There was something about prepositions that I did not cover in the book or the lecture but it does come up in the screen cast, so let me say something about it here.
The ends of prepositions can change depending on the following word. It is a matter of pronunciation, somewhat like changing "a" to "an" when the following word begins with a vowel.
When certain prepositions are followed by a word beginning with a vowel, they will drop their final vowel.
ἀπό ► ἀπ᾿
διά ► δι᾿
ἐπί ► ἐπ᾿
κατά ► κατ᾿
μετά ► μετ᾿
ὑπό ► ὑπ᾿
The negation also changes its end depending on the following word.
οὐ ► οὐκ ► οὐχ
Some consonants also change their final consonant when the following word begins with a vowel and rough breathing.
ἐπί ► ἐπ᾿ ► ἐφ᾽
κατά ► κατ᾿ ► καθ᾽
μετά ► μετ᾿ ► μεθ᾽
ὑπό ► ὑπ᾿ ► ὑφ᾽