Albert E. Hurd

Indeholder "Preface", "Chapter I. Infinitesimals and The Calculus", " I.1 The Hyperreal Number System as an Ultrapower", " I.2 *-Transforms of Relations", " I.3 Simple Languages for Relational Systems", " I.4 Interpretation of Simple Sentences", " I.5 The Transfer Principle for Simple Sentences", " I.6 Infinite Numbers, Infinitesimals, and the Standard Part Map", " I.7 The Hyperintegers", " I.8 Sequences and Series", " I.9 Topology on the Reals", " I.10 Limits and Continuity", " I.11 Differentiation", " I.12 Riemann Integration", " I.13 Sequences of Functions", " I.14 Two Applications to Differential Equations", " I.15 Proof of the Transfer Principle", "Chapter II. Nonstardard Analysis on Superstructures", " II.1 Superstructures", " II.2 Languages and Interpretation for Superstructures", " II.3 Monomorphisms between Superstructures: The Transfer Principle", " II.4 The Ultrapower Construction for Superstructures", " II.5 Hyperfinite Sets, Enlargements, and Concurrent Relations", " II.6 Internal and External Entities; Comprehensiveness", " II.7 The Permanence Principle", " II.8 k-Saturated Superstructures", "Chapter III. Nonstandard Theory of Topological Spaces", " III.1 Basic Definitions and Results", " III.2 Compactness", " III.3 Metric Spaces", " III.4 Normed Vector Spaces and Banach Spaces", " III.5 Inner-Product Spaces and Hilbert Spaces", " III.6 Nonstandard Hulls of Metric Spaces", " III.7 Compactifications", " III.8 Function Spaces", "Chapter IV. Nonstandard Integration Theory", " IV.1 Standardizations of Internal Integration Structures", " IV.2 Measure Theory for Complete Integration Structures", " IV.3 Integration on R^n: the Riesz Representation Theorem", " IV.4 Basic Convergence Theorems", " IV.5 The Fubini Theorem", " IV.6 Applications to Stochastic Processes", "Appendix", " Ultrafilters", "References", "List of Symbols", "Index".

Noget om nonstandard analyse, men jeg har ikke kigget nærmere på det. Ideen er at give en definition af infinitesimaler, som faktisk holder vand.… (mehr)