Synthetic Differential Geometry - Further Reading

Further Reading

  • John Lane Bell, Two Approaches to Modelling the Universe: Synthetic Differential Geometry and Frame-Valued Sets (PDF file)
  • F.W. Lawvere, Outline of synthetic differential geometry (PDF file)
  • Anders Kock, Synthetic Differential Geometry (PDF file), Cambridge University Press, 2nd Edition, 2006.
  • R. Lavendhomme, Basic Concepts of Synthetic Differential Geometry, Springer-Verlag, 1996.
  • Michael Shulman, Synthetic Differential Geometry


Infinitesimals
History
  • Adequality
  • Infinitesimal calculus
  • Leibniz's notation
  • Integral symbol
  • Criticism of non-standard analysis
  • The Analyst
  • The Method of Mechanical Theorems
  • Cavalieri's principle
Related branches
  • Non-standard analysis
  • Non-standard calculus
  • Internal set theory
  • Synthetic differential geometry
  • Constructive non-standard analysis
Formalizations
  • Differentials
  • Hyperreal numbers
  • Dual numbers
  • Surreal numbers
Individual concepts
  • Standard part function
  • Transfer principle
  • Hyperinteger
  • Increment theorem
  • Monad
  • Internal set
  • Levi-Civita field
  • Hyperfinite set
  • Law of Continuity
  • Overspill
  • Microcontinuity
  • Transcendental law of homogeneity
Scientists
  • Gottfried Wilhelm Leibniz
  • Abraham Robinson
  • Pierre de Fermat
  • Augustin-Louis Cauchy
  • Leonhard Euler
  • Physics
  • Engineering
  • Infinitesimal strain theory
  • Infinitesimal oscillations of a pendulum
Textbooks
  • Analyse des Infiniment Petits
  • Elementary Calculus

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