>>13444858Hoffman's book fits into the intermediate category, between Tao and Pugh imo
ideally, i'd recommend Hubbard, it has pretty much everything you want: the material is very concrete, the setting is Euclidean space through and through (not a peep of metric spaces and other abstractions), it has pretty much everything you'd want to learn in a multivariable calculus course and more, is very rigorous, but not at all autistic, the exposition is very lively and there are plenty of examples and illustrations
but i don't really like it for 2 reasons (why i didn't finish the book) - like i mentioned already, it's fucking enormous (1000+ pages iirc), so i could never find the time to work through it in its entirety (which is why Tao and Pugh are much more preferable, owing to their compactness) and it has too much notation, i found myself constantly flicking to the index to see what this or that symbol meant. every page was oversaturated with symbolic language to the point that it turned into hieroglyphics in places
also it's entirely multivariable, it assumes knowledge of singlevariable calculus
>>13444890>I'll check out Courant and Tao then, since you say they are more entry-level.that's a good idea, i think. Tao's book is very much like what was taught in university in Analysis 2 to me, so i'm biased in thinking it's got the best selection of topics. Courant's is very classical to the point of being old-fashioned, so i'd recommend using Tao over it