I have the Calculus, Differential Equations, and Introduction to Topology and Modern Analysis by G. Thank you very much for the suggestion! I am going to check them out during this weekend and to see which suits my taste. as stated here often before, rudin's books do not provide any insight or motivation at all into the material presented, just bare proofs. If it is comfortable with you, could you recommend me some alternative books for the multivariable-analysis portions of the Rudin and L/S? Also I see that Rudin's RCA is not as popular as a first introduction to the real analysis and complex analysis.Is there a reason why RCA is not popular as Follnd, Royden, Stein/Sharkachi, and Ahlfors?īooks i recommend include spivak's calculus, apostol's calculus, courant's calculus, spivak's calculus on manifolds, wendell fleming's calculus of several variables, lang's anaklysis I, lang's complex analysis, henri cartan's book on complex analysis, and anything by george simmons or sterling berberian. I heard that Rudin's treatment of multivariable analysis is not great, so my plan is to read L/S.
After completing my current Analysis I course, I am planning to start studying the multivariate analysis (later chapters on Rudin and Loomis/Sternberg) and Rudin's RCA together starting on the winter. I can say my mathematical maturity and thinking we're exponentially increased by studying with the Rudin's PMA. I really like Rudin's PMA for the same reason.
Thank you very much for your detailed advice! I did not take a deep look into the Loomis/Sternberg, but it seems that the book suits my style as it is very concise and leaving details for me to figure out. In particular I do not understand your question "is it safe.?" what harm could possibly be done by reading these books? But only you can answer the question of whether they help you, and you should not rule them out based on what I say without vetting them yourself, as many people swear by them. Rudin's books did not even make the cut of what to keep on my shelf when I moved. The material is so tightly packaged in those books it is difficult to unpackage it and get it into my brain.
I seldom consult any of those books any more, since they just don't offer me much insight. I took the advanced calculus class from Loomis, taught out of PMA to seniors, and studied out of RCA as a grad student preparing for PhD prelims. I would say you could read L&S alongside PMA profitably, but none of those books are recommended for their user friendliness to learners in my opinion, although all are considered authoritative for their content.
#ADVANCED CALCULUS PLUS#
Rudin's PMA is an austere treatment of some more basic material on constructing real numbers, convergence in metric spaces, and then differential and integral calculus in finite dimensions, not Banach spaces or manifolds I believe, but including elementary measure theory, Then the book RCA repeats measure theory for reals, again in finite dimensions and probably abstract measure spaces, plus complex analysis, including some pretty advanced approximation results. L&S is a very abstract treatment of differential calculus in Banach spaces and on manifolds, and treats integration in finite dimensions a la the theory of "content", which is less advanced than measure theory, and yields less useful theorems of convergence.
0 kommentar(er)
