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This page gives an overview on how to use LyX for specific scientific fields. Feel free to add tips for your specific field here ...
Of course, math has always been one of the core strengthes of LyX. LyX features an excellent math editor, you can define math macros and LyX supports many math constructs. The features are well documented in the User Guide (chapter 5), so there's not much to add here.
Here are some pages that are dedicated to mathematics:
See the LinguistLyX page.
See the HumanitiesLyX page.
For typesetting chemical formulae, the LaTeX package mhchem is useful. LyX does not yet provide natural support for mchem, thus they have to be entered as LaTeX commands. However, you can (mis)use the preview function of LyX's math editor to display the formulae inside LyX in a WYSIWYG way. Here's how it works.
That's all. If the everything is installed correctly, this formula will display inside LyX in a WYSIWYG way as soon as you leave the math editor.
Here's an example LyX file.