ChemTexts

, 4:1 | Cite as

How Grünwald unified and generalized the calculus, and how his discovery helps electrochemists

Lecture Text
  • 77 Downloads

Abstract

2017 is the sesquicentennial of Grünwald’s demonstration that differentiation and integration can be united into a single operation which, moreover, could then be extended to unlimited orders. This text provides an overview of how such “differintegration” may be defined and implemented. The basis of its valuable application in electrochemistry is explained.

Keywords

Grünwald Calculus Differentiation Integration Differintegration Algorithm Electrochemistry 

Notes

Compliance with ethical standards

No such standard is compromised by publication of this unfunded work.

References

  1. 1.
    Oldham KB, Spanier J (1974) The fractional calculus. Academic Press, New YorkGoogle Scholar
  2. 2.
    Xue D (2017) Fractional-order control systems. de Gruyter, BerlinCrossRefGoogle Scholar
  3. 3.
    Dold A, Eckmann B (1975) Fractional calculus and its applications. Springer, BerlinGoogle Scholar
  4. 4.
    Hilfer R (2000) Fractional calculus in physics. World Scientific, SingaporeCrossRefGoogle Scholar
  5. 5.
    Oldham KB, Myland JC, Bond AM (2012) Electrochemical science and technology. Wiley, ChichesterGoogle Scholar
  6. 6.
    Korn GA, Korn TM (1968) Mathematical handbook. McGraw-Hill, New YorkGoogle Scholar
  7. 7.
    Grṻnwald AK (1867) Über “begrenzte” Derivitionen und deren Anwendung. Z Math Phys 12:441–480Google Scholar
  8. 8.
    Oldham K, Myland J, Spanier J (2009) An atlas of functions, 2nd edn. Springer, New YorkCrossRefGoogle Scholar
  9. 9.
    Letnikov AV (1874) Bull Sci Math Astron 3:233–238Google Scholar
  10. 10.
    Post EL (1930) Generalized differentiation. Trans Am Math Soc 33:723–778CrossRefGoogle Scholar
  11. 11.
    Oldham KB (1997) Tables of semiintegrals. J Electroanal Chem 430:1–14CrossRefGoogle Scholar
  12. 12.
    Oldham KB, Zoski CG (1983) Analogue instrumentation for processing polarographic data. J Electroanal Chem 157:27–52Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Department of ChemistryTrent UniversityPeterboroughCanada

Personalised recommendations