Rudin's book summartizes cauch theory one chapter but it is not at all a good acount as series expansions are neglected. Also the algorithm for winding number is difficult to figure out how it works . a simpler algorithm is presented in alhfors. butt looking at usefulness value( ? is there the...
Soory . rudin's principles of math nalysis is not a good text not beacuse it is terse. but
1) It offers atreatemtn of riemann integral heavily fdepndent on order and unsuitanle gfor generalization to vector valued maps. se bartle excellent
2) it does not offer good treatment of riemann integral...
baby rudin is terse! and not a good book.
reasons: riemann integral is defined for realvalud functions and definition heavily relies on order properties of R. With very less efort the whole theory works in banach space setting see Dieuodenne or lang analysis I
treastment of stokes theorem is...
no i find analysis /II is one of the best books to learm measure theory.
measure theoy is simply a tool. in analysis II lang has elat with banch space bvalued mappings ( rathr than real valued ) and treats petis/bochner integrals. the trreatment is noit readily available elsewhere.
lots of...
The classic of alfhors is excellent but terse.
the conway book is boring. It introduces analytic functions as continuously differentiable functions and messes up simple integration . it has messed up a simple problem of integrating multivalued function by avoiding the use of branches.a very...
serge lang's nalysis I ois the best book. it also introduces to nalysis in banach spaces. the analysis II by serge lang ( addision wesley ) is masterpiece. these two books take you to the frontiers rather quickly.
lang's book is great and easy to read. and there is agreat sequel analysis Ii. with one uniform notation u can study measures spectral thm, manifolds, calculs in banaqch spaces etc. The treatment of mesure theory is perhaps best and lucid yet comphrensive.It prepares u for research...
i agree that dieuodenne is great . aso try lang analysis i and Ii easy to readand comphrensive goldberg book method of real abnalysis bartle and sherbat intro to real analysis bartke (elements of real analysis are all excellent.
but dieuodene lang and cartan all suffer ias they use regulated...
lang's analysis I and analysis Ii are good. lang;s treatment of measure theory is complete and beautiful! also hl royden is good for measure theory. rr goldberg is better than rudin for one variable stuff. bartle has excellent tratement on integration. also bartle and sherbat have good chapter...
henry cartan is too advances but has a good treatmnment of both one and several variables. silvermann is good for aplications. knopp is good but dated.
Alhfors is a pioneering text but lacks examples. Churchill is good but treatment of cauchy's theorem is incomplete. Conway is a mess as he starts with misleading def a function is analytic if it has continuous derivative and then shows continuity assunption is redundant. lang is good especially...