Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Books
  3. A Primer of Infinitesimal Analysis
  • Cited by 39
Publisher:
Cambridge University Press
Online publication date:
January 2010
Print publication year:
2008
Online ISBN:
9780511619625
DOI:
https://doi.org/10.1017/CBO9780511619625
Subjects:
Mathematics, Logic, Categories and Sets
Information

Book description

One of the most remarkable recent occurrences in mathematics is the refounding, on a rigorous basis, of the idea of infinitesimal quantity, a notion which played an important role in the early development of the calculus and mathematical analysis. In this new edition basic calculus, together with some of its applications to simple physical problems, are presented through the use of a straightforward, rigorous, axiomatically formulated concept of 'zero-square', or 'nilpotent' infinitesimal - that is, a quantity so small that its square and all higher powers can be set, literally, to zero. The systematic employment of these infinitesimals reduces the differential calculus to simple algebra and, at the same time, restores to use the “infinitesimal” methods figuring in traditional applications of the calculus to physical problems - a number of which are discussed in this book. This edition also contains an expanded historical and philosophical introduction.

Reviews

'This might turn out to be a boring, shallow book review: I merely LOVED the book...the explanations are so clear, so considerate; the author must have taught the subject many times, since he anticipates virtually every potential question, concern, and misconception in a student's or reader's mind.'

Source: MAA Reviews

‘John Bell has done a first rate job in presenting an elementary introduction to this fascinating subject ... I recommend it highly.’

J. P. Mayberry Source: British Journal for the Philosophy of Science

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

Contents

Contents
References
References
Aristotle, (1980). Physics, Vol. II. Cambridge, MA: Harvard University Press.
Banach, S. (1951). Mechanics (trans. E. J. Scott). Warszawa: PWN.
Baron, M. E. (1969). The Origins of the Infinitesimal Calculus. Oxford: Pergamon Press.
Barr, M. and Wells, C. (1985). Toposes, Triples and Theories.Berlin: Springer-Verlag.
Bell, J. L. (1986). From absolute to local mathematics. Synthese, 69, 409–26.
Bell, J. L. (1988a). Infinitesimals. Synthese, 75, 285–315.
Bell, J. L.(1988b). Toposes and Local Set Theories.Oxford: Clarendon Press.
Bell, J. L. (1995). Infinitesimals and the continuum. Mathematical Intelligencer, 17(2), 55–7.
Bell, J. L. and Machover, M. (1977). A Course in Mathematical Logic.Amsterdam: North-Holland.
Bell, J. L. (2005a). The Continuous and the Infinitesimai in Mathematics and Philosophy. Milano: Polimetrica.
Bell, J. L.(2005b). Continuity and Infinitesimals. Stanford Encyclopedia of Philosophy.
Boyer, C. B. (1959). The History of the Calculus and its Conceptual Development.New York: Dover.
Brouwer, L. E. J. (1964). Intuitionism and formalism. In Philosophy of Mathematics, Selected Readings, eds Benacerraf, P. and Putnam, H.. Oxford: Blackwell.
Cascuberta, C. and Castellet, M., eds (1992). Mathematical Research Today and Tomorrow: Viewpoints of Six Fields Medallists.Berlin: Springer-Verlag.
Courant, R. (1942). Differential and Integral Calculus. London: Blackie.
Dubuc, E. (1979). Sur les modeles de la geometrie differentielle synthetique. Cahiers de Topologie et Geometrie Differentielle, XX-3, 231–79.
Dummett, M. (1977). Elements of Intuitionism.Oxford: Clarendon Press.
Freyd, P. J. and Scedrov, A. (1990). Categories, Allegories.Amsterdam: North-Holland.
Gibson, G. (1944). An Introduction to the Calculus.London: Macmillan.
Goldblatt, R. I. (1979). Topoi: The Categorial Analysis of Logic.Amsterdam: North-Holland.
Heyting, A. (1971). Intuitionism: An Introduction.Amsterdam: North-Holland.
Hohn, F. E. (1972). Introduction to Linear Algebra.New York: Macmillan.
Johnstone, P. T. (1979). Topos Theory.London: Academic Press.
Kant, I. (1964). Critique of Pure Reason.New York: Macmillan.
Kleene, S. C. (1952). Introduction to Metamathematics.Amsterdam: North-Holland and New York: Van Nostrand.
Kock, A. (1977). A simple axiomatics for differentiation. Mathematica Scandinavica, 40, 183–93.
Kock, A.(1981). Synthetic Differential Geometry. Cambridge: Cambridge University Press. (Second edition, 2006)
Lambek, J. and Scott, P. J. (1986). Introduction to Higher-Order Categorical Logic.Cambridge: Cambridge University Press.
Lavendhomme, R. (1987). Lecons de Geometrie Synthetique Differentielle Naive.Louvain-La-Neuve: Institut de Mathematique.
Lavendhomme, R.(1996). Basic Concepts of Synthetic Differential Geometry.Dordrecht: Kluwer.
Lawvere, F. W. (1979). Categorical dynamics. In Topos Theoretic Methods in Geometry, Aarhus Math. Inst. Var. Publ. series 30.
Lawvere, F. W. (1980). Toward the description in a smooth topos of the dynamically possible motions and deformations of a continuous body. Cahiers de Topologie et Geometrie Difféentielle, 21, 377–92.
Lawvere, F. W. and Schanuel, S. (1997). Conceptual Mathematics: A First Introduction to Categories. Cambridge University Press.
Lane, Mac S. (1971). Categories for the Working Mathematician.New York: Springer-Verlag.
Lane, Mac S. and Moerdijk, I. (1992). Sheaves in Geometry and Logic: A First Introduction to Topos Theory.New York: Springer-Verlag.
McLarty, C. (1988). Defining sets as sets of points of spaces. Journal of Philosophical Logic, 17, 75–90.
McLarty, C. (1992). Elementary Categories, Elementary Toposes.Oxford: Clarendon Press.
Misner, C., Thorne, K., and Wheeler, J. (1972). Gravitation. Freeman.
Moerdijk, I. and Reyes, G. E. (1991). Models for Smooth Infinitesimal Analysis.New York: Springer-Verlag.
Peirce, C. S. (1976). The New Elements of Mathematics, Vol. III, ed. Eisele, C.. Atlantic Highlands, NJ: Humanities Press.
Rescher, N. (1967). The Philosophy of Leibniz.Englewood Cliffs, NJ: Prentice-Hall.
Robinson, A. (1966). Non-Standard Analysis.Amsterdam: North-Holland.
Russell, B. (1937). The Principles of Mathematics, 2nd edn. London: George Allen and Unwin Ltd.
Spivak, M. (1979). Differential Geometry, 2nd edn. Berkeley: Publish or Perish.
Dalen, D. (1995). Hermann Weyl's intuitionistic mathematics. Bulletin of Symbolic Logic, 1(2), 145–69.
Wagon, S. (1985). The Banach–Tarski Paradox.Cambridge: Cambridge University Press.
Weyl, H. (1921). Uber die neue Grundlagenkrise der Mathematik. Mathematische Zeitschrift, 10, 39–79.
Weyl, H.(1922). Space–Time–Matter.New York: Dover.
Weyl, H. (1940). The ghost of modality. In Philosophical Essays in Memory of Edmund Husserl. Cambridge, MA: Harvard University Press.
Weyl, H. (1987). The Continuum: A Critical Examination of the Foundation of Analysis (transl. S. Pollard and T. Bole). Philadelphia: Thomas Jefferson University Press.

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.