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A Companion to Analysis: A Second First and First Second Course in Analysis
About this Title
T. W. Körner, University of Cambridge, Cambridge, England
Publication: Graduate Studies in Mathematics
Publication Year:
2004; Volume 62
ISBNs: 978-0-8218-3447-3 (print); 978-1-4704-2105-2 (online)
DOI: https://doi.org/10.1090/gsm/062
MathSciNet review: MR2015825
MSC: Primary 26-01
Table of Contents
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Front/Back Matter
Chapters
- Chapter 1. The real line
- Chapter 2. A first philosophical interlude
- Chapter 3. Other versions of the fundamental axiom
- Chapter 4. Higher dimensions
- Chapter 5. Sums and suchlike
- Chapter 6. Differentiation
- Chapter 7. Local Taylor theorems
- Chapter 8. The Riemann integral
- Chapter 9. Developments and limitations of the Riemann integral
- Chapter 10. Metric spaces
- Chapter 11. Complete metric spaces
- Chapter 12. Contraction mappings and differential equations
- Chapter 13. Inverse and implicit functions
- Chapter 14. Completion
- Appendix A. Ordered fields
- Appendix B. Countability
- Appendix C. The care and treatment of counterexamples
- Appendix D. A more general view of limits
- Appendix E. Traditional partial derivatives
- Appendix F. Another approach to the inverse function theorem
- Appendix G. Completing ordered fields
- Appendix H. Constructive analysis
- Appendix I. Miscellany
- Appendix J. Executive summary
- Appendix K. Exercises