Click here for the course syllabus.
Click here for homework problems, test answers, etc.
My book, "The Laplacian on a Riemannian Manifold," now in its second (corrected) printing, is also available. This book is aimed at graduate students who have had a basic course in manifolds through integration of forms. The goal is to get students to appreciate current areas of research in global geometry. The book covers Hodge theory, basics of differential geometry, heat flow on functions and forms, the heat equation/supersymmetric proof of the Chern-Gauss-Bonnet theorem, an overview of the Atiyah-Singer Index Theorem, the zeta function for Laplacians and analytic torsion. There are lots of exercises. You can preview the introduction. The price is $128.00 for hardcover (ISBN 0 521 46300 9) and $51.00 for paperback (ISBN 0 521 46831 0). You can order copies (no upper limit) from the publisher, Cambridge University Press. Alternatively, you can view the book here. Feel free to print it out, but consider making a donation to a good cause in lieu of buying the text. I would like to thank Cambridge University Press for allowing me to make the text available online, in contrast to the attitude of other math text publishers.
For an antiquated streaming video of a lecture at MSRI in 1998, click here and select the "start 56kps video" option in the top left corner. Good luck.
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Creation Date: March 29,1996
Last Serious Update: November 8, 2005