Asymptotic Differential Algebra and Model Theory of Transseries : : (AMS-195) / / Matthias Aschenbrenner, Joris van der Hoeven, Lou van den Dries.
Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logar...
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| Superior document: | Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2017 |
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| Place / Publishing House: | Princeton, NJ : : Princeton University Press, , [2017] ©2017 |
| Year of Publication: | 2017 |
| Language: | English |
| Series: | Annals of Mathematics Studies ;
195 |
| Online Access: | |
| Physical Description: | 1 online resource (880 p.) :; 12 line illus. |
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Table of Contents:
- Frontmatter
- Contents
- Preface
- Conventions and Notations
- Leitfaden
- Dramatis Personæ
- Introduction and Overview
- Chapter One. Some Commutative Algebra
- Chapter Two. Valued Abelian Groups
- Chapter Three. Valued Fields
- Chapter Four. Differential Polynomials
- Chapter Five. Linear Differential Polynomials
- Chapter Six. Valued Differential Fields
- Chapter Seven. Differential-Henselian Fields
- Chapter Eight. Differential-Henselian Fields with Many Constants
- Chapter Nine. Asymptotic Fields and Asymptotic Couples
- Chapter Ten. H-Fields
- Chapter Eleven. Eventual Quantities, Immediate Extensions, and Special Cuts
- Chapter Twelve. Triangular Automorphisms
- Chapter Thirteen. The Newton Polynomial
- Chapter Fourteen. Newtonian Differential Fields
- Chapter Fifteen. Newtonianity of Directed Unions
- Chapter Sixteen. Quantifier Elimination
- Appendix A. Transseries
- Appendix B. Basic Model Theory
- Bibliography
- List of Symbols
- Index