Math 220 (section AD?) Quiz 11 Fall 2012
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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
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composite function (f o g) ?
(F wax? 74: (x/2 %
2. (3 points) Given
Math 220 (section AD?) Quiz 9 Fall 2012
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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.
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5 area (RIP-parea029944rg,
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5 977 +6 8
s
2. (3 p
Math 220 (section AD?) Quiz 6 Fall 2012
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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
Math 371 - Introduction to Numerical Methods - Winter 2011
Homework 2
Assigned: Friday, January 14, 2011.
Due: Thursday, January 27, 2011 at 2PM.
Include a cover page. You do not need to hand in a problem sheet. Write the
problems in order and indicate c
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