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Introduction to Electricity
Based on the way it is taught in engineering school, you are actually looking for about four textbooks.
The physics of electricity is taught in an electricity and magnetism course (sometimes even from a physics textbook). RC and RLC circuits is taught in a circuit theory course. Op-Amps diodes and FETs are taught in an electronics course. Flip-flops and gates are taught in a computer organization course.
All of the courses include more topics than you mention, but many topics can be ignored depending on your goals. Circuit theory is really a one course topic, the other three can be taken to great depth, even at the under-grad level. Finally, circuit theory is a prerequisite to electronics, and calculus is a prerequisite to all but the most basic understanding of any of it, otherwise they are actually quite independent topics.
I duno if that is helpful, but I thought I would offer some context. Finally, similar questions have been asked before:
- Fundamental Understanding of AV Electronics?
- I'm interested in learning electronics/electronics repair
- I want to learn how to make simple electronics
- Do Radio Shack's "50 in 1" electronic kits really teach EE skills?
- What are some good resources to learn about basic electricity?
And a couple of related, but more specific questions (well I've decided this doesn't really belong here, but since it is already typed out...):
This article originated with an answer by Chuckles to the "Learning about electricity, the bright and colorful but not completely dumbed-down way?" question on Ask MetaFilter.