
1. (2 pts.) Find the supremum/maximum/inmum/minimum (write DNE if a number does not exist) of each of the
following subsets of R. Recall: The number sup A (inf
Math 307
THE COMPLEX EXPONENTIAL FUNCTION
(These notes assume you are already familiar with the basic properties of complex
numbers.)
We make the following denition
cw:cos9+zsin9. (1)
This formula is
1. (a) (5 pts.) Give the denition of a nite set and of a countably innite set.
(b) (10 pts.) Show that if E Q R is a bounded nite set then sup E E E. (Hint: You may
want to use the Approximation Prope
SHGW ALL WGRKII i
1. (5pm) Below are for directiens fields Circle the direction dd that gags with the
differential equatien y' : 4+1,
yhm
"'f Il"~-~x\
dww /.«r_m\
*7. f: .6,»
Problem 1.vLet R be the region bounded by the curves 9: = y2 and y = 53.
A. Find the volume of the solid generated by revolving the region R around the
arc-axis.
Answer:
Heres the picture of the regio
Applications to Physics (Motion of a mass on a spring)
Sequences
What does it mean for a sequence to be increasing or decreasing? How do you show
that a sequence is increasing or decreasing?
Innite Se
Final Exam Review Math 131 L. Ballou
3x
x
1. If f(x)= , nd What is the domain of
The function, is not defined at X : 0, and the
composite is not dened at X I 3, so the domain is all reals not equ