编辑推荐
本书是世图“俄罗斯数学经典”书系中的一种，被沃尔夫奖得主、俄罗斯科学院院士阿诺尔德（V. I. Arnold）誉为现有数学分析现代教材的best。与其他数学分析教科书相比，它更多地运用了现代数学（包括代数学、几何学和拓扑学）的思想和方法，而且也更贴近自然科学（特别是物理学和力学）的应用。本书被清华大学数理基础科学班精品课程选用为授课教材。
图书目录
Prefaces
9. Continuous Mappings (General Theory)
10. Differential Calculus from a General Viewpoint
11. Multiple Integrals
12. Surfaces and Differential Forms in Rn
13. Line and Surface Integrals
14. Elements of Vector Analysis and Field Theory
15. Integration of Differential Forms on Manifolds
16. Uniform Convergence and Basic Operations of Analysis
17. Integrals Depending on a Parameter
18. Fourier Series and the Fourier Transform
19. Asymptotic Expansions
Topics and Questions for Midterm Examinations
Examination Topics
Examination Problems (Series and Integrals Depending on a Parameter)
Intermediate Problems (Integral Calculus of Several Variables)
Appendix A. Series as a Tool (Introductory Lecture)
Appendix B. Change of Variables in Multiple Integrals
Appendix C. Multidimensional Geometry and Functions of a Very Large Number of Variables
Appendix D. Operators of Field Theory in Curvilinear Coordinates
Appendix E. Modern Formula of Newton-Leibniz
References
Index of Basic Notation
Subject Index
Name Index
