## Mathematics 430## Calculus on Manifolds |

* Munkres, Chapter 5: Manifolds*

Here is an interesting exercise which relates well to problems 22.2 and 21.1 from the Munkres text.

These notes on orthogonal matrices viewed as compact manifolds were suggested by exercise 24.6 of Munkres.

The following Mathematica notebooks are available in three formats. Download the Mathematica notebook (nb) to your machine and use Mathematica to interpret its contents, or click on the pdf link (pdf) or the web page link (html) to see a static image of the evaluated notebook.

- 21 The Volume of a Parallelopiped (nb pdf html)
- 22 The Volume of a Parametrized-Manifold (nb pdf html)
- 25 Integrating a Scalar Function over a Manifold (nb pdf html)