I was once a regional manager for a small retail chain. In a manager's staff meeting one day we were discussing how to improve the shopping experience with music. Managers were complaining that they didn't have the equipment necessary to pipe Pandora to their customer's ears. I knew they all had CD radios in inventory and suggested they set one up and bring in some of their favorite disks. After a moment of silence, one manager (very much a smart aleck) raised his hand and asked, "what's a CD?"
What's a book?
We are on the verge of never using printed books again in the fundamental education process. The technology is that good... that close... the time when all of Humanity's knowledge could fit on a single CD-ROM passed a long, long time ago (if it were ever true). And yet we're asking about three books... Yes, it's in just one field, but still....
I believe the biggest problem with this kind of question is that it's basically asinine. What three books about electrical engineering would I take (being a EE) that would bring my survivors back to the original level in as short a time as possible?
It doesn't matter! The amount of time needed to re-invent what's missing from those three books is so long that having the three books won't significantly speed you along.
Please understand, it's not enough to have a textbook about semiconductor physics, you also need to know how to build and operate a fab. That takes more than just one book! Then you need the chip assembly plant (more books!), then you need the computer assembly plant (more books!), then you need an operating system (more books!) and finally a book on programming (have you seen what it takes to program C in the Windows environment lately?) And that's ignoring the entire computer design process (the more complex EDA tools used to ship with an entire shelf of user's guides)....
Technology is a massive mountain.1 Today, right now, we're standing on the top of that mountain. What's below us is a nearly unfathonable amount of knowledge and experience. Choosing "just three books" (at least one of which must teach you what a resistor is... that's not the book that will help you build a fab) is like picking up three rocks on the mountain (presumably one at the bottom, one in the middle, one at the top) — and then expecting those three rocks to lift you high enough that you can rebuild the mountain in less time than it took to build it in the first place.
The premise of the question is worldbuilding from the perspective that recovery from an apocalyptic event is always about worldbuilding. The first problem is that without a "point of entry" the question is utterly meaningless and irrelevant to answer.
The "point of entry" is the amount of surviving, sustainable technology. The OP would need to explain exactly how far back the indicated science (chemistry, physics, EE, etc.) is set. Knowing where to start tells you how far up the mountain you need to climb.
But even then, just three
Let's say the point-of-entry was 1977 (we were still using LS7400 NAND chips back then folks! Do you have any idea how many generations of CPU have come and gone since I last saw an LS7400 NAND chip on a motherboard?) The technological difference between the LS7400 and today's CPUs (we don't use "microprocessors" anymore because the prefix "micro" hasn't been valid for 20 years) is massive. There aren't three books that can get you from the LS7400 to today's CPUs without reinventing a lot of wheels — and that takes time.
Let's be more practical and say the point-of-entry was 2005. The technology in the cellphone sitting next to me right now (NOT a top-of-the-line phone!) did not exist in 2005. And not just the knowlege, the manufacturing ability didn't exist, either. Not for the chips, the display, the software, the NVRAM, the battery, nada. Zip. Zilch.
And that's the second problem. The time required to reinvent what didn't arrive in those three books is so great that it might not matter which three books you picked. Any three would do.
Which makes the question primarily opinion-based by definition. But I'm not done....
There's one more problem. The odds of the OP being schooled in my EE expertise is darn close to zero. Why does this matter? Because if the OP is expected to judge which answer is best. Any OP that could do that wouldn't need to ask the question in the first place. Every OP that can't do that is picking an answer, not on the suitability of the books, but on the trust the OP has in the answerer.
Here's an example, the odds are very much in my favor that no one but myself (on this site) has experience in the physics of and design of BiCMOS ICs. It's a very specialized field of engineering, but it's important for satellites (among other applications). I could suggest a book title that would reinstate the lost knowledge of BiCMOS design. But how many of you could read the title and a couple of sentences of description and judge if it is the best book? (it was in the late 90s) or even a necessary book? (it isn't). The average participant on this site probably wouldn't even know what I was talking about.
The third and final problem is that the OP is almost certainly selecting an answer in a manner that is "primarily opinion-based." I know that's not the original intent of the VTC reason, but it's just as relevant.
Which is a long and fancy way of saying, what's the point of allowing these questions in the first place?
These questions should be arbitrarily closed.
That these questions are being asked proves the OP has no blooming idea what it takes to climb the technology mountain.
Without a point-of-entry we must assume technology has been set back to the 1940s or earlier. But even with a PoE...
Three books in every field wouldn't hold enough information to rebuild the tech mountain quickly. The time required to reinvent what's missing would overwhelm whatever advantage you had with the books.
The answers can't be judged in a meaningful way by the OP.
Three books... the only valuable way to ask this question might be (MAYBE!) "which three university libraries...?"
1 Moore's Law originally stated that the number of transistors on a chip would double every two years. Most people today think of it as "technology doubles every two years," but that's because they have no idea what it takes to double that count. What far too few people realize is that the knowledge it takes to meet the expectation of Moore's Law far exceeds simple doubling because of the number of fields that must advance just to double the number of transistors on a chip. The mountain of knowledge grows exponentially, not geometrically, and to make it worse... people have discovered that the transistor count is doubling faster than every two years....
I came back and re-read this post quite some time after writing it — and I can't even imagine what had darkened my mood that day. Somebody or something obviously moved my cheese, kicked my cat, called my baby ugly, and beat me at Trivial Pursuit all at the same time. I'm going to leave the answer in its original condition because modifying it would change more than a few of the comments. However, I would like to offer a sincere apology to both Lio and Green for being a bully. That's not the kind of person I want to be and I failed to listen to the better angels of my nature when I wrote this.