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I too watched the anime and then proceeded to read the novels. And it was also due the the fact that I couldn't wait for a second season.
I don't know if I can say the anime is not as good as the novels, because KyoAni does a pretty damn good job of adapting what they could in 14 episodes.
As for time skipping, they jump around a bit between volumes initially, like vol. 2 doesn't occur directly after vol. 1, and such. But later volumes have been chronological for the most part.
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