Schwabacher and Bâtarde are fairly closely related, within the larger category of blackletter, but are distinct enough to exist as separate sub-categories. This is especially true in manuscript, in which Bâtarde styles tend towards greater informality and faster writing. In type, the similarities may be more obvious, as the Bâtarde will tend to be formalised. To get a feel for the differences, I recommend doing Google image searches on the two terms.

Conventionally, use of blackletter in mathematics had tended to be a fairly light form of fraktur. A Bâtarde along the lines of the Duc de Berry type would be appropriate weight, but I couldn't say whether the letterforms would be readily accepted by mathematicians. Remember, in the context of mathematics, these characters are being used a symbols, not as regular text, so it is important that they correspond sufficiently to expectations.

You could not have gotten a better answer from a calligrapher :-)

Which mathematical symbols are supposed to be fraktur glyphs?

Algebraists use them to denote Lie algebras, for example.
http://mathoverflow.net/questions/87627/fraktur-symbols-for-lie-algebras-mathfrakg-etc

So what about handwritten lecture notes in mathematics?

Good question. Since most mathematics students don’t carry their broad-nib alongside a bottle of ink to their lectures, they often use Sütterlin to reproduce fraktur denotations.

Hi John,

Thanks for your detailed reply. It was definitely helpful. Sorry I didn't respond earlier.

André