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Bell J.L. A primer of infinitesimal analysis (2ed., CUP, 2008)(ISBN 0521887186)(O)(138s)_MCat_

Bell J.L. A primer of infinitesimal analysis (2ed., CUP, 2008)(ISBN 0521887186)(O)(138s)_MCat_

Bell J.L. A primer of infinitesimal analysis (2ed., CUP, 2008)(ISBN

  • Page 6: 100.00-2 GENERAL PROVISIONSEEI - Ed
  • Page 12: Once again, to Mimi
  • Page 18: viiiContents5 Multivariable calculu
  • Page 22: xPrefaceA final remark: The theory
  • Page 28: IntroductionAccording to the Encycl
  • Page 32: Introduction 3mathematicians have o
  • Page 36: Introduction 5continuous 4 .For thi
  • Page 40: Introduction 7For such an entity wo
  • Page 44: Introduction 9If this procedure is
  • Page 48: Introduction 11to the curve is give
  • Page 52:

    Introduction 13Toposes may be sugge

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    Introduction 15ensuring that all qu

  • Page 60:

    Basic features of smooth worlds 17m

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    (5) either 0 < a or a < 1.(6) a ≠

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    Basic features of smooth worlds 21O

  • Page 72:

    Basic features of smooth worlds 23(

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    2.1 The derivative of a function 25

  • Page 80:

    2.2 Stationary points of functions

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    2.3 Areas under curves and the Cons

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    We assume the familiar relations2.4

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    2.4 The special functions 33possess

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    3First applications of the differen

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    3.1 Areas and volumes 37Assuming th

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    3.1 Areas and volumes 39Fig. 3.3int

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    3.2 Volumes of revolution 41Fig. 3.

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    3.3 Arc length; surfaces of revolut

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    3.3 Arc length; surfaces of revolut

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    3.3 Arc length; surfaces of revolut

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    4Applications to physicsIn this cha

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    4.1 Moments of inertia 51where S is

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    4.1 Moments of inertia 53Fig. 4.6Th

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    4.3 Pappus’ theorems 55so that, c

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    4.3 Pappus’ theorems 57where S i

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    4.4 Centres of pressure 59Fig. 4.9s

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    4.6 Flexure of beams 61Fig. 4.10and

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    4.7 The catenary, the loaded chain

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    4.7 The catenary, the loaded chain

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    4.8 The Kepler-Newton areal law of

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    5Multivariable calculus and applica

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    5.1 Partial derivatives 71Theorem 5

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    5.2 Stationary values of functions

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    5.3 Theory of surfaces. Spacetime m

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    5.3 Theory of surfaces. Spacetime m

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    5.3 Theory of surfaces. Spacetime m

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    5.4 The heat equation 81To quote a

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    5.5 The basic equations of hydrodyn

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    5.6 The wave equation 85By Newton

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    5.7 The Cauchy-Riemann equations fo

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    6The definite integral. Higher-orde

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    6.1 The definite integral 91Now, by

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    6.2 Higher-order infinitesimals and

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    6.3 The three natural microneighbou

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    7.1 Tangent vectors and tangent spa

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    for τ in S . Since, for ε in ,7.

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    7.3 Differentials and directional d

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    Smooth infinitesimal analysis as an

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    anging over R,Smooth infinitesimal

  • Page 240:

    Smooth infinitesimal analysis as an

  • Page 244:

    8.1 Natural numbers in smooth world

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    8.2 Nonstandard analysis 111and onl

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    Appendix. Models for smoothinfinite

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    Appendix 115(ii) Stability: ifS cov

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    Appendix 117Suitable refinements of

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    Note on sources and further reading

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    ReferencesAristotle (1980). Physics

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    Indexacceleration function 83analyt