Mathematical methods for economic theory: a tutorial
by Martin J. Osborne

THIS TUTORIAL USES THE UNICODE CHARACTER ENCODING. It displays correctly in modern standards-compliant browsers, in any operating system, but you may want to give your system a character check before using it. (Note that IE 6, for example, is not standards-compliant.) If your system does not pass the test, try an alternative version of the tutorial that uses a symbol font.

Introduction

• Several books provide additional examples, discussion, and proofs. The level of Mathematics for economic analysis by Knut Sydsaeter and Peter J. Hammond (Prentice-Hall, 1995) is roughly the same as that of the tutorial. Mathematics for economists by Carl P. Simon and Lawrence Blume is pitched at a slightly higher level, and Foundations of mathematical economics by Michael Carter is more advanced still.
• The only way to learn the material is to do the exercises!
• I welcome comments and suggestions. Please let me know of errors and confusions.
• The entire tutorial is copyrighted, but you are welcome to provide a link to the tutorial from your site. (If you would like to translate the tutorial, please write to me.)
• Acknowledgments: I have consulted many sources, including the books by Sydsaeter and Hammond, Simon and Blume, and Carter mentioned above, Mathematical analysis (2ed) by Tom M. Apostol, Elementary differential equations and boundary value problems (2ed) by William E. Boyce and Richard C. DiPrima, and Differential equations, dynamical systems, and linear algebra by Morris W. Hirsch and Stephen Smale. I have taken examples and exercises from several of these sources. I am grateful to many readers for pointing out errors and suggesting improvements.

Instructions

• 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 "Contents".
• 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 ten buttons (though on this initial page there are only six), with the following meanings.
  • Go to the next main page.
  • Go to the next top-level section.
  • Go back to the previous main page.
  • Go back to the previous top-level section.
  • Go to the main page ("text") for this section.
  • Go to the exercises for this section.
  • Go to the solutions to the exercises for this section.
  • Go to the table of contents.
  • Search through all pages of the tutorial for a string.
  • View technical information about viewing and printing pages.
• If you'd like to try using the buttons now, press the black right-pointing arrow (on a yellow background), which 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, press the white "Text" button to return to the 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, the abbreviated title is "Introduction".) Pages of examples and solutions to exercises have orange backgrounds to make it easier to know where you are. If you get lost, press the "Text" button or "Contents" button.

Technicalities

• The tutorial uses "frames" extensively. All modern browsers support frames; if you have a very old one, the pages may look strange.
• Some very old browsers that support frames do not handle the "Back" and "Forward" buttons correctly in frames.
• HTML has no tags to display math. I have "faked" the math by using text italic fonts for roman letters, unicode characters 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.

  MathML, a variant of HTML, has extensive capabilities for beautifully displaying math, but is currently supported by only a few browsers. I have long-run plans to create a MathML version of the tutorial.