Mth 351 Documents

Last updated January 18, 2005

This page lists current and old assignments, old tests, notes, Maple worksheets, sample problems, etc., for Mth 351. You may find this material useful for studying. Expect some overlaps in the various files. Eventually very old files will dribble off the bottom.

Many of the documents are in Portable Document Format (PDF) or are Maple worksheets (MWS). PDF files are "Portable Document Files." You can use the free Adobe Acrobat Reader, available at http://www.adobe.com, to view or print PDF files. The Acrobat Reader plug-in is installed in the browser(s) on many campus computers. There are many other software packages for reading PDF files. Maple Worksheets require Maple to be useful.

Problems viewing or printing PDF files. Please report any problems you have reading or printing my PDF files.

2005 Fall Mth 351 Elementary Numerical Analysis Final Exam
PDF, xx KB, x problems, x pages
To be posted.
2005 Fall Mth 351 Elementary Numerical Analysis Test 2
PDF, 45 KB, 8 problems, 3 pages
This test was given in class Wednesday November 16, 2005. The answers are:   B   C   E   A   D   C   B   C.
2005 Fall Mth 351 Elementary Numerical Analysis Assignment 1
PDF, 17 KB, 3 pages
Code: ur.c, 1.4 KB
This assignment is due September 4, 2005. It involves computing the unit round (precision) for various computers. If writing and compiling a program is not your forte you might consider testing what results are obtained from a spreadsheet. If you decide to test a calculator you may need to convert the code to assume base 10. Above all, experiment and have fun! (October 31: I altered the code ur.c a bit to remove the long lines that were being truncated in the PDF file.)
2005 Fall Mth 351 Elementary Numerical Analysis Test 1
PDF, 44 KB, 8 problems, 3 pages
This test was given Wednesday October 19, 2005. Note I corrected problem number 1 here so answer C now says 1.37 10-4 and is the only correct answer. The test as given in class had 1.35 10-4. This is the correctly rounded error but not really an upper bound. For an upper bound one would have to choose B 8.64 10-3. For the class test either B or C is accepted as the correct answer for problem number 1. There was also a sign error in problem 8 which was corrected during the test and which has also been corrected on the test posted here. The answers are:   C   B   B   A   D   C   B   D.
2005 Fall Mth 351 Lab Visit - October 7
PDF, 71 KB, 13 pages
MWS, 22 KB Maple Worksheet
This Maple 8 worksheet (it should work in Maple 10 too) presents a very brief introduction to Maple. Some simple interactive techniques are described, but there is no discussion of programming. The PDF file contains all of the Maple output including the plots. The worksheet does not include any Maple output. You have to create the output by executing the commands in the worksheet. Anyone content simply to execute the worksheet the way it is, lacks courage or is missing the point! Change things! Experiment! You can always download a fresh copy if you get in trouble. You should be able to use the browser to download the MWS file and then double-click on the download image icon to start Maple. The PDF file is provided for use if you are somewhere where Maple is not available and you want to read about it. Have fun!
2005 Summer Mth 351 Elementary Numerical Analysis Test 2
PDF, 41 KB, 9 problems, 3 pages
This test was given Wednesday August 10, 2005.
2005 Summer Mth 351 Elementary Numerical Analysis Test 1
PDF, 43 KB, 10 problems, 3 pages
This test was given Monday July 25, 2005.
2005 Summer Mth 351 Elementary Numerical Analysis Sample Problems
PDF, 51 KB, 5 pages, 20 problems
Sample problems for final test. The final test will have multiple choice problems. Since multiple choice problems take longer to compose, the sample problems here are not in the multiple choice format.
2005 Summer Mth 351 Elementary Numerical Analysis Assignment 4
PDF, 22 KB, 1 page, 4 problems
This set of problems deals with interpolation polynomials. The first 3 problems require a lot of calculation and some plotting. You may find spreadsheet software very useful. If you have Maple, Mathematica, Matlab, Octave or MathCad, and know how to use it, that would greatly simplify the calculations (while perhaps introducing some new difficulties!).
2005 Summer Mth 351 Elementary Numerical Analysis Assignment 3
PDF, 26 KB, 1 page, 3 problems
One roundoff problem (decimal) and two root finding problems (methods of Olver, Halley and Regula Falsi).
2005 Summer Mth 351 Elementary Numerical Analysis Assignment 2
PDF, 25 KB, 1 page, 3 problems
Floating point. Significant figures.
2005 Summer Mth 351 Elementary Numerical Analysis Assignment 1
PDF, 18 KB, 1 page, 1 problem
One problem on Taylor polynomial approximation.
2004 Summer Mth 351 Elementary Numerical Analysis Problems - 20040806
PDF, 299 KB, 45 pages
Sample problems for the entire quarter.
2003 Fall Mth 351 - Solution to problem 18.3
PDF, 27 KB, 2 pages
Here is a sample solution rendered more interesting by an error in the problem.
2003 Fall Mth 351 - Mth 351 Problem Collection 2003 Fall - 20031203
PDF, 207 KB, 44 pages
I will add many problems to this list during the term. The current version was created Dec  3. Some of the problems in this list are new this quarter. Others are from old tests, assignments and sample problem sets. I am in the process of removing duplicates below, but it is hardly a priority task.
2003 Summer Mth 351 Elementary Numerical Analysis
All the files from Summer 2003 Mth 351 have been incorporated in the Mth 351 Problem Collection 2003 Fall listed above.
2003 Winter Mth 351 Sample Problems for the Final Exam
PDF, 43 KB, 3 pages, 9 problems
These sample problems do not cover all of the material for the final. If I find the time I will post a few more problems for you to look at. You should also look at some of the old final exams and old sample problems on the Documents page.
2003 Winter Mth 351 Elementary Numerical Analysis Assignment 3
PDF, 27 KB, 1 page, 6 problems
Numeric quadrature rules.
2003 Winter Mth 351 Elementary Numerical Analysis Assignment 2
PDF, 18 KB, 1 page, 2 problems
Newton's method for systems of nonlinear equations
2003 Winter Mth 351 Elementary Numerical Analysis Midterm Test
PDF, 43 KB, 8 problems, 4 pages
This midterm was given Feb 17, 2003.
2003 Winter Mth 351 Elementary Numerical Analysis Sample Problems for the Midterm
PDF, 39 KB, 7 problems, 2 pages
2003 Winter Mth 351 Elementary Numerical Analysis Assignment 1
PDF, 29 KB, 1 page, 2 problems
Significant decimal digits. Numeric differentiation.
2002 Fall Mth 351 Elementary Numerical Analysis Exam
PDF, 115 KB, 6 pages, 8 problems
2002 Fall Mth 351 Newton's Iterative Method for Systems of Nonlinear Equations
MWS, 31 KB, Maple Worksheet
This worksheet illustrates Newton's root iteration for a system of two nonlinear equations.
2002 Fall Mth 351 Elementary Numerical Analysis Midterm
PDF, 113 KB, 3 pages, 6 problems
2002 Fall Mth 351 Assignment 3 - Maple's linalgpackage
MWS, 64 KB, 6 problems, Maple Worksheet
PDF, 117 KB, 30 pages
Problems on LU factorization, Cholesky factorization, symbolic row reduction, cubic interpolation polynomial, roundoff in calculating the matrix inverse, Vandermonde determinant.
2002 Fall Mth 351 Elementary Numerical Analysis MLC Lab Visit
MWS, 36 KB, Maple Worksheet
PDF, 307 KB, 26 pages
2002 Fall Mth 351 Assignment 2
PDF, 24 KB, 1 page, 2 problems
Some things that can go wrong with the Newton - Raphson method.
2002 Fall Mth 351 Assignment 1 Newton-Raphson and Newton-Halley iterations for estimating roots
PDF, 26 KB, 1 page, 2 problems
2002 Summer Mth 351 Elementary Numerical Analysis Test 2
PDF, 93 KB, 3 pages, 8 problems
2002 Summer Mth 351 Elementary Numerical Analysis Sample Problems for Test 2
PDF, 43 KB, 2 pages, 10 problems
2002 Summer Mth 351 Gauss Qudrature MWS, 14 KB, Maple Worksheet
PDF, 44 KB, 5 pages
2002 Summer Mth 351 Elementary Numerical Analysis Assignment 3
MWS, 31 KB, 7 problems, Maple Worksheet
PDF, 69 KB, 1 page
This assignment includes Matlab instructions.
2002 Summer Mth 351 Elementary Numerical Analysis Assignment 2
HTML, 4 KB, 2 problems
Least squares.
2002 Summer Mth 351 Elementary Numerical Analysis Assignment 2 Cigarette Data File
TXT, 2 KB
2002 Summer Mth 351 Least Squares Polynomials in Matlab
HTML, 3 KB, Matlab
2002 Summer Mth 351 Linear Least Squares in Maple
MWS, 19 KB, Maple Worksheet
PDF, 70 KB, 5 pages
2002 Summer Mth 351 Elementary Numerical Analysis Test 1
PDF, 42 KB, 3 pages, 8 problems
2002 Summer Mth 351 Elementary Numerical Analysis Sample Problems for Test 1
PDF, 60 KB, 5 pages, 29 problems
2002 Summer Mth 351 Introduction to Maple - MLC Lab Visit
MWS, 78 KB, Maple Worksheet
PDF, 420 KB, 49 pages
Introduction. Login. Logout. Getting started. The worksheet. Assignment and ditto operators. Constants. Digits. Functions and expressions. Derivatives. Integration. Some plots. More plots. Taylor series and Taylor polynomials. Interpolation polynomials. Interpolation splines. Trapezoidal and Simpson's rules. Sums and products. Number theory. Solving equations. Linear algebra (linalg package). Limits. Recursion and remember. Set theory.
2002 Summer Mth 351 Introduction to Matlab - MLC Lab Visit
HTML, 27 KB, Matlab
An introduction to Matlab and some Matlab programming. Some material from Fall 2001.
2002 Summer Mth 351 Assignment 1 - Logistic Equation
PDF, 20 KB, 1 page, 2 problems
2002 Summer Mth 351 Fixed Point Iteration - Logistic Equation
MWS, 124 KB, 2 problems, Maple Worksheet
PDF, 54 KB, 3 pages
2002 Summer Mth 351 Taylor Polynomials
MWS, 31 KB, Maple Worksheet
PDF, 86 KB, 6 pages
2001 Fall Mth 351 Elementary Numerical Analysis Final Exam
PDF, 97 KB, 2 pages, 8 problems
2001 Fall Mth 351 Elementary Numerical Analysis Test
PDF, 117 KB, 3 pages, 8 problems
2001 Fall Mth 351 Assignment 2. Least squares for Steinhart-Hart equation
MWS, 11 KB, Maple Worksheet
PDF, 46 KB, 3 pages, 1 problem
2001 Fall Mth 351 Assignment 1. Newton and secant methods
MWS, 13 KB, 4 problems, Maple Worksheet
PDF, 44 KB, 4 pages
2001 Fall Mth 351 Midpoint Method for Estimating Roots
MWS, 7 KB, Maple Worksheet
PDF, 16 KB, 3 pages
2001 Fall Mth 351 Introduction to Maple - MLC Lab Visit
MWS, 58 KB, Maple Worksheet
PDF, 378 KB, 36 pages
2001 Fall Mth 351 Method of Least Squares in Maple
MWS, 13 KB, Maple Worksheet
PDF, 114 KB, 11 pages
2001 Summer Mth 351 Elementary Numerical Analysis Test 1
PDF, 43 KB, 3 pages, 6 problems
2001 Summer Mth 351 Elementary Numerical Analysis Test 2
PDF, 49 KB, 2 pages, 6 problems
2001 Summer Mth 351 Elementary Numerical Analysis Assignment 5
MWS, 80 KB, Maple Worksheet
PDF, 108 KB, 10 pages
Interpolation and extrapolation. Egyptian cereal imports.
2001 Summer Mth 351 Some Interpolation Examples. Splines and Polynomials
MWS, 91 KB, Maple Worksheet
PDF, 193 KB, 14 pages
2001 Summer Mth 351 MLC Lab Visit
MWS, 35 KB, Maple Worksheet
PDF, 316 KB, 24 pages
2001 Summer Mth 351 Elementary Numerical Analysis Assignment 4
PDF, 39 KB, 4 pages
Newton divided differences. Interpolation.
2001 Summer Mth 351 Source Code for Assignment 4
c-source, 5 KB
Divided differences - divdiff.c
2001 Summer Mth 351 Elementary Numerical Analysis Assignment 3
PDF, 39 KB, 6 pages
Newton's root iteration.
2001 Summer Mth 351 Source Code for Assignment 3
c-source, 5 KB
Newton's method - newton.c
2001 Summer Mth 351 Elementary Numerical Analysis Assignment 2
PDF, 36 KB, 4 pages
Determination of unit round or floating point precision.
2001 Summer Mth 351 Source Code for Assignment 2
c-source, 2 KB
Code eps2.c
2001 Summer Mth 351 Elementary Numerical Analysis Assignment 1
PDF, 45 KB, 4 pages, 1 problem
Horner's method or synthetic division.
2001 Summer Mth 351 Source Code for Assignment 1
c-source, 3 KB
Source code for Horner's method - horner.c
2001 Summer Mth 351 Data File for Assignment 1
text file, 1 KB
Coefficients for assignment 1 - coef.dat
2001 Summer Mth 351 Table of Derivative Approximations
PDF, 30 KB, 1 page
2001 Spring Mth 351 Elementary Numerical Analysis Archive
PDF, 121 KB, 15 pages, 16 problems
Test, final exam and four assignments: 1. Hermite interpolation, 2. Application of numeric differentiation, 3. Unit round, 4. Lagrange interpolation polynomials.
2001 Spring Mth 351 Visit to the MLC Computer Lab
MWS, 31 KB, Maple Worksheet
PDF, 164 KB, 20 pages
This Maple 6 worksheet (it should work in Maple 5 too) presents an introduction to Maple in the MLC Computer Lab. Some examples relevant to Mth 351 are also given: interpolation polynomials, natural cubic splines, trapezoidal and Simpson's rules, etc. Some simple but useful interactive techniques are described (but there is no discussion of programming). The PDF file contains all of the Maple output including the plots. The worksheet does not include any Maple output. You have to create the output by executing the commands in the worksheet. Anyone content simply to execute the worksheet the way it is lacks courage or is missing the point! Change things! Experiment! You can always download a fresh copy if you get in trouble.
2001 Spring Mth 351 Interpolation Polynomials
MWS, 26 KB, Maple Worksheet
PDF, 209 KB, 6 pages
This worksheet provides a routine finterp() to compute interpolation polynomials for functions. It's not much of a routine - you can think of it as a wrapper for Maple's built-in interp() routine. I also provide a routine to compute equispaced nodes and Chebysev nodes for any interval. These are simple tools that allow you to experiment rapidly and conveniently with interpolation polynomials.
2001 Spring Mth 351 Newton Divided Differences and Interpolation
MWS, 10 KB, Maple Worksheet
PDF, 17 KB, 4 pages
This worksheet provides a simple recursive procedure to compute Newton divided differences and a procedure which uses the divided differences and Horner's method to compute an interpolation polynomial for a function. The nodes do not need to be distinct. Of course, interpolation polynomials may more conveniently be computed by using Maple's built in routine interp(). The code presented in this worksheet is intended only to demonstrate the Newton formula for the interpolation polynomial.
2001 Spring Mth 351 Derivative Estimates by Undetermined Coefficients
MWS, 25 KB, Maple Worksheet
PDF, 31 KB, 9 pages
Maple is very handy for algebraic manipulations that are difficult to get right by hand (even if they are easy to do). Here we use Maple to obtain numeric estimates of various kinds for low order derivatives of functions.
2001 Spring Mth 351 Table of Derivative Approximations
PDF, 29 KB, 1 page
2001 Spring Mth 351 Intel 80x87 Floating Point Data Types - IEEE Std. 754
HTML, 16 KB
1999 Summer Mth 351 Elementary Numerical Analysis Archive
PDF, 114 KB, 10 pages
Test. Final exam. Four assignments: 1. Taylor polynomials, 2. Discrete derivatives, 3. Interpolation, 4. Quadrature
1999 Summer Mth 351 Simpson's Rule and Cubics
MWS, 16 KB, Maple Worksheet
PDF, 22 KB, 4 pages
Simpson's quadrature rule is exact for cubics. The reason is that for any three points on a cubic, with equispaced abscissas, the area under the graph of the cubic from the first to the last point is the same as the area under the graph of the unique interpolating quadratic through the three points. There is an analogous property for the case of polynomials of degree 2n+1 and 2n. This worksheet illustrates this property by computing the integrals symbolically (through degree 7).
1999 Summer Mth 351 Newton-Cotes Quadrature
MWS, 19 KB, Maple Worksheet
PDF, 24 KB, 7 pages
We develop a Maple routine to do Newton-Cotes quadrature of any degree and any order. We note the weights are not positive in degree 8 and some higher degrees, though they are positive in degree 9 and in degrees 1 through 7. We note Boole's rule is no more difficult to use than Simpson's rule but may be much more accurate for smooth functions.
1999 Summer Mth 351 Romberg Quadrature
MWS, 25 KB, Maple Worksheet
PDF, 26 KB, 9 pages
We develop a simple Maple procedure to do Romberg quadrature and experiment with its behavior.
1999 Summer Mth 351 Gauss Quadrature
MWS, 14 KB, Maple Worksheet 
PDF, 19 KB, 4 pages
This worksheet introduces some Maple procedures that allow one to experiment with Gauss quadrature. The required Gauss nodes and Gauss weights are computed by a simple Maple procedure. A comparison with Simpson's rule for a few examples, is given.
1999 Winter Mth 351 Elementary Numerical Analysis Archive
PDF, 169 KB, 28 pages
Test. Final exam. Five assignments: 1. Latitude of Vinland, 2. Harmonic series, 3. Newton's iteration for roots, 4. Numerical differentiation, 5. Numerical quadrature. Maple notes: 1. LaTeX 2e and plots in Maple, 2. Least squares fitting in Maple, 3. Gauss quadrature in Maple, 4. Spline interpolation in Maple, 5. More spline interpolation in Maple
1998 Summer Mth 351 Elementary Numerical Analysis Archive
PDF, 188 KB, 41 pages, 13 problems
Final exam and six assignments: 1. Floating point unit round, 2. Stirling's formula and roundoff, 3. Taylor polynomials and roundoff, 4. Newton's method for roots, 5. Least squares fitting, 6. Interpolation polynomials. Interpolation in Maple. Interpolation in C. Note on Chebyshev nodes
1996 Fall Mth 351 Introduction to Maple in the MLC Lab
MWS, 11 KB (partial contents only), Maple Worksheet
PDF, 102 KB, 10 pages, 5 problems
Starting Maple. Integer examples. Functions in Maple. Integrals. Limits. Solutions of equations. Taylor polynomials.
1996 Fall Mth 351 Elementary Numerical Analysis Archive
PDF, 112 KB, 20 pages, 16 problems
Two tests, final exam, four assignments: 1. Amortized loan, 2. Newton's method for roots, 3. Interpolation polynomials, 4. Cubic spline interpolation
1995 Fall Mth 351 Using Maple in the Mathematics Computer Lab
PDF, 63 KB, 5 pages
1995 Fall Mth 351 Elementary Numerical Analysis Archive
PDF, 138 KB, 22 pages, 64 problems
Sample problem set, test, final exam and four assignments: 1. Derivative estimates, 2. Taylor polynomials, 3. Least squares interpolation, 4. Economizing a polynomial
1994 Spring Mth 351 Elementary Numerical Analysis Archive
PDF, 135 KB, 24 pages, 68 problems
Sample problems, test, final exam and six assignments: 1,2. Taylor polynomial estimates. 3. Numerical derivatives. 4. Newton's method. Roots of Polynomials. 5. Wilkinson's polynomial. 6. Lagrange interpolation polynomial.

Copyright © 19xx-2004 Bent E. Petersen. The documents and the Maple worksheets described here, may be used, copied and distributed freely, entire and intact, for any educational noncommercial purpose, but may not be distributed in an altered form. If you want to improve on anything, which certainly can be done, then please write your own version(s).

petersen@math.oregonstate.edu

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