Other critical books should include philosophy and science: it took a long time to build a technological civilization, and the Scientific Method is the cornerstone of this. (And yet even now, much of the world is still mired superstition/religion.)
More crucial lessons from John Wyndham's The Day of the Triffids: 'The most valuable part of our flying start is knowledge. That's the short cut to save us starting where our ancestors did. We've got it all there in books if we take the trouble to find out about it...
'From my reading of history, the thing you have to have to use knowledge is leisure. Where everybody has to work hard just to get a living and there is no leisure to think, knowledge stagnates, and people with it. The thinking has to be done largely by people who are not directly productive - by people who appear to be living almost entirely on the work of others, but are, in fact, a long-term investment. Learning grew up in the cities and in great institutions - it was the labour of the countryside that supported them...
'A community of our present size cannot hope to do more than exist and decline. If we stay here as we are, just ten of us now, the end is, quite inevitably, a gradual and useless fade-out. If there are children we shall be able to spare only enough time from our labour to give them just a rudimentary education; on generation further, and we shall have savages or clods. To hold our own, to make any use of all the knowledge in the libraries we must have the teacher, the doctor, and the leader, and we must be able to support them while they help us.'
I would suggest Musashi (http://en.wikipedia.org/wiki/The_Book_of_Five_Rings), Clausewitz, Influence of Seapower Upon History (Mahan), and of course Sun Tzu. While some are more specific than others (Musashi is actually about swordsmanship specifically, but conflict generally) they all have insightful things to teach.
For a broader discussion look at Bobbitt's Shield of Achilles. He still has a significant portion on conflict, however it is also a discussion on the interplay of technology, legal development, and conflict.
You might want to look at what kinds of people (culturally and ethnically) are behind most innovation and engineering, and look at the differences and influences there. (It may be interesting to look at the historical trend of their power, as well, for futurological purposes.) If the culture that produces civilization stays around through a collapse, there probably is less to worry about than if that culture doesn't survive.
Thus among your important books may be some of the books of industrial culture, like Atlas Shrugged, most good science fiction, some enlightenment philosophy and poetry, Paul Graham's writing, etc.
Unless a comet or asteroid hit the earth. Here's some good sci-fi reading for you: http://www.amazon.com/Lucifers-Hammer-Jerry-Pournelle/dp/044...
But whether it's cosmically sudden or self-inflicted, we'll likely be more concerned with the fast or slow moving catastrophe than with future generation, and the Time Traveler's three books aren't going to matter when it's eat or be eaten. Once a collapse happens I think we have to play through the whole cycle.
Speaking of fiction, I've always liked this as an exploration of how society would respond to a collapse: https://en.wikipedia.org/wiki/Earth_Abides