Author | Jost, Jรผrgen. author |
---|---|
Title | Postmodern Analysis [electronic resource] / by Jรผrgen Jost |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2003 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-3-662-05306-5 |
Descript | XVII, 371 p. online resource |
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 -- II. Topological Concepts -- 7. Metric Spaces: Continuity, Topological Notions, Compact Sets -- III. Calculus in Euclidean and Banach Spaces -- 8. Differentiation in Banach Spaces -- 9. Differential Calculus in ?d -- 10. The Implicit Function Theorem. Applications -- 11. Curves in ?d. Systems of ODEs -- IV. The Lebesgue Integral -- 12. Preparations. Semicontinuous Functions -- 13. The Lebesgue 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. Jensenโs Inequality. The Theorem of Egorov -- 18. The Transformation Formula -- V. Lp and Sobolev Spaces -- 19. The Lp-Spaces -- 20. Integration by Parts. Weak Derivatives. Sobolev Spaces -- 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 of Notation