This page lists notes, Maple worksheets, assignments, etc., for Mth 480. 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.

2008 Spring Mth 480 Maple Worksheet 2
MWS, 19 KB, Maple Worksheet
PDF, 47 KB, 15 pages

This Maple worksheet contains 6 examples of using Maple to investigate the solutions of differential equations. If you finished working through the previous worksheet on Wednesday, this worksheet will give you a bit more material to play with on Friday. I regret I didn't have time to make up more examples, but I hope there is enough material here to convince you that Maple can be very useful in investigating mathematical problems.

It is not difficult to write a worksheet to integrate (numerically) the 3 or 4 body problems for various initial conditions. You might try that as a project for rainy days this summer. In any case, have a great summer!

You can use the command "Open URL..." on the File menu of Maple to download the worksheet as

http://oregonstate.edu/~peterseb/mth480/docs/maple02.mws or you can just click on this link to load the worksheet as a text file into the browser, and then save it, or, as before, whatever you can think of. Most sensible things should work.

2008 Spring Mth 480 Maple Worksheet
MWS, 84 KB, Maple Worksheet
PDF, 91 KB, 29 pages

This Maple worksheet gives a brief introduction to interactive use of Maple. I have removed all the Maple output from the worksheet so you'll have to execute the commands to see what happens. I did this in part to give you a bit of exercise, but mostly because with the output present the worksheet is over 10 MB! As usual, you should of course experiment by making changes. The PDF file is just a static PDF image of the Maple file and is not very exciting, but it has the expected Maple output in it and, of course, you don't need Maple to look at it.

If I manage to reserve the MLC Lab on Wednesday and Friday of week 10 of Spring quarter we will work through the examples in this worksheet in the lab. You are expected to experiment and to have fun. If thrash the whole worksheet you can always download a fresh copy. By the way the Maple MWS file is actually a plain text file so any way you get in onto a lab PC should give you a functioning worksheet file. You can use the command "Open URL..." on the File menu of Maple to download the worksheet as

http://oregonstate.edu/~peterseb/mth480/docs/maple01.mws or you can just click on this link to load the worksheet as a text file into the browser, and then save it, or -- well, whatever you can think of.

Here's an ancient Maple worksheet from Mth 351 (Numerical Analysis). It overlaps quite a bit with the one above but has some additional material. There are additional worksheets covering assorted material on this web site under Mth 351 and quite a few under Mth 355(399).

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.

2008 Spring Mth 480 Poincare-Bendixson Example
MWS, 150 KB, Maple Worksheet
PDF, 57 KB PDF file

This Maple worksheet plots several solutions to a system which by the Poincare-Bendixson theorem has a stable limit cycle. The MWS file is a Maple 8 worksheet which you can play with in various ways if you have Maple available. As far as I know it doesn't use any recent Maple features so it should work with some earlier versions of Maple. The PDF file is just a static PDF image of the Maple file and is not very exciting, but you don't need Maple to look at it.

2008 Spring Mth 480 Lorenz' attractor
MWS, 124 KB, Maple Worksheet
PDF, 32 KB PDF file

(Updated May 31 2008) This Maple worksheet plots the Lorenz attractor. The MWS file is a Maple 8 worksheet which you can play with in various ways if you have Maple available. As far as I know it doesn't use any recent Maple features so it should work with some earlier versions of Maple. Please note that the image of the attractor is live in the sense that you can grab it with the mouse and rotate it to view it from different angles. If you rotate it just right you can see the butterfly-wings shape (sort of). The PDF file is just a static PDF image of the Maple file and is not very exciting, but you don't need Maple to look at it.

2008 Spring Mth 480 Kepler's Problem notes
PDF, 77 KB, 12 pages, 2 problems

This note discusses the solution of the gravitational 2-body problem. In addition I derive Bessel's solution of Kepler's problem - the problem determining the position explicitly as function of time. I added a couple of simple problems for your amusement. Turn in your solutions if you wish.

2008 Spring Mth 480 Problem Set 3
PDF, 16 KB, 1 page, problems 5-9

These problems deal with computing the exponential of matrices.

2008 Spring Mth 480 Problem Set 2
PDF, 13 KB, 1 page, no problems

Here are a few hints for Problem Set 1.

2008 Spring Mth 480 Problem Set 1
PDF, 25 KB, 2 pages, problems 1-4

These problems deal with a simple vibrating system described by four linear differential equations. Due April 21. It's quite a bit of work to do them by hand, so in a few days I may post some helpful tidbits of information. (This problem set had a typographical error and has been corrected.)

2007 Spring Mth 480 Maple Worksheet for MLC Lab
MWS, 37 KB, Maple Worksheet
PDF (in progress),

This Maple Worksheet is a short introduction to a small fraction of Maple's facilities for solving and studying systems of differential equations. Just download the MWS file and load it into Maple. In MS Windows you can probably just double click the file after downloading it. Once the file is open in Maple place the cursor on the first command line (restart) and then press Enter. Each time you press enter the corresponding command(s) is (are) executed and the cursor drops to the next command. Be sure to read the intervening text as well! When you get tired of just reading start modifying some of the commands or write your own. I had some difficulty with my computer and with Maple while writing this worksheet. Large chunks of it were deleted when I saved intermediate versions. Hence it took "forever" to get a moderately complete version. I just hope it works.

2007 Spring Mth 480 Note: The Picard Iteration
PDF, 130 KB, 14 pages, several exercises

These notes deal mostly with the application of the contraction mapping principle to proving existence of solutions to the initial value problem for ordinary differential equations.

2007 Spring Mth 480 Problem Set 4
PDF, 28 KB, 3 pages, 1 problem (Problem 7)

Here is a "simple" circuit problem - a band reject or notch filter. You may find the calculations quite overwhelming to do by hand. Your solutions are due Wednesday, May 9, 2007. Addendum: This is now the updated version with more suggestions. It should be less overwhelming.

2007 Spring Mth 480 Problem Set 3
PDF, 22 KB, 2 pages, 3 problems (Problem 4-6)

Here are a few problems related to the Floquet theorem. Your solutions are due Wednesday, April 25, 2007.

2007 Spring Mth 480 Problem Set 2
PDF, 17 KB, 1 page, 1 problem (Problem 3)

Here is a simple Laplace transform problem just to recall your fond memories of Mth 256. Your solution is due Monday, April 16, 2007.

2007 Spring Mth 480 Problem Set 1
PDF, 17 KB, 1 page, 2 problems (Problems 1-2)

This assignment is our first homework assignment. Your solutions are due Monday, April 16, 2007. These problems are simple examples of systems of two linear differential equations in two variables.

2006 Spring Mth 480 Problem Set 6
PDF, 14 KB, 1 page, 1 problem (Problem 15)

Your solution is due Friday, June 9, 2006. This problem gives a simple example of a stable periodic solution.

2006 Spring Mth 480 Problem Set 5
PDF, 25 KB, 3 pages, 7 problems (Problems 8-14)

Your solution are due Wednesday, May 31, 2006. These problem deals with linearization of systems of two differential equations at critical points. In a sense, there is only one problem repeated 7 times, so this assignment is not as large as it appears.

2006 Spring Mth 480 Problem Set 4
PDF, 18 KB, 1 page, 1 problem (Problem 7)

Your solution is due Wednesday, May 31, 2006. This problem deals with the Floquet form of the solution to a system of ordinary differential equations with periodic coefficients.

2006 Spring Mth 480 Problem Set 3
PDF, 18 KB, 1 page, 2 problems (Problems 5-6)

Your solutions are due Friday, April 28, 2006. These problems deal with Cauchy-Euler systems.

2006 Spring Mth 480 Problem Set 2
PDF, 20 KB, 1 page, 1 problem (Problem 4)

Your solutions are due Wednesday, April 26, 2006. This problem requires some linear algebra (and a lot of calculation).

2006 Spring Mth 480 Problem Set 1
PDF, 25 KB, 1 page, 3 problems

This is our first homework assignment. Your solutions are due Friday, April 14, 2006. These problems require some linear algebra concepts. If you have questions about the problems feel free to send email to me petersen@math.oregonstate.edu (plain text only please).

Copyright © 2006-7 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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