《天元基金影印數(shù)學(xué)叢書：分析2（影印版）》是作者在巴黎第七大學(xué)講授分析課程數(shù)十年的結(jié)晶，其目的是闡明分析是什么，它是如何發(fā)展的。本書非常巧妙地將嚴(yán)格的數(shù)學(xué)與教學(xué)實際、歷史背景結(jié)合在一起，對主要結(jié)論常常給出各種可能的探索途徑，以使讀者理解基本概念、方法和推演過程了作者在本書中較早地引入了一些較深的內(nèi)容，如在第一卷中介紹了拓?fù)淇臻g的概念，在第二卷中介紹了Lebesgue理論的基本定理和Weierstrass橢圓函數(shù)的構(gòu)造。
　　 　　《天元基金影印數(shù)學(xué)叢書：分析2（影印版）》第一卷的內(nèi)容包括集合與函數(shù)、離散變量的收斂性、連續(xù)變量的收斂性、冪函數(shù)、指數(shù)函數(shù)與三角函數(shù)；第二卷的內(nèi)容包括Fourier級數(shù)和Fourier積分以及可以通過Fourier級數(shù)解釋的Weierstrass的解析函數(shù)理論。

　　“天元基金影印數(shù)學(xué)叢書”主要包含國外反映近代數(shù)學(xué)發(fā)展的純數(shù)學(xué)與應(yīng)用數(shù)學(xué)方面的優(yōu)秀書籍，天元基金邀請國內(nèi)各個方向的知名數(shù)學(xué)家參與選題的工作，經(jīng)專家遴選、推薦，由高等教育出版社影印出版�！斗治觥芬粫�第一卷的內(nèi)容包括集合與函數(shù)、離散變量的收斂性、連續(xù)變量的收斂性、冪函數(shù)、指數(shù)函數(shù)與三角函數(shù)；第二卷的內(nèi)容包括Fourier級數(shù)和Fourier積分以及可以通過Fourier級數(shù)解釋的Weierstrass的解析函數(shù)理論。《分析》可作為高年級本科生教材或參考書。

V - Differential and Integral Calculus
1. The Riemann Integral
1 - Upper and lower integrals of a bounded function
2 - Elementary properties of integrals
3 - Riemann sums. The integral notation
4 - Uniform limits of integrable functions
5 - Application to Fourier series and to power series
2. Integrability Conditions
6 - The Borel-Lebesgue Theorem
7 - Integrability of regulated or continuous functions
8 - Uniform continuity and its consequences
9 - Differentiation and integration under the f sign
10 - Semicontinuous functions
11 - Integration of semicontinuous functions
3. The \"Fundamental Theorem\" （FT）
12 - The fundamental theorem of the differential and integral calculus
13 - Extension of the fundamental theorem to regulated functions
14 - Convex functions; Holder and Minkowski inequalities
4. Integration by parts
15 - Integration by parts
16 - The square wave Fourier series
17- Wallis formula
5. Taylors Formula
18 - Taylors Formula
6. The change of variable formula
19 - Change of variable in an integral
20 - Integration of rational fractions
7. Generalised Riemann integrals
21 - Convergent integrals： examples and definitions
22 - Absolutely convergent integrals
23 - Passage to the limit under the fsign
24 - Series and integrals
25 - Differentiation under the f sign
26 - Integration under the f sign
8. Approximation Theorems
27 - How to make C a function which is not
28 - Approximation by polynomials
29 - Functions having given derivatives at a point
9. Radon measures in R or C
30 - Radon measures on a compact set
31 - Measures on a locally compact set
32 - The Stieltjes construction
33 - Application to double integrals
10. Schwartz distributions
34 - Definition and examples
35 - Derivatives of a distribution
Appendix to Chapter V - Introduction to the Lebesgue Theory

VI - Asymptotic Analysis
1. Truncated expansions
1 - Comparison relations
2 - Rules of calculation
3 - Truncated expansions
4 - Truncated expansion of a quotient
5 - Gauss convergence criterion
6 - The hypergeometric series
7 - Asymptotic study of the equation xex = t
8 - Asymptotics of the roots of sin x log x = 1
9 - Keplers equation
10 - Asymptotics of the Bessel functions
2. Summation formulae
11 - Cavalieri and the sums 1k + 2k + ... + nk
12 - Jakob Bernoulli
13 - The power series for cot z
14 - Euler and the power series for arctan x
15 - Euler， Maclaurin and their summation formula
16 - The Euler-Maclaurin formula with remainder
17 - Calculating an integral by the trapezoidal rule
18 - The sum 1 + 1/2 ... + l/n， the infinite product for the F function， and Stirlings formula
19 - Analytic continuation of the zeta function

VII - Harmonic Analysis and Holomcrphic Functions
1 - Cauchys integral formula for a circle
1. Analysis on the unit circle
2 - Functions and measures on the unit circle
3 - Fourier coefficients
4 - Convolution product on
5 - Dirac sequences in T
2. Elementary theorems on Fourier series
6 - Absolutely convergent Fourier series
7 - Hilbertian calculations
8 - The Parseval-Bessel equality
9 - Fourier series of differentiable functions
10 - Distributions on
3. Dirichlets method
11 - Dirichlets theorem
12 - Fejers theorem
13 - Uniformly convergent Fourier series
4. Analytic and holomorphic functions
14 - Analyticity of the holomorphic functions
15 - The maximum principle
16 - Functions analytic in an annulus. Singular points. Meromorphic functions
17 - Periodic holomorphic functions
18 - The theorems of Liouville and dAlembert-Gauss
19 - Limits of holomorphic functions
20 - Infinite products of holomorphic functions
5. Harmonic functions and Fourier series
21 - Analytic functions defined by a Cauchy integral
22 - Poissons function
23 - Applications to Fourier series
24 - Harmonic functions
25 - Limits of harmonic functions
26 - The Dirichlet problem for a disc
6. From Fourier series to integrals
27 - The Poisson summation formula
28 - Jacobis theta function
29 - Fundamental formulae for the Fourier transform
30 - Extensions of the inversion formula
31 - The Fourier transform and differentiation
32 - Tempered distributions
Postface. Science， technology， arms
Index
Table of Contents of Volume I