巴舍沃夫著的《數學分析原理(英文版)/國外優
秀數學著作原版繫列》主要介紹了從初級到高級數學
分析原理的相關知識，包括純粹數學、應用數學和與
之相關的物理學等內容，可使讀者更全面繫統地掌握
數學分析以及應用數學方面的知識。本書內容全面，
知識點豐富，適合高等院校師生和數學愛好者參考閱
讀。

Preface
1 Sets and Proofs
1.1 Sets， Elements， and Subsets
1.2 Operations on Sets
1.3 Language of Logic
1.4 Techniques of Proof
1.5 Relations
1.6 Functions
1.7 Axioms of Set Theory
Exercises
2 Numbers
2.1 System N
2.2 Systems Z and Q
2.3 Least Upper Bound Property and Q
2.4 Systeml R
2.5 Least Upper Bound Property and R
2.6 Systems R， C， and R
2.7 Cardinality
Exercises
3 Convergence
3.1 Convergence of Numerical Sequences
3.2 Cauchy Criterion for Convergence
3.3 Ordered Field Structure and Convergence
3.4 Subsequences
3.5 Numerical Series
3.6 Some Series of Particular Interest
3.7 Absolute Convergence
3.8 Numbere
Exercises
4 Point Set Topology
4.1 Metric Spaces
4.2 Open and Closed Sets
4.3 Completeness
4.4 Separability
4.5 Total Boundedness
4.6 Compactness
4.7 Perfectness
4.8 Connectedness
4.9 Structure of Open and Closed Sets
Exercises
5 Continuity
5.1 Definition and Examples
5.2 Continuity and Limits
5.3 Continuity and Compactness
5.4 Continuity and Connectedness
5.5 Continuity and Oscillation
5.6 Continuity of Rk—valued Functions
Exercises
6 Space C（E， E'）
6.1 Uniform Continuity
6.2 Uniform Convergence
6.3 Completeness of C（E， E'）
6.4 Bernstein and Weierstrass Theorems
6.5 Stone and Weierstrass Theorems
6.6 Ascoli—Arzela Theorem
Exercises
7 Differentiation
7.1 Derivative
7.2 Differentiation and Continuity
7.3 Rules of Differentiation
7.4 Mean—Value Theorems
7.5 Taylor's Theorem
7.6 Differential Equations
7.7* Banach Spaces and the Space C1 （a， b）
7.8 A View to Differentiation in Rk
Exercises
8 Bounded Variation
8.1 Monotone Functions
8.2 Cantor Function
8.3 Functions of Bounded Variation
8.4 Space BV（a， b）
8.5 Continuous Functions of Bounded Variation
8.6 Rectifiable Curves
Exercises
9 Riemann Integration
9.1 Definition of the Riemann Integral
9.2 Existence of the Riemann Integral
9.3 Lebesgue Characterization
9.4 Properties of the Riemann Integral
9.5 Riemann Integral Depending on a Parameter
9.6 Improper Integrals
Exercises
10 Generalizations of Riemann Integration
10.1 Riemann—Stieltjes Integral
10.2 Helly's Theorems
10.3 Reisz Representation
10.4 Definition of the Kurzweil—Henstock Integral
10.5 Differentiation of the Kurzweil—Henstock Integral
10.6 Lebesgue Integral
Exercises
11 Transcendental Functions
11.1 Logarithmic and Exponential Functions
11.2 Multiplicative Calculus
11.3 Power Series
11.4 Analytic Functions
11.5 Hyperbolic and Trigonometric Functions
11.6 Infmite Products
11.7 Improper Integrals Depending on a Parameter
11.8 Euler's Integrals
Exercises
12 Fourier Series and Integrals
12.1 Trigonometric Series
12.2 Riemann—Lebesgue Lemma
12.3 Dirichlet Kernels and Riemann's Localization Lemma
12.4 Pointwise Convergence of Fourier Series
12.5 Fourier Series in Inner Product Spaces
12.6 Cesaro Summability and Fejer's Theorem
12.7 Uniform Convergence of Fourier Series
12.8 Gibbs Phenomenon
12.9 Fourier Integrals
Exercises
Bibliography