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Informationen zum Autor Anders Kock is an Associate Professor of Mathematics at the University of Aarhus, Denmark. Klappentext This book, first published in 2006, details how limit processes can be represented algebraically. Zusammenfassung Synthetic Differential Geometry is a method of reasoning in differential geometry and calculus! where use of nilpotent elements allows the replacement of the limit processes of calculus by purely algebraic notions. In this 2006 second edition of Kock's classical text! many notes have been included commenting on new developments. Inhaltsverzeichnis Preface to the second edition (2005); Preface to the first edition (1981); Part I. The Synthetic Ttheory: 1. Basic structure on the geometric line; 2. Differential calculus; 3. Taylor formulae - one variable; 4. Partial derivatives; 5. Taylor formulae - several variables; 6. Some important infinitesimal objects; 7. Tangent vectors and the tangent bundle; 8. Vector fields; 9. Lie bracket; 10. Directional derivatives; 11. Functional analysis - Jacobi identity; 12. The comprehensive axiom; 13. Order and integration; 14. Forms and currents; 15. Currents - Stokes' theorem; 16. Weil algebras; 17. Formal manifolds; 18. Differential forms in terms of simplices; 19. Open covers; 20. Differential forms as quantities; 21. Pure geometry; Part II. Categorical Logic: 1. Generalized elements; 2. Satisfaction (1); 3. Extensions and descriptions; 4. Semantics of function objects; 5. Axiom 1 revisited; 6. Comma categories; 7. Dense class of generators; 8. Satisfaction (2); 9. Geometric theories; Part III. Models: 1. Models for axioms 1, 2, and 3; 2. Models for epsilon-stable geometric theories; 3. Well-adapted models (1); 4. Well-adapted models (2); 5. The algebraic theory of smooth functions; 6. Germ-determined T-infinity-algebras; 7. The open cover topology; 8. Construction of well-adapted models; 9. Manifolds with boundary; 10. Field property - germ algebras; 11. Order and integration in cahiers topos; Appendices; Bibliography; Index....
