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I don't understand the difference between Rigorous Calculus books (Hubbard's "Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approch", Loomis and Sternberg's "Advanced Calculus", Spivak's "Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced Calculus") and Analysis books (Pugh's "Real Mathematical Analysis" and Rudin's "Principles of Mathematical Analysis")?
Casually looking through Sternberg's book, it looks not a thing like a regular Calculus book, but very much like a regular Analysis text (Pugh's), except it contains a lot of seemingly unrelated content, too. Seems like a lot of topics in these Calculus and Analysis books overlap.So, would you say Sternberg's Advanced Calculus book= Pugh's Analysis book?
Casually looking through Sternberg's book, it looks not a thing like a regular Calculus book, but very much like a regular Analysis text (Pugh's), except it contains a lot of seemingly unrelated content, too. Seems like a lot of topics in these Calculus and Analysis books overlap.So, would you say Sternberg's Advanced Calculus book= Pugh's Analysis book?