For the mathematicians - The origin of rapid pH change - Ignore this if you don't like it
Imagine a strong alkali being added to a strong acid.
Lets look at the pH of the solution 1 drop before and 1 drop after the equivalence point:
Assume that 1 drop has a volume of 0.05cm3
Also that 1 drop does not appreciably change the total volume at neutralisation. Total volume = 50cm3
1 drop before = acidic
Calculate the pH of the solution 1 drop before neutralisation.
1 drop after = alkali
Calculate the pH of the solution 1 drop after neutralisation.
See your chemistry teacher if you require help in this calculation