|
|
| Tom M. Apostol是加州理工学院数学系荣誉教授。他于1946年在华盛顿大学西雅图分校获得数学硕士学位，于1948年在加州大学伯克利分校获得数学博士学位。他的著述很多，除本书外，还著有《Calculus,Multi-Variable Calculus and Algebra with Applications》、《Calculus,One-Variable Calculus with an Introduction to Linear Algebra》等。
|
| Chapter 1 The Real and Complex Number Systems 1.1 Introduction 1.2 The field axioms 1.3 The order axioms 1.4 Geometric representation of real numbers 1.5 Intervals 1.6 Integers 1.7 The unique factorization of real numbers 1.8 Rational numbers 1.9 Irrational numbers 1.10 Upper bounds ,maximum element,least upper bound 1.11 The completeness axiom 1.12 Some properties of the supremum 1.13 Properties of the integers deduced from the completeness axiom 1.14 the Archimedean property of the real-number systen 1.15 Rational numbers with finite decimal representation 1.16 Finite decimal approximations to real numbers 1.17 Infinite decimal representation of the real-numbers 1.18 Absolute values and the triangle inequality 1.19 The Cauchy-Schwarz inequality 1.20 Plus and minus infinity and the extended real number system R* 1.21 Compex numbers 1.22 geometric representation of complex numbers 1.23 The imaginary unit 1.24 Absolute value of a complex number 1.25 Impossinbility of ordering the complex numbers 1.26 Complex exponentials 1.27 Further properties of complex exponentials 1.28 The argument of a complex number 1.29 Integral powers and roots of complex numbers 1.30 Complex logarithms 1.31 Complex powers 1.32 Complex sines and cosines 1.33 Infinity and the extended complex plane C* Exercises Chapter 2 Some Basic Notions of Set Theory Chapter 3 elements of Point Set topology Chapter 4 Limits and Continuity Chapter 5 Derivatives Chapter 6 Functions of bounded Variation and Rectifiable Curves Chapter 7 The Riemann-Stieltjes Integral Chapter 8 Infinite Series and Infinite Products Chapter 9 Sequences of Functions Chapter 10 The Lebesgu Integral Chapter 11 Fourier Series and fourier Integrals Chapter 12 Multivariable Differential Calculus Chapter 13 Implicit Functions and Extremum Problems Chapter 14 Multiple Riemann Integrals Chapter 15 Multiple Lebesgue Integrals Chapter 16 Cauchy's Theorem and the Residue Calculus Index of Special Symbols Index |
内容加载中，请稍后...
商品评论（0条）