"Anticipation" and "expectation" CAN be synonyms, but they're not always. Generally speaking, "anticipation" is used more for future events we're certain about, whereas "expectation" is for events where there is a good degree of uncertainty. For example:
"I haven't seen my best friend in two years. Her plane just touched down on the tarmac. The anticipation is killing me!"
^ Here, the speaker is almost 100% certain that she is about to see her best friend (barring something unbelievable). Thus, "anticipation" is the correct word to use.
"The university's ads made it seem like such a perfect school. I hope it actually meets my family's expectations."
^ Here, while the speaker and her family hope the university is everything they want, it's too uncertain whether or not the university will actually match their standards.
On Dictionary.com, "anticipation" has the following three definitions that are not shared by "expectation":
1) realization in advance; foretaste.
2) previous notion; slight previous impression.
3) intuition, foreknowledge, or prescience.
Similarly, "expectation" has the following definition not shared by "anticipation":
- the degree of probability that something will occur
I hope my answer helps. Please let me know if you have any questions =)