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 interpolation,
|f (x) p1 (x)|
1
max |f (x)|h2 , where h
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 component, bound state)
thm : Assume A is real and symmetri
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 subplot command to compare multiple plots Include
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 polynomials pn (x) of degree n = 1, 3, 5, 7 on the same plot
on
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-programmable calculator to do arithmetic,
but to receive full cr
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 supervisors name and describe your
project. One paragraph is
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 may use a non-programmable
calculator to do arithmetic, b
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 command to compare multiple plots Include printouts
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 command to compare multiple plots Include printouts
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 the subplot command to compare multiple plots Inclu
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 the end of the exam.
No calculators allowed.
Pro
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 notes, but calculators are not allowed. Here is a
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 command to compare multiple plots Include printout
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 subplot command to compare multiple plots Include p
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 may use a non-programmable
calculator to do arithmetic, b
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 command to compare multiple plots Include printouts of
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.
Double column 1,
halve row 3,
add row 3 to row 1,
inte
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 command to compare multiple plots Include printouts o
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 actuarial and nancial applications.
The emphasis is ev
Math 471 - Introduction to Numerical Methods - Winter 2015
Assignment # 2.
Due: Thursday, January 29, 2015.
1. Peculiar behavior.
a) Compute 10n (10n 1) for n = 1, 2, , 30. What answer do you expect?
What answer do you get? Explain your observations.
b) C
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 to base 2: (2006)10
2. The oating point representation
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 areas, volumes and integrals
2.1. Examples
2.1.1. Exam
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 dn1 d1 d0 .d1 d2 )
= dn n + dn1 n1 + + d1 1 + d0 0 + d1 1
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 areas, volumes and integrals
2.1. Examples
2.1.1. Exam
Chapter 6
Numerical integration
Let us consider numerical integration such as
1
0
n
f (x)dx wi fi ,
i=0
where wi are coefcients and fi = f (xi ) for xi (i = 0, 1, . . . , n).
Trapezoid rule
Let us consider
1
0
2
ex dx = 0.7468 . . . ,
with uniform points:
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 s i n ( pi x e x a c t )+ x e x a c t ;
9 for i =1: n
1
Chapter 3
Numerical linear algebra
Review of linear algebra
We consider the following system of linear equations which has n unknowns
x1 , . . . , xn .
a11 x1 + a12 x2 + + a1n xn = b1
a21 x1 + a22 x2 + + a2n xn = b2
.
.
.
an1 x1 + an2 x2 + + ann xn =