后现代分析-第3版 内容简介

whatisthetitleofthisbookintendedtosignify,whatconnotationsistheadjective"postmodern"meanttocarry?apotentialreaderwillsurelyposethisquestion.toanswerit,ishoulddescribewhatdistinguishestheaptoanalysispresentedherefromwhathasbyitsprotagonistsbeencalled"modernanalysis"."modernanalysis"asrepresentedintheworksofthebourbakigrouporinthetextbooksbyjeandieudonnischaracterizedbyitssystematicandaxiomatictreatmentandbyitsdrivetowardsahighlevelofabstraction.given

后现代分析-第3版 目录

chapter i. calculus for functions of one variable
0. prerequisites
properties of the real numbers, limits and convergence of sequences of real numbers, exponential function and logarithm. exercises
1. limits and continuity of functions
definitions of continuity, uniform continuity, properties of continuous functions, intermediate value theorem, hslder and lipschitz continuity.exercises
2. differentiability
definitions of differentiability, differentiation rules, differentiablefunctions are continuous, higher order derivatives. exercises
3. characteristic properties of differentiable functions. differential equations
characterization of local extrema by the vanishing of the derivative, mean value theorems, the differential equation f' = rf, uniqueness of solutions of differential equations, qualitative behavior of solutions of differential equations and inequalities, characterization of local maxima and minima via second derivatives, taylor expansion. exercises
4. the banach fixed point theorem. the concept of banach space

后现代分析-第3版 节选

《后现代分析(第3版影印版)(Postmodern Analysis)》，What is the title of this book intended to signify, what connotations is the adjective ""Postmodern"" meant to carry? A potential reader will surely pose this question.