Recommend me a calculus textbook that is similar to Apostol but isn't Apostol.
>inb4 just read Apostol
I generally like Apostol but I have some beef with some of the stuff he does.
Anyway, I would like a book that fits the following criteria:
1. It should cover both one-variable calculus and multi-variable calculus, plus the necessary linear algebra (like Apostol does in his two volumes).
2. It should avoid invoking elementary geometry in its proofs. For example, there are some calculus books that invoke the law of cosines to prove the Cauchy-Schwarz inequality, while other books (like Apostol) do not rely on synthetic geometry and prove the Cauchy-Schwarz inequality algebraically and then use it to DEFINE the cosine of the angle between two vectors (instead of assuming that the angle exists an using the law of cosines to prove the inequality).
3. It should prove all the major theorems instead of asking me to accept them on faith. Some books, like Lang, ask you to accept Green's theorem or some other important theorem on faith with the excuse that "you will learn the proof later in an analysis course".
>inb4 just read Apostol
I generally like Apostol but I have some beef with some of the stuff he does.
Anyway, I would like a book that fits the following criteria:
1. It should cover both one-variable calculus and multi-variable calculus, plus the necessary linear algebra (like Apostol does in his two volumes).
2. It should avoid invoking elementary geometry in its proofs. For example, there are some calculus books that invoke the law of cosines to prove the Cauchy-Schwarz inequality, while other books (like Apostol) do not rely on synthetic geometry and prove the Cauchy-Schwarz inequality algebraically and then use it to DEFINE the cosine of the angle between two vectors (instead of assuming that the angle exists an using the law of cosines to prove the inequality).
3. It should prove all the major theorems instead of asking me to accept them on faith. Some books, like Lang, ask you to accept Green's theorem or some other important theorem on faith with the excuse that "you will learn the proof later in an analysis course".
