In a French language textbook I'm reading, I've noticed that while the translation of to when it occurs in the middle of the sentence is à, simply A is used if it is at the beginning of the sentence.
Examples:
Il va à la bibliothèque. vs A la faculté; je suis pressée!
I'm wondering whether this is a printing mistake as the book has quite a few.
As far as spelling is concerned, you need an accent on à, even in upper case.
Historically, the practice has not been consistent. Mostly because it often was technically difficult, if not possible. When faced with a (lead) font without that letter, printers have sometimes jury rigged one (I've seen examples in some typography related book), sometimes just done without. An issue with lead font and accent on upper case letter is that at least on some font the accent tend to be fragile, so it breaks easily. Another issue is jury rigging an accent tend to cause issues with keeping the interline spacing. The typographical practice was thus to use accents if possible; but other considerations (such as keeping the typographical gray consistent or just the practical difficulty to jury rig one in some case) make it possible to omit them.
On typewriter, the same issue happened. Most typewriters -- if not all -- just don't provide accented upper-case letters. Thus typing them is slow and again causes issues with the interline spacing. The rules for typist was just to omit accent on upper-case letters, and some have propagated that rule further (even teachers), forgetting that the rationale was the constraints of typewriters.
Nowadays, in most fonts accented upper case letter exist and aren't disturbing the typographical gray, so there is only one technical reason to omit them: the difficulty to type them. That difficulty depend on the set up. People who pay attention to that matter tend to configure their system so that accented upper-case letters are easy to type. People less sensible to that aspect or having been drilled to hard with the typewriter rule omit them.
Organizations producing lot of texts have usually their own set of rules (called marche in French, I don't know the correct word in English, people like to cite the one of the Imprimerie nationale which has been published, but organizations tend to diverge from it on some points) about such matters at the boundary between spelling and typography. And, we are coming to your question, it is true that some have (had?) an exception to the general rule of using accent on upper-case letters for a à starting a sentence. The rationale I've seen for that exception was esthetic, and that seems to me very tied to the font in use.
As a final note, it is still common to omit all accents when they are difficult to type (email in French from people using a qwerty keyboad for instance). French is still quite understandable without although it is easy to find out ambiguous sentences when the accents are omitted and you can from time to time find them in the wild, the case of a whole upper case newspaper title DUPOND-MORETTI A LA BARRE has been cited some years ago on a typography mailing list (it is not a true ambiguity as the context of a newspaper title makes one of the meaning very improbable).
I admit that I am not even sure how to type a capital à on a standard French azerty keyboard (without using html codes or a hotkey), though this normally has all the French special characters.
I think in some books they simply use fonts without capital à, which cannot lead to confusion: à is confusable with a of avoir (third person singular of the present tense), but in the beginning of a phrase the latter may only occur in a question where it is marked by a hyphen: A-t-on/il/elle...
Remark:
Actually ALT-GR + ` followed by a capital latter solves it (at least under Ubuntu): À,È,Ù,Ỳ Ò, Ì
