Math 471
Fall 2009
Homework 8
due: Mon Dec 14
chapter 5, polynomial approximation and interpolation
1. page 351, problem 9
Note: This problem asks you to derive an error bound for linear polynomial in
Math 471
Fall 2009
Homework 5
due: Fri Nov 13
1. Find the eigenvalues and eigenvectors of the following matrices. Do this by hand, but you
may check your answers using Matlab.
2 1
0
0 1
20
02
2 1
a)
b
Math 471
Fall 2009
Homework 7
due: Mon Dec 7
chapter 5, polynomial approximation and interpolation
1. a) Find the Taylor series for f (x) = sin x about x = 0.
b) Using Matlab, plot the Taylor polynomi
Homework 4 Solutions
Math 471, Fall 2007 Assigned: Friday, September 28, 2007 Due: Friday, October 5, 2007 Include a cover page Clearly label all plots using title, xlabel, ylabel, legend Use the
Homework 3
Math 471, Fall 2007 Assigned: Monday, September 24, 2007 Due: Monday, October 1, 2007 Include a cover page Clearly label all plots using title, xlabel, ylabel, legend Use the subplot co
24. Mon 11/9
1
chapter 4 : computing eigenvalues
problem : Given A, nd and x = 0 such that Ax = x.
: e-value (e.g. frequency, growth rate, energy level)
x : e-vector (e.g. normal mode, principal comp
Math 471
Fall 2009
Homework 1
due: Mon Sept 21
0. (optional) Give a brief description of your academic background and research interests.
If you work in a lab or research group, please give your super
Math 471, Section 002 Coverage for Midterm 1
The first midterm will be administered from 6-8 pm on Wednesday, October 17 in East Hall 1084. You may use both sides of an 8.5" by 11" piece of paper for
Homework 5
Math 471, Fall 2007 Assigned: Friday, October 5, 2007 Due: Friday, October 12, 2007 Include a cover page Clearly label all plots using title, xlabel, ylabel, legend Use the subplot comm
Homework 2 Solutions
Math 471, Fall 2006 Assigned: Friday, September 15, 2006 Due: Friday, September 22, 2006 Include a cover page Clearly label all plots using title, xlabel, ylabel, legend Use th
Math 471
Review Sheet for Final Exam
Fall 2009
The nal exam will cover the entire course. You may use two sheets of notes (e.g. two sides
of one page, i.e. a total of 187 in2 = 2 8.5 in 11 in). You ma
Math 471
Review Sheet for Midterm Exam
Fall 2009
The midterm exam is on Friday October 30 in class. You may use one sheet of notes (i.e. one
side of one page, 8.5 in11 in). You may use a non-programma
Homework 10
Math 471, Fall 2007 Assigned: Friday, November 16, 2007 Due: Monday, December 3, 2007 Include a cover page Clearly label all plots using title, xlabel, ylabel, legend Use the subplot c
Math 471
Review Sheet for Final Exam
Fall 2009
The nal exam will cover the entire course. You may use two sheets of notes (e.g. two sides
of one page, i.e. a total of 187 in2 = 2 8.5 in 11 in). You ma
Homework 1
Math 471, Fall 2007 Assigned: Friday, September 7, 2007 Due: Friday, September 14, 2007 Include a cover page Clearly label all plots using title, xlabel, ylabel, legend Use the subplot
Homework 8
Math 471, Fall 2007 Assigned: Friday, November 2, 2007 Due: Friday, November 9, 2007 Include a cover page Clearly label all plots using title, xlabel, ylabel, legend Use the subplot com
Homework 6 Solutions
Math 471, Fall 2006 Assigned: Friday, October 20, 2006 Due: Friday, October 27, 2006 Include a cover page Clearly label all plots using title, xlabel, ylabel, legend Use the s
Math 471 Midterm 1
17 October 2007, 6-8 pm
Name: Instructor:
Show all work and circle your final answers.
If you need additional space, continue on the back of the page or on the extra sheet at t
Math 471 - Introduction to Numerical Methods - Winter 2015
Assignment # 3.
Due: Thursday, February 6, 2015.
1. Elementary Matrices
Let B be a 4 4 matrix to which we apply the following operations.
Do
Math 472
Numerical Methods with Financial Applications
Fall 2007
Course description
This is a survey of the basic numerical methods that are used to solve scientic problems,
especially ones arising in
Chapter 1
Finite precision arithmetic
Floating point representation
Let us consider
2013.9 = 2 103 + 0 102 + 1 101 + 3 100 + 9 101 = (2013.9)10 .
In general, a real number x is expressed as
x = (dn dn
Math 471 - Introduction to Numerical Methods - Winter 2015
Assignment # 1.
Due: Thursday, January 22, 2015.
1. Do the following calculations by hand.
(a) Convert to base 10: (1100101.001)2
(b) Convert
An Introduction to
Monte Carlo Simulations
Notes by
Mattias Jonsson
Version of October 4, 2006
Math 472, Fall 2006
Numerical Methods with Financial Applications
2
Contents
1. Introduction
2. Computing
Chapter 7
Time-dependent differential equations
Eulers method
First-order ordinary differential equations (ODE) are written as
dx = f (x), t > 0,
dt
x(0) = x0 .
If x(t) is the position of a particle
Chapter 2
Rootnding
Given a function f (x), a root is number r satisfying f (r) = 0. For example, for
a
f (x) = x2 3, the roots are r = 3. We want to nd the roots of a general function
f (x) using a c
Supplement for Lecture 14 (Fri, 10/4)
1 % y = r , y ( 0 ) = a l p h a , y ( 1 ) = b e t a
2 clear ; clf ;
3 alpha =0;
4 beta =1;
5 n =3;
6 h =1/( n +1);
7 x exact =0:0.0025:1;
8 y e x a c t =25/ pi 2
Homework 2
Math 471, Winter 2018
(1)
(Order of convergence of a sequence30 points) The following sequence converges to
5. Let p0 = 1. For n 0, define
5
1
pn +
pn+1 =
2
pn
Define the absolute error en
Homework 3, Solution Sketches
Math 471, Fall 2007
Assigned: Friday, September 24, 2007
Due: Friday, October 1, 2007
(1) (Newton versus Secant) Bradie, p. 113, #12.
The sequence of iterates generated b
Homework 5
Math 471, Winter 2018
Assigned: Friday, February 2, 2018
Due: Friday, February 9, 2018
(1) (Tridiagonal Matrices) A tridiagonal matrix Ais a matrix where the only nonzero elements are of th
Homework 1
Math 471, Winter 2018
(1) (Finite precision numbers15 points) The floating point representation of a real number takes the form x = (0.a1 a2 . . . an ) e , where a1 6= 0, M e M . Suppose
th
Homework 4
Math 471, Winter 2018
Assigned: Friday, January 26, 2018
Due: Friday, February 2, 2018
(1) (Counting Flops)
The inverse of an n n matrix can be computed by performing Gauss-Jordan eliminati
Homework 1
Math 471, Winter 2018
Assigned: Friday, January 5, 2018
Due: Friday, January 12, 2018
In your submission, please label all problems (with answers boxed when appropriate), and
submit in the
Homework 3
Math 471, Winter 2018
Assigned: Friday, January 19, 2018
Due: Friday, January 26, 2018
(1) (Order of Convergence) Apply the theorems on pp. 90-91 to the following problems:
a is a fixed poi