《分析基础:微积分理论》由世界图书出版公司出版。 |
| preface 1 introduction 1 theset n of natural numbers 2 the set q of rational numbers 3 the set r of real numbers 4 the completeness axiom 5 the symbols +oo and -oo 6 * a development of r 2 sequences 7 limits of sequences 8 a discussion.about proofs 9 limit theorems for sequences 10 monotone sequences and cauchy sequences 11 subsequences 12 lim sap's and lim inf's 13 * some topological concepts in metric spaces 14 series 15 aternatin4g series and integral tests 16 * decimal expansions of real numbers 3 continuity . 17 continuous functions 18 properties of continuous functions 19 uniform continuity 20 limits of functions 21 * more on metric spaces: continuity 22 * more on metric spaces: connectedness 4 sequences and series of functions 23 power series 24 uniform convergence 25 more on uniform convergence 26 differentiation and integration of power series 27 * weierstrass's approximation theorem 5 differentiation 28 basic properties of the derivative 29 the mean value theorem 30 * uhospital's rule 31 taylor s theorem 6 integration 32 the riemann integral 33 properties of the riemann integral 34 fundamental theorem of calctflus 35 * riemann-stieltjes integrals 36 * improper integrals 37 * a discussion of exponents and logarithms appendix on set notation selected hints and answers references symbols index index |
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