3.0 Answer:
PHB, page 155:
near the top, right column...
"Spells Gained at a New Level: Wizards perform a certain
amount of spell research between adventures. Each time a wizard
achieves a new level, she gains two spells of her choice to add to her
spellbook. These spells represent the results of her research. The two
free spells must be of levels the wizard can cast. If she has chosen to
specialize in a school of magic, one of the two free spells must be
from the wizard’s specialty school."
later it adds...
"Note that a wizard does not have to pay these costs in time or gold
for the spells she gains for free at each new level. The wizard adds
these to her spellbook as part of her ongoing research."
The implication is that spells gained from a gaining a new level don't have a cost associated with them. It's a logical leap to assume that would include the spellbook, but it's not explicitly stated here.
It does state, on page 55 (bottom left, to top right columns):
"Picking up a new class is not exactly the same as starting a
character in that class. Some of the benefits for a 1st-level character
represent the advantage of training while young and fresh, with lots
of time to practice. When picking up a new class, a character does
not receive the following starting bonuses given to characters who
begin their careers in that class:
Maximum hit points from the first Hit Die.
Quadruple the per-level skill points.
Starting equipment.
Starting gold.
An animal companion (druid only)."
Since starting equipment might be construed as the spellbook itself, the answer is a solid "dunno."