Mth 351 Exam
Name:
Bent Petersen
Dec 5, 2001
351f2001_exam.tex
Instructions: =
ID:
Time: 110 minutes.
You may use one note-sheet prepared in advance. You must put your name on your
note-sheet, but do not turn in your note-sheet. Your note-sheet must be l
Mth 351 Sample Problems
Bent Petersen
Name:
ID:
351w2003_exam_samples.tex March 12, 2003
Instructions: =
If you do not read the instructions, then how will
you know what to do? Read
them now.
Time: xxx minutes.
You may use one note-sheet prepared in adva
Problem 18.3
Use N EWTONs method for systems to approximate a solution to the system of equations
x2 + y 2 + z 3
x + 2y 2z
x3 + y 3 3z 2
=3
=0
= 2.
Use the initial point [1.0, 1.0, 0] and iterate three times. Given that the actual solution is [1.44825, 0.
Our goal is to approximate a function by a Taylor polynomial of degree
n of the form
n
X
f (k) (a)
(x a)k .
Tn (x) =
k!
k=0
In this approximation the functions f (x) and Tn (x) have derivatives that are
equal at x = a and all of their higher order derivat
2-! V3
12 Z/3
3 rohm of
50m e amewqu we flaw, = 1 _7. o m 1' i '19 , :1:
n mm A
3 wmo 12x61,
1 x'Io 3H , 15x16:
b
_1x_"';o -22mo 3m
onv n 2
53 at] 4 in]: H. uni 11.1 I In (a 144.; ' 1r
Raft; . n, o r 0/1/27 .14 I.
1.11' J 11 1., c 1 n I IS I cfw_II
Sample Midterm Problems
MTH 351
Fall 2015
1. Consider the following calculation
1+x1
x
(a) Explain why errors might occur if x is very small.
f (x) =
(b) Reformulate the expression to reduce computational errors.
(c) What is the value of the limit of f (x
Mth 351
Assignment 3 Winter 2003
Due:
Mar 14, 2003
Bent Petersen 351w2003_asg03.tex
For a certain function f on the interval [0, 3] the (compound) trapezoidal rule with 2k subintervals yields the following
3
estimates for the integral 0 f (x) dx,
k
0
1.60
Summer
Mth 351 Test 2
2005
(This test requires you use the provided scantron)
Bent Petersen 351u2005-test2.tex Test date: August 10 2005 Time: 70 minutes
Instructions: =
This test is a multiple-choice test. Be sure you put your name on the scantron.
If y
Mth 351 Test 1
Summer
(This test requires you use the provided scantron)
2005
Bent Petersen 351u2005-test1.tex Test date: July 25 2005 Time: 70 minutes
Instructions: =
This test is a multiple-choice test. Be sure you put your name on the scantron.
If you
Mth 351 Exam
Name:
Bent Petersen
Thursday Dec 12, 2002
351f2002_exam.tex
Instructions: =
If you do not read the instructions, then how will
you know what to do?
Read them now.
ID:
Time: 110 minutes.
You may use one note-sheet prepared in advance. You mus
Maple linalg package
Mth 351 October 27 2002 Maple 6
Bent E. Petersen
Assignment 3 - Due Nov 5 - see below
Introduction
Maple 6 comes with two packages for linear algebra, linalg and LinearAlgebra. In this worksheet we
will only explore the linalg package
Mth 351 Midterm
Bent Petersen
Name:
351f2002_midterm.tex
Instructions: =
If you do not read the instructions, then how will
you know what to do?
Read them now.
Nov 8, 2002
ID:
Time: 50 minutes.
You may use one note-sheet prepared in advance. You must put
Mth 351 Test 1
Fall
(This test requires you use the provided scantron)
2005
Bent Petersen 351f2005-test-1.tex Test date: October 19 2005 Time: 50 minutes
Instructions: =
This test is a multiple-choice test. Be sure you put your name on the scantron.
If y
Mth 351 Test 2
Fall
(This test requires you use the provided scantron)
2005
Bent Petersen 351f2005-test-2.tex Test date: xxxx 2005 Time: xx minutes
Instructions: =
This test is a multiple-choice test. Be sure you put your name on the scantron.
If you do
3 51 A SSIGNMENT 1
Due: November 4, 2005
1 Introduction
The (very inelegant) c code below can be used to determine the unit round (also called precision or
epsilon) for the three standard c oating point data types. These unit rounds are frequently dened
Elementary Numerical Analysis
Bent E. Petersen
Summer 2004 20040806
Contents
13 Interpolation polynomials and N EWTON
divided differences
19
1
TAYLOR Polynomials
2
2
Errors
7
14 Interpolation and C EBY S EV polynomials 21
15 Interpolation Splines
16 Least
Mth 351 Assignment 1
Summer
2005
Name:
Bent Petersen 351u2005-001.tex Due date: Wed June 29, 2005
Instructions: Please supply your solution(s) by the due date in the space provided below. Continue on to the
back of the sheet if you need more space. If you
Mth 351 Assignment 2
Summer
2005
Name:
Bent Petersen 351u2005-002.tex Due date: Wed July 6, 2005
Instructions: Please supply your solution(s) by the due date in the space provided below. Continue on to the
back of the sheet if you need more space. If you
Mth 351 Assignment 3
Summer
2005
Name:
Bent Petersen 351u2005-003.tex Due date: Wed July 13, 2005
Instructions: Please supply your solution(s) by the due date in the space provided below. Continue on to the
back of the sheet if you need more space. If you
Mth 351 Assignment 4
Summer
2005
Name:
Bent Petersen 351u2005-004.tex Due date: Wed June 27, 2005
Instructions: Please supply your solution(s) by the due date in the space provided below. Continue on to the
back of the sheet if you need more space. If you
Mth 351 Sample Problems
Summer
2005
(This test requires you use the provided scantron)
Bent Petersen 351u2005-sample.tex Test date: August 10 2005 Time: 70 minutes
Instructions: =
This test is a multiple-choice test. Be sure you put your name on the scan