Skip to main content

Differential calculus and integrals

  • Chapter

Part of the book series: Kluwer Texts in the Mathematical Sciences ((TMS,volume 13))

Abstract

Mathematicians or physicists often speak, with some neglect, of first order approximation, as if they were manipulating numbers d so small that they have null square.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Commented bibliography

  1. WEIL, A., Théorie des points proches sur les variétés différentiables, in Conference Geom. Diff., Strasbourg, 1953, took up again in “Oeuvres scientifiques, collected papers”, vol. II, Springer 1979, 103–109.

    Google Scholar 

  2. EHRESMANN, Ch., Oeuvres complètes et commentées I.1 et I.2, Suppléments 1 et 2 au vol. XXIV des Cahiers de Topologie et Géométrie Différentielle, (1983).

    Google Scholar 

  3. GROTHENDIECK, A., in collaboration with J. DIEUDONNE, Eléments de géométrie algébrique, Inst. Hautes Et. Sc., publ. math. nos 4, 8, 11, 17, 20, 24, 28, 32 (de 1960 à 1967 ).

    Google Scholar 

  4. F.W. LAWVERE, Categorical Dynamics, in [25], 1–28.

    Google Scholar 

  5. KOCK, A.,(ed), Topos theoretic Methods in Geometry, edited by A. Kock, Various Publications Series n30, Aarhus, 1979.

    Google Scholar 

  6. KOCK, A., Synthetic Differential Geometry, London Math. Soc. Lect. Note Series 51, Cambridge Univ. Press, 1981.

    Google Scholar 

  7. MOERDIJK, I., and REYES, G.E., Models for Smooth Infinitesimal Analysis, Springer, 1991.

    Google Scholar 

  8. KOCK, A.,(ed), Topos theoretic Methods in Geometry, edited by A. Kock, Various Publications Series n30, Aarhus, 1979.

    Google Scholar 

  9. KOCK, A.,(ed), Category theoretic Methods in Geometry, edited by A.Kock, Various Publications Series n35, Aarhus, 1983.

    Google Scholar 

  10. KOCK, A., A simple axiomatic for differentiation, Math. Scand. 40 (1977), 183–193.

    Google Scholar 

  11. KOCK, A., Taylor Series calculus for ring objects of line type, Journ. Pure Appl. Mg. 18 (1978), 271–293.

    Google Scholar 

  12. KOCK, A., REYES, G.E., and VEIT, B., Forms and integratin in synthetic differential geometry,Aarhus Preprint Series, n31 (1979/80).

    Google Scholar 

  13. BELAIR„L., Calcul infinitésimal en géométrie différentielle synthétique, Master Thesis, Montréal, 1981.

    Google Scholar 

  14. MacLARTY, C., Local and some global results in synthetic differential geometry, in ([26]), 226–256.

    Google Scholar 

  15. BUNGE, M., and DUBUC, E.J., Archimedean local C°°-rings and models of synthetic differential geometry, Cahiers Top. Géom. Diff. Cat. 27 (1986), 3–22.

    MathSciNet  MATH  Google Scholar 

  16. BUNGE, M., and DUBUC, E.J., Local concepts in synthetic differential geometry and germ representability, in “Mathematical Logic and Theoretical Computer Sciences”, D. Kueher, E.G.K. Lopez-Escobar and C. Smith eds., Dekker, New York, 1987, pp. 39–158.

    Google Scholar 

  17. PENON, J., De l’infinitésimal au local, State PhD. Thesis, Paris, 1985, 191 pp.

    Google Scholar 

  18. BUNGE, M., Synthetic aspects of C°°-mappings, J. Pure Appl. Algebra 28 (1983), 41–63.

    Article  MathSciNet  MATH  Google Scholar 

  19. BUNGE, M. and GAGO, F., Synthetic aspects of C°°-mappings II: Mather’s theorem for infinitesimally represented germs, J. Pure Appl. Algebra 55 (1988), 213–250.

    Article  MathSciNet  MATH  Google Scholar 

  20. GAGO, F., Morse germs in SDG,in “Categorial Algebra and its Applications”, F. Borceux ed., Springer Lecture Notes 1348 (1988), 125–129.

    Google Scholar 

  21. GAGO, F., Singularités dans la géometrie différentielle synthétique, Bull. Soc. Math. Belgique, Ser. A, 41 (1989), 279–287.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1996 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

Lavendhomme, R. (1996). Differential calculus and integrals. In: Basic Concepts of Synthetic Differential Geometry. Kluwer Texts in the Mathematical Sciences, vol 13. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-4588-7_1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4757-4588-7_1

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4419-4756-7

  • Online ISBN: 978-1-4757-4588-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics