Tutorial on optimization theory and difference and differential equations by Martin J. Osborne
Copyright © 1997-2002 Martin J. Osborne.
Version: 2002/10/21.
This tutorial is a hypertext version of my lecture notes for a course in optimization theory and difference and differential equations. The approach and most of the notation is consistent with Mathematics for economic analysis by Knut Sysdaeter and Peter J. Hammond (Prentice-Hall, 1995), a book that I highly recommend.
THE TUTORIAL USES CHARACTERS FROM A SYMBOL FONT. If your operating system is not Windows or your browser is not Netscape Navigator version 3 or 4 or you think you may have deleted your symbol font, please give your setup a character check before using the tutorial. If your
browser is Netscape Navigator version 6 or later, or Mozilla, you need to make a small change in the browser setup to access the symbol font: here's how.
General
- The tutorial is intended to be a complement for a book rather than a substitute. Many books contain a lot of excellent discussion, examples, and proofs, which I do not duplicate.
- Whether or not you read all or part of this tutorial, you should work through all the problems assigned in class! The only way to learn the material is to do the problems.
- I very much welcome comments and suggestions. If you find something erroneous or confusing please let me know!
- The entire tutorial is copyrighted.
How to use the tutorial
- The tutorial is a collection of "main" pages, with cross-references to each other, and links to pages of exercises (which in turn have cross-references and links to pages of solutions).
- The main pages are listed in the table of contents, which you can go to at any point by pressing the button on the left marked "Index".
- Each page has navigational buttons on the left-hand side, which you can use to make your way through the main pages. The meaning of each button displays in your browser's status box (at the bottom of the screen for Netscape Navigator) when you put the mouse over that button. On most pages there are six buttons, (though on this initial page there are only four), with the following
meanings.
Go to the next main page in the order given on the index page.
Go to the next top-level section in the order given on the index page.
Go back to the previous main page in the order given on the index page.
Go back to the previous top-level section in the order given on the index page.
Go to the index page.
Search through all pages of the tutorial for a string.
- If you'd like to try using the buttons now, pressing the black right-pointing arrow (on a yellow background) will take you to the next main page; to come back here afterwards, press the black left-pointing arrow on that page.
- After you follow a link on a main page, use your browser's "Back" button to return to that page if you wish to do so before going to the next main page. To help you know where you are, an abbreviated title for the main page to which the buttons on the left correspond is given at the top of the light yellow panel. (For this page, for example, it says "Introduction".) Pages of examples and
solutions to exercises have orange backgrounds to make it easier to know where you are. If you get "lost", you can always press the index button and go to a main page from there.
Some technical stuff
- The tutorial uses "frames" extensively. If your browser doesn't support frames, I'm not sure what you'll see; I suggest you get a recent version of Netscape Navigator. (Other features that I use may also not be supported by other browsers.)
- Some older browsers that support frames do not handle the "Back" and "Forward" buttons correctly in frames.
- HTML currently has no tags to display math. I have "faked" the math by using text italic fonts for roman letters, the Windows symbol font for most symbols (gifs for others), small fonts for subscripts and superscripts, and tables for alignments. The result is reasonable using Netscape Navigator with a 12 or 14 point base font and a relatively high resolution monitor, but may not be so
great under other circumstances. If what you see on your screen looks awful, let me know and I'll see if I can do anything about it. One day HTML will be able to display math ....
Copyright © 1997-2002 by Martin J. Osborne