Samantha Fisher
Lab 1
Professor Sloughter
Math 2310
Activity 1 (Survey):
Activity 2 (Snow geese):
a) Construct a histogram for the amount of acid-detergent fiber for all geese. You should notice
that this results in a very bimodal histogram. Looking at th
Cloning of genes from genomic DNA:
Part 3-Restriction Enzyme Digestion and Agarose Gel Electrophoresis
Continuing from our isolation of genomic DNA and PCR amplification of either the evenskipped gene or the twist gene, we will now move on to the third st
Math 220 (section AD?) Quiz 11 Fall 2012
Name ; 2; 5 :
a You have 15 minutes 0 N 0 calculators 0 Show sufcient work
10x
1. (4 points) Determine the average value of the function f = on the interval [1, 3].
$2 2. (3 points each) Let R be the nite region
Math 220 (section AD?) Quiz 2 Fall 2012
Name
o No calculators 0 Show sufcient work
0 You have 15 minutes
1. (4 points) A bacterial culture starts with 200 bacteria and triples in size every 2 hours.
(a) Find a formula for the number of bacteria as a func
Math 220 (section AD?) Quiz 1 Fall 2012
0 You have 15 minutes 0 No calculators 0 Show sufcient work
1. (3 points) Suppose that f = and g(x) : x/x 2. What is the domain of the
V5 :c
composite function (f o g) ?
(F wax? 74: (x/2 %
2. (3 points) Given
Math 220 (section AD?) Quiz 9 Fall 2012
Name /
0 You have 15 minutes 0 No calculators 0 Show sufcient work
8
1. (3 points) The graph of f(:1:) is shown below. Evaluate 4 f (:12) dzv.
Y
5 area (RIP-parea029944rg,
/
$3771; wWWPmw
5 977 +6 8
s
2. (3 p
Math 220 (section AD?) Quiz 6 Fall 2012
/
Name WC
0 You have 15 minutes 0 No calculators - Show sufcient work
1. (3 points) A ladder 12 feet long rests against a vertical wall. If the bottom of the ladder
slides away from the wall at a rate of 0.5 feet p
Ch. 3: Trees
Due: Beginning of class on Wednesday, April 16
4-14-14
Denition: A tree is a connected graph with no cycles.
1. Draw 5 examples of trees.
2. Prove that deleting any edge from a tree results in a disconnected graph.
3. Let G be a graph with th
Ch. 4: Planar Graphs
4-28-14
1. Draw three planar graphs. How many vertices, edges, and regions does each one have?
2. Prove that every tree is planar. How many vertices, edges, and regions does a planar
drawing of a tree have?
3. In class, we looked at t
Ch. 5: Graph Colorings
5-7-14
This assignment is due on Monday, May 12.
At some point between now and Mondays class, nd a quiet place to sit down and focus
on math for (at least) two hours. During that time, your objective is to try to prove the
Four Colo
Ch. 2: Eulerian and Hamiltonian Graphs
Due: Beginning of class on Monday, April 14
4-11-14
Decide whether or not each of these graphs is Eulerian and/or Hamiltonian. If the graph
is Eulerian and/or Hamiltonian, exhibit an Eulerian and/or Hamiltonian circu
Ch. 1: Denitions and Examples
Due: Beginning of class on Friday, April 4
4-2-14
1. Compute the degree sequences of each of the graphs from Mondays homework.
2. Is it possible to nd a graph with 5 vertices such that each vertex has degree 3?
3. Is it possi
Ch. 1: Denitions and Examples
Due: Beginning of class on Monday, April 7
4-4-14
1. Here is a graph that doesnt appear to be bipartite. First, verify that each of its cycles
only has even length. Next, nd a way to draw it in a bipartite manner.
2. Can a ki
Math 371 - Introduction to Numerical Methods - Winter 2009
Homework 3
Assigned: Wednesday, February 2, 2011.
Due: Friday, February 11, 2011 at 2 PM.
Include a cover page. You do not need to hand in a problem sheet. Write the
problems in order and indicat
Rate of Convergence
Sequence 1. This computes a sequence xn that converges to 2. This sequence has a rate of convergence O 1 n3 . A possible
value of 5. Looking at the table below we can see that indeed, the error xn
x n_
n_
x 5;
2 n^3 1
1 n^3 ;
Grid Ta
Newton vs. Secant Method
Newton's Method
First we define a function f(x) and ask Mathematica to find a root of this function close to 1.
f x_
Exp x
x
4
root
x
x^2
x
4
x2
x
FindRoot f x ,
x, .5
1.28867796682387
act
x . root
1.28867796682387
For Newton's Me
Chebyshev Nodes
Definitions and Basics
In this notebook I will do an example where the nodes of an interpolating polynomial are determined by using the zeros of a Chebyshev Polynomial.
The Chebyshev Polynomials are defined for x in the interval [-1, 1] an
Cubic Spline
Suppose we are given a set of interpolating points (xi , yi ) for i = 0, 1, 2, 3 . . . n. We
seek to construct a piecewise cubic function s(x) that has the for x [xj , xj+1 ] we have:
s(x) = sj (x) = aj + bj (x xj ) + cj (x xj )2 + dj (x xj )
Math 371 - Introduction to Numerical Methods - Winter 2011
Homework 4
Assigned: Friday, February 11, 2011.
Due: Monday, February 28, 2011 at 2 PM.
1. In this problem we will investigate the Cubic Spline problem and compare the
convergence using dierent bo
Accelerating Convergence
Suppose we have a fixed point method that converges linearly. Then we talked about
the fact that:
en
p
g' p
1 g' p
pn
pn
pn
1
and
g' p
pn pn 1
pn 1 pn 2
So, if we put these two expressions together we have that
p
pn pn 1 2
pn pn 2
Math 371 - Introduction to Numerical Methods - Winter 2011
Homework 2
Assigned: Friday, January 14, 2011.
Due: Thursday, January 27, 2011.
Include a cover page. You do not need to hand in a problem sheet. Write the
problems in order and indicate clearly
Math 371 - Introduction to Numerical Methods - Winter 2011
Homework 5
Assigned: Friday, February 28, 2011.
Due: Monday, March, 14, 2011 at 2 PM.
All normal rules apply
1. Section 3.1 #3 Do this by hand and show your work clearly.
Solve the following syste
Math 371 - Introduction to Numerical Methods - Winter 2011
Homework 4
Assigned: Friday, February 11, 2011.
Due: Monday, February 28, 2011 at 2 PM.
All normal rules apply
1. In this problem we will investigate the Cubic Spline problem and compare the
conve
Math 371 - Introduction to Numerical Methods - Winter 2011
Homework 5
Assigned: Friday, February 28, 2011.
Due: Monday, March, 14, 2011 at 2 PM.
All normal rules apply
1. Section 3.1 #3 Do this by hand and show your work clearly.
2. Section 3.2 # 4 Do thi