| 《分析方法(修订版)(英文版)》是由世界图书出版公司出版的。 |
| preface 1 preliminaries 1.1 the logic of quantifiers 1.2 infinite sets 1.3 proofs 1.4 the rational number system 1.5 the axiom of choice* 2 construction of the real number system 2.1 cauchy sequences 2.2 the reals as an ordered field 2.3 limits and completeness 2.4 other versions and visions 2.5 summary 3 topology of the real line 3.1 the theory of limits 3.2 open sets and closed sets 3.3 compact sets 3.4 summary 4 continuous functions 4.1 concepts of continuity 5 differential calculus 5.1 concepts of the derivative 5.2 properties of the derivative 5.3 the calculus of derivatives 5.4 higher derivatives and taylor's theorem 5.5 summary 6 integral calculus 6.1 integrals of continuous functions 6.2 the riemann integral 6.3 improper integrals* 6.4 summary 7 sequences and series of functions 7.1 complex numbers 7.2 numerical series and sequences 7.3 uniform convergence 7.4 power series 7.5 approximation by polynomials 7.6 equicontinuity 7.7 summary 8 transcendental functions 8.1 the exponential and logarithm 8.2 trigonometric functions 8.3 summary 9 euclidean space and metric spaces 9.1 structures on euclidean space 9.2 topology of metric spaces 9.3 continuous functions on metric spaces 9.4 summary 10 differential calculus in euclidean space 10.1 the differential 10.2 higher derivatives 10.3 summary 11 ordinary differential equations 11.1 existence and uniqueness 11.2 other methods of solution* 11.3 vector fields and flows* 11.4 summary 12 fourier series 12.1 origins of fourier series 12.2 convergence of fourier series 12.3 summary 13 implicit functions, curves, and surfaces 13.1 the implicit function theorem 13.2 curves and surfaces 13.3 maxima and minima on surfaces 13.4 arc length 13.5 summary 14 the lebesgue integral 14.1 the concept of measure 14.2 proof of existence of measures* 14.3 the integral 14.4 the lebesgue spaces l1 and l2 14.5 summary 15 multiple integrals 15.1 interchange of integrals 15.2 change of variable in multiple integrals 15.3 summary index |
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