I used Foundations of Astrophysics by Ryden and Peterson in my first college astronomy course, which focused on stars, the ISM, and galaxies. The textbook itself goes far beyond those topics, delving into cosmology, planetary science, and more, and we actually use it for another intro-level course for majors covering those topics. I think it could be used well as the text for any such course.
I liked a couple of things about Ryden and Peterson:
- The style is casual and accessible to a beginning astrophysics student. There's also humor tucked away in footnotes here and there; the book certainly doesn't try to be imposing - and it's not. I think that's important to have from time to time in an introductory text.
- It covers everything, as I alluded to before. I do wish that the authors provided some resources for going further into particular subtopics, if the reader so desired, but then again, most students would have access to a professor/TA to go to for that.
- I actually agree with the point that the problems go slightly beyond the scope of each chapter in some cases, but I also don't think that's a bad thing. The extra critical thinking helped me. I don't remember them making me want to bang my head against the wall as much as some other physics textbooks I could mention - maybe because Ryden and Peterson had a habit of breaking each problem into more manageable chunks, if I remember correctly.
I do think Ryden and Peterson satisfies the other requirements quite well; it doesn't use more than single-variable calculus (and even that only sparingly, I think), and it actually doesn't require much mechanics or electricity and magnetism, so in turns of prerequisites, you should be fine. One thing to note is that Ryden and Peterson doesn't include example problems done out in the same way many physics textbooks do - I don't know if that's a turn-off for you.
I should add a disclaimer that my opinion might be slightly skewed because of the textbook used in my seminar this past semester, LeBlanc's An Introduction to Stellar Astrophysics. LeBlanc is comparatively drier, denser, and more specialized (on, of course, stellar astrophysics). I found it substantially less accessible, even though I had much more experience in the subject at that point. This, then, may have affected my hindsight view of Ryden and Peterson. Ironically, we did use Carroll & Ostlie as supplementary reading (as well as Ryden and Peterson) on certain sections, which was much more helpful, and I daresay a refreshing change of pace.