Advanced Calculus

I used Advanced Calculus by Fitzpatrick for a class, and honestly, it was one of the better textbooks I’ve had. It starts from the basics but gradually builds into pretty serious analysis, covering everything from continuity and differentiability to the Inverse Function Theorem and even integration on manifolds. What I liked most was how everything is clearly defined and explained. The writing isn’t too dense, and it feels like the author really wants you to understand, not just throw theorems at you. It’s proof-based, so you definitely need to be comfortable with linear algebra and earlier calculus, but it doesn’t assume you already know analysis. That said, there’s no solutions manual, which made the harder exercises a bit frustrating at times. But the explanations are solid enough that if you sit with the material, it eventually makes sense. Overall, I think it’s a great book to learn from and also something I’ll keep around to look things up later. It’s clear, structured, and actually teaches you how to think about advanced calculus—not just memorize it.