Conservative time-discretization for stiff Hamiltonian systems, and molecular chain models

Why Markdown?

• For those of us who like the control of a markup language (HTML, LaTeX etc.) rather than a “What You See is Approximately What You Will Get” method (as with common word processing software and the Visual interface to WordPress), MarkDown allows that with a far more concise notation that HTML.
• The notation is also readable itself, before processing into final displayed form. This is because it is mostly based on conventions already used in email and some blogs to indicate formatting in a plain typed text.

Warning: editing later can cause problems.

Sometimes, editing a post after publishing it does not work right: for example, list formatting can get messed up a bit. So it is best to get it right the first time, or to fix errors by creating a new replacement post and deleting the original.

A Few Markdown Features (Aside: this is a level three heading)

Note: I will post next the raw input file that produces this post. Here is a list of the basics.

1. Enumerated lists like this one. Note that errors in the numbering get fixed!
2. Non-enumerated lists as in the previous section, Why Markdown?
3. Section headings, like “A Few Markdown Features”
4. Text that is emphasized and so probably appears in italics (using either underscores or stars)
5. Text that is strongly emphasized and so probably appears in boldface (double the underscores or stars)
6. Block quotes, using the common “>” notation from email. This is illustrated next.
7. Links, like the one above from the text “Jonathan Gruber’s markdown” to his page about it.
8. Simple links where the text that appears is the address for the link can be done as http://en.wikipedia.org/wiki/Markdown

Block quoting (Aside: this is a level four heading)

Some of the text so far, quoted, with the list as a quote within the quote:

I think that I overlooked describing another optional feature in these blogs: using Jonathan Gruber’s markdown notation instead of HTML or the WYSIWIG “Visual” composing options.

Why Markdown?

• For those of us who like the control of a markup language (HTML, LaTeX etc.) rather than a “What You See is Approximately What You Will Get” method (as with common word processing software and the Visual interface to WordPress), MarkDown allows that with a far more concise notation that HTML.
• The notation is also readable itself, before processing into final displayed form. This is because it is mostly based on conventions already used in email and some blogs to indicate formatting in a plain typed text.

How to use Markdown at this site

1. To enable Markdown (one time only): when logged in, go to the item at left for Plugins, find Markdown on Save, and select Activate
2. To use Markdown when composing a post: find and check the box for “This post is formatted with Markdown”, at the top-right.

Note that even if you have activated the Markdown plug-in, you have the option of using Markdown or not on each individual post.

The raw Markdown input for the above

I think that I overlooked describing another optional feature in these blogs: using
[Jonathan Gruber's markdown](http://daringfireball.net/projects/markdown/)
notation instead of HTML or the WYSIWIG "Visual" composing options.

### Why Markdown?

- For those of us who like the control of a markup language (HTML, LaTeX etc.) rather than a "What You See is Approximately What You Will Get" method (as with common word processing software and the Visual interface to WordPress), MarkDown allows that with a far more concise notation that HTML.
- The notation is also readable itself, before processing into final displayed form. This is because it is mostly based on conventions already used in email and some blogs to indicate formatting in a plain typed text.

**Warning: editing later can cause problems.**

Sometimes, editing a post after publishing it does not work right: for example, list formatting can get messed up a bit. So it is best to get it right the first time, or to fix errors by creating a new replacement post and deleting the original.

### A Few Markdown Features (Aside: this is a level three heading)

Note: I will post next the raw input file that produces this post. Here is a list of the basics.

3. Enumerated lists like this one. Note that errors in the numbering get fixed!
2. Non-enumerated lists as in the previous section, __Why Markdown?__
1. Section headings, like "A Few Markdown Features"
5. Text that is *emphasized* and so probably appears _in italics_ (using either underscores or stars)
5. Text that is **strongly emphasized** and so probably appears __in boldface__ (double the underscores or stars)
1. Block quotes, using the common ">" notation from email. This is illustrated next.
1. Links, like the one above from the text "Jonathan Gruber's markdown" to his page about it.
1. Simple links where the text that appears is the address for the link can be done as 

#### Block quoting (Aside: this is a level four heading)
Some of the text so far, quoted, with the list as a quote within the quote:

>I think that I overlooked describing another optional feature in these blogs: using [Jonathan Gruber's markdown](http://daringfireball.net/projects/markdown/) notation instead of HTML or the WYSIWIG "Visual" composing options.

>### Why Markdown?

>>- For those of us who like the control of a markup language (HTML, LaTeX etc.) rather than a "What You See is Approximately What You Will Get" method (as with common word processing software and the Visual interface to WordPress), MarkDown allows that with a far more concise notation that HTML.
>>- The notation is also readable itself, before processing into final displayed form. This is because it is mostly based on conventions already used in email and some blogs to indicate formatting in a plain typed text.

### How to use Markdown at this site

1. To enable Markdown (one time only): when logged in, go to the item at left for Plugins, find _Markdown on Save_, and select *Activate*
2. To use Markdown when composing a post: find and check the box for "This post is formatted with Markdown", at the top-right.

Note that even if you have activated the Markdown plug-in, you have the option of using Markdown or not on each individual post.

In addition to the explanation in the video by Mike Wheatland at Sydney University here is a mathematical/physical explanation done as a project in a Stanford undergraduate physics course.

Via http://kottke.org/12/06/holy-levitating-slinky

For students enrolled in my courses, the main contact point is OAKS, the College’s Learning Management System [LMS] at lms.cofc.edu

New to WordPress blogs? Some hints:

• The lists to the right, from “Applets for Math” down, are links to other web resources
• Hovering your mouse over a link in those lists should give a brief description of the linked item
• See the page on using these blogs as fully fledged websites and the resources linked there.

1. Login at https://blogs.cofc.edu
2. Go to the Dashboard
3. At left, select plug-ins
4. Find JetPack by WordPress.com and select “Activate”. (Settings are not needed for the latex part: Jetpack does lots of things!)
5. Go to the bottom of the plug-ins page and click button “Apply”.
6. You will be asked to cite a wordpress.com account: if you do not already have one, create one when asked. This account is free (and wordpress.com a nice place for a personal blog), and you will need to confirm that account creation by responding to an email message.
7. Here I get fuzzy … I think some confirmation is asked for.

To learn about using this feature, see the item LaTeX at http://jetpack.me/ or the more detailed introduction at http://en.support.wordpress.com/latex/

If these instructions need revision, let me know in a comment on this post.

I would like to be able to can now post mathematical stuff like the following here, but the mathematical notation cannot be displayed nicely, so instead see it at http://brentonlemesurier.wordpress.com:
posting to a blog hosted at WordPress using the WordPress blogging software is the only option I currently know of that allows mathematical notation. I am thinking of moving my professional web presence there, for the sake of being about to talk mathematically.

On the other hand, most people who understand the math probably also understand the latex-like notation used for it below, or should learn latex as a critical communication tool in mathematics and related sciences, so here goes:

———————————————————————–
As background for the colloquium that I will be giving at the College on Friday November 18 (details at math.cofc.edu/colloquium), here are the canonical forms of Hamiltonian equations, in both the most familiar real form

and the complex form,

which is often convenient in situations involving either Schroedinger’s equation or other conservative equations involving complex quantities, such as in optics.