这本《后现代分析(第3版)》德国Jurgen Jost所著，内容是：This edition corrects some misprints and minor inconsistencies that were kindly pointed out to me by several readers, in particular Bruce Gould, aswell as an error in the proof of theorem 19.16 that was brought to my attention by Matthias Stark. I have also used this opportunity to introduce anotherimportant tool in analysis, namely covering theorems. Useful references forsuch results and further properties of various classes of weakly differentiable functions are W.Ziemer, Weakly differentiable functions, Springer, 1989, andL.C.Evans, R.Gariepy, Measure theory and fine properties of functions, CRCPress, 1992, as well as the fundamental H.Federer, Geometric measure theory,Springer, 1969.

Chapter Ⅰ. Calculus for Functions of One Variable

 0. Prerequisites

 1. Limits and Continuity of Functions

 2. Differentiability

 3. Characteristic Properties of Differentiable Functions. Differential Equations

 4. The Banach Fixed Point Theorem. The Concept of Banach Space

 5. Uniform Convergence. Interchangeability of Limiting Processes. Examples of Banach Spaces. The Theorem of Arzela-Ascoli

 6. Integrals and Ordinary Differential Equations

Chapter Ⅱ. Topological Concepts

 7. Metric Spaces: Continuity, Topological Notions, Compact Sets

Chapter Ⅲ. Calculus in Euclidean and Banach Spaces

 8. Differentiation in Banach Spaces

 9. Differential Calculus in Rd

 10. The Implicit Function Theorem. Applications

 11. Curves in Rd.Systems of ODEs

Chapter Ⅳ. The Lebesgue Integral

 12. Preparations. Semicontinuous Functions

 13. The Lehesgue Integral for Semicontinuous Functions. The Volume of Compact Sets

 14. Lebesgue Integrable Functions and Sets

 15. Null Functions and Null Sets. The Theorem of Fubini

 16. The Convergence Theorems of Lebesgue Integration Theory

 17. Measurable Functions and Sets. Jensen's Inequality. The Theorem of Egorov

 18. The Transformation Formula

Chapter Ⅴ. Lp and Sobolev Spaces

 19. The LP-Spaces

 20. Integration by Parts. Weak Derivatives. Sobolev Spaces

Chapter Ⅵ. Introduction to the Calculus of Variations and Elliptic Partial Differential Equations

 21. Hilbert Spaces. Weak Convergence

 22. Variational Principles and Partial Differential Equations

 23. Regularity of Weak Solutions

 24. The Maximum Principle

 25. The Eigenvalue Problem for the Laplace Operator

Index